TRANSFER OF ACQUIRED RULE TO CONDITIONAL REASONING AS A

FUNCTION OF CONTENT SIIv11LARITY, ATTRIBUTE DIMENSION SIZE, AN])

ACQUISITION MODE

by

JOHN VAVRIKB.Sc. The University of British Columbia, 1979M.A. The University of British Columbia, 1987

A THESIS SUBMITTED N PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

in

THE FACULTY OF GRADUATE STUDIES

(Department of Educational Psychology and Special Education)

We accept this thesis as conforming to therequired standard

THE UNWERSITY OF BRITISH COLUIVIBIA

July, 1995

©John Vavrik, 1995

In presenting this thesis in partial fulfilment of the requirements for an advanced

degree at the University of British Columbia, I agree that the Library shall make it

freely available for reference and study. I further agree that permission for extensive

copying of this thesis for scholarly purposes may be granted by the head of my

department or by his or her representatives. It is understood that copying or

publication of this thesis for financial gain shall not be allowed without my written

permission.

(Signature)

Department of Z’’1T/O-&L t)Oj- 7 EP’’ (/17/O-€,1

The University of British ColumbiaVancouver, Canada

Date 1ttct, /‘Z /5S

DE-6 (2)88)

ABSTRACT

In this study, deductive reasoning with conditional statements of the form IF x

THEN y was investigated in a transfer of training paradigm. Subjects induced conditional

rules under different training conditions and then solved a series of deductive syllogisms

based on conditional rules the content of which was either related (near-transfer) or

unrelated (far-transfer) to that of the previously induced rules. The conditions under which

the conditional rules were induced varied in terms of the acquisition mode

(prediction/diagnosis) and in terms of the size of the attribute dimensions from which rule

instances were drawn (binary/trinary). The deductive reasoning task, as the criterion task

for transfer, included all four types of conditional syllogisms (Modus Ponens, MP;

Denying the Antecedent, DA, Affirming the Consequent, AC, and Modus Tollens, MT).

The accuracy of deductive performance on near-transfer was significantly higher than

response accuracy on far-transfer on the DA & AC but not on the MP & MT argument

forms. Transfer of conditional rule knowledge induced in a predictive mode was

significantly better compared to a diagnostic mode on the AC form. Overall, near as well

as far-transfer performance was similar for the binary and trinary conditions. In addition,

neither the binary nor the trinary condition resulted in improved far-transfer performance

compared to controls. The results provide evidence against purely instance-based as well

as purely rule-based models of deductive reasoning. Instead, they suggest that conditional

knowledge is represented at an intermediate level of abstraction, and that conditional

reasoning is adaptive to the form of the deductive argument. Different types of deductive

argument types may trigger different reasoning strategies.

11

TABLE OF CONTENTS

Abstract

Table of Contents iii

List of Tables v

List ofFigures vi

Acknowledgement vii

I. ANALYSIS OF RESEARCH PROBLEMS AND ISSUES 1

A.INm0DUCTION 1

B. RATIONALE FOR THE STUDY 3

C. RESEARCH ON INDUCTIVE RULE ACQuIsITIoN 6

D. RESEARCH ON DEDUCTIVE REASONING WITH A CONDITIONAL RuLE 111. ANALYSIS OF RESEARCH IssuEs RELATED TO RULE TRANSFER AS A FUNCTION OF

CONTENT SIMiLARITY. 13

2. ANALYSIS OF RESEARCH ISSUES RELATED TO THE EFFECTS OF ArrEIBuTE DIMENSIONSIZE ON FAR-TRANSFER OF AN AcQuIRED RULE. 153. ANALYSIS OF RESEARCH ISSUES RELATED TO THE INTERACTION EFFECTS BETwEEN

ATTRIBuTE DIMENSION SIZE AND DEDUCTIVE ARGUMENT TYPES IN NEAR-TRANSFER OF AN

AcQUIRED RULE. 17

4. ANALYSIS OF RESEARCH IssUES RELATED TO THE EFFECTS OF INDUCTIVE AcQUISmONMODE IN NEAR-TRANSFER OF AN ACQUIRED RULE. 21

E. SUMMARY OF HYPOTHESES AND EXPERIMENTAL PREDICTIONS 25

II. METHOD 28

A. SUBJECTS AND DESIGN 28

B. ExPERIMENTAL TAsKS AN]) MATERIALS 31

C. APPARATUS 35D. PROCEDURE 35

III. RESULTS 38

A. ANALYSIS OF INDUCTiVE RULE TRAINING PERFORMANCE 38

B. ANALYSIS OF DEDUCTIVE REAsoNING PERFORMANCE 46

C. ADDITIONAL ANALYSIS OF TRANSFER DATA 57

IV. DISCUSSION 61

111

A. SUMMAT1VE OVERVIEW 61B. IMPLICATIONS FOR THEORIES OF CoNDITIoNAL REASONING 62

C. PROPOSED ACcoUNT OF CONDITIONAL REASONING 70

D. IMPLICATIONS FOR EDUCATION 74

E. LIMITATIONS OF THE STUDY AND SuGGESTIoNs FOR FURTHER RESEARCH 75

REFERENCES 80

APPENDICES 85

APPENDIX A: AN ILLUSTRATION OF RULE TRANSFER BASED ON THE PROPOSED

hYPOTHESES 86APPENDIX B: INSTRUCTIONS TO SUBJECTS 90

iv

LIST OF TABLES

Table 1: Means and standard deviations of number of instances and total processingprocessing time for differenr inductive rule acquisition conditions 39

Table 2: Category frequencies for reported inductive learning strategies 42

Table 3: Response frequencies for each option on a rule assessment item 44

Table 4a: Target rule selection by reported strategy for binary group 45

Table 4b: Target rule selection by reported strategy for trinary group 45

Table 5: Scoring key for eight types of conditional syllogisms 47

Table 6: Mean scores and standard deviations on deductive reasoning performancefor the binary group 48

Table 7: Mean scores and standard deviations on deductive reasoning performancefor the binary group 49

Table 8: Mean scores and standard deviations on deductive reasoning performancefor the binary group 50

Table 9: Mean scores and standard deviations for overall deductive reasoningperformance 52

Table 10: Proportion of subjects following either a conditional or biconditionalinterpretation 58

Table 11: Transfer scores summed over all argument types by rule selection score 59

V

LIST OF FIGURES

Figure 1: Experimental Design Layout 30

Figure 2: Causes and effects under different rule truth-table classes 31

Figure 3: Types of content used in the inductive learning task 32

Figure 4: Task sequences used for each group 36

Figure 5: Number of instances for rule acquisition 39

Figure 6: Processing time for rule acquisition 40

Figure 7: Overall transfer performance 53

Figure 8: Far transfer by dimension size 54

Figure 9: Near transfer by dimension size 55

Figure 10: Near transfer by acquisition mode 57

Figure 11: Transfer performance by rule score 60

vi

ACKNOWLEDGMENTS

This document is dedicated to myself in keeping with the inescapable conclusionthat the pursuit of a Doctoral Dissertation is essentially a selfish process of symbolic selfcompletion during which I alienated my friends, taxed the patience and goodwill of mysupervisor, and neglected to hug my wife each time she endured yet another thesisinduced mood swing. My dedication is also a celebration of the fact that this is the onlyparagraph I got to write without someone editing it.

vii

I. ANALYSIS OF RESEARCH PROBLEMS AND ISSUES

A.Introduction

The overall aim of this study is to gain a better understanding of how people

reason with logical rules or propositions, particularly those that can be expressed in the

aform “IF X THEN Y”. Such statements are called conditional statements, and reasoning

with them is referred to as conditional reasoning. Below are some illustrative examples of

conditional reasoning in different contexts:

A physics student has learned that if two particles have opposite electric chargesthen they will attract each other. At some later time she observes two particles that attracteach other. What can she conclude about the electric properties of the particles?

A school psychologist remembers from his graduate training that damage to thefrontal lobes results in poor performance on problems requiring metacognitive monitoring.He is presented with a student who does poorly on problems requiring metacognitivemonitoring (such as the Towers of Hanoi problem). What can he conclude about theneurological cause of the disability?

An intern on an emergency ward remembers from her medical training that acertain toxic agent Tx causes skin to turn blue. She observes that a patient suspected ofpoisoning has pink colored skin. What can she conclude about the cause of the poisoning?

These examples point to the ubiquity of conditional reasoning in decision making,

problem solving, and scientific reasoning. (See also Braine & O’Brien, 1991; Lee, 1985;

Piburn, 1990; Popper, 1959; Rips, 1990; Sternberg, 1986). Yet, despite their importance,

most people reason poorly with conditionals, and the cognitive process underlying this

fundamental form of reasoning is not well understood (Evans, 1982; Evans, Barston &

Pollard, 1983; Marcus & Rips, 1979; Markovits & Nantel, 1989).

1

As the examples illustrate, conditional reasoning typically involves two distinct

situations: an acquisition phase, where the “IF X THEN Y” rule is learned, and an

application phase where the rule is used in conjunction with other information to make

deductive inferences leading to some general conclusion. Both situations occur naturally in

academic, professional, and everyday reasoning contexts, and both have been studied

intensely, but mostly independently, for over three decades (Lee, 1985). One reason for

the limited number of studies investigating inductive rule acquisition together with

deductive rule application may be the fact that the inductive learning phase typically

involves considerable time commitment by subjects, and often requires detailed and time

consuming design and development of appropriate instructional materials (Pollard &

Evans, 1983; and Markovits 1988).

Most of the work on rule acquisition has been traditionally carried out within the

concept-learning research paradigm. Typically, these studies investigated learning of

concepts which were defined by simple logical rules from a set of positive and negative

instances of the concept. In other words, these studies have been concerned with inductive

reasoning (e.g. Bourne, 1970; Bruner, Goodnow, & Austin, 1956;).

Research on the application, or utilization, of a conditional rule, on the other hand,

has been the focus of another research tradition dealing with the other mode of human

reasoning, namely deductive reasoning (e.g. Evans, 1982; Johnson-Laird, Byrne, &

Schaeken, 1992). Within this research tradition, the interest has been on observing

reasoning performance on deductive reasoning tasks such as the Wason Selection Task,

and various forms of syllogistic arguments.

A key assumption motivating this study is that we cannot fully understand and

improve conditional reasoning unless we consider both the acquisition of the rule

2

(inductive learning), and the application of the rule (deductive reasoning) together (Lee,

1985). It is well established now that many types of declarative and procedural knowledge

are often not used (accessed) in situations where they clearly ought to be used because f

differences between acquisition and application conditions (e.g. Bereiter & Scardamalia,

1985; Morris, Bransford, & Franks, 1977; Vosniadou & Ortony, 1989). It is reasonable to

assume that the knowledge structures underlying logical rules, including the conditional,

are no exception. Deductive use of a conditional rule may, therefore, depend on how the

rule was inductively acquired in the first place.

The purpose of this study, therefore, is to determine whether the conditions

under which a conditional rule is learned (induced) influence transfer of the rule to

conditional (deductive) reasoning with the rule.

The following section contains a discussion of current research problems and

issues pertaining to the basic purpose of the study outlined above. The discussion has two

aims: (a) to help explain the rationale for this study, and (b) to develop a conceptual

framework from which research hypotheses can be articulated. Since each of these aims

requires a slightly different treatment of the issues, the rationale will be presented first,

followed by a more detailed analysis of the research issues needed to develop the

conceptual framework for specific hypotheses.

B. Rationale for the Study

One reason for studying transfer of an acquired rule is that it would advance

current understanding of human reasoning on the basis of past learning. To see why this

may be of interest, consider that despite a long history of research on deductive reasoning,

3

there is not an agreed upon position on the cognitive mechanism underlying deductive

reasoning in general, and conditional reasoning in particular. Currently, there are at least

three different views. According to one prominent perspective, people make deductions

by systematically applying logical rules of inference to argument premises and conclusions

(Inhelder & Piaget, 1958; Newell and Simon, 1972). The opposing view holds that

reasoning is carried out by retrieving specific instances from memory (Griggs & Cox,

1982; Polard & Evans, 1981). According to the third view, some combination of logical

rules and specific experience-based instances might be involved in propositional reasoning

(Rips, 1990).

Currently, the hybrid view appears most promising since consistent evidence for

purely content-free rules or specific instances has not been forthcoming (Smith, Langston,

& Nisbett 1992). However, the current hybrid models of propositional reasoning have not

been articulated in enough detail to allow the formulation of specific predictions that can

be empirically tested, or to inform educators interested in designing learning conditions

conducive to the acquisition of conditional knowledge (Lee & Lee, 1992).

If differential reasoning performance was found with rules induced from two

different sets of instances, then a more detailed specification of the role of rules and

instances in hybrid models would be possible. An example of such a situation would be

two sets of instances that both have a flill conditional relational structure but differ in

some other ways, such as in terms of the number of unique positive and negative instances

of the rule in each set. A concrete example would be the number of distinct cases of

symptoms in the presence or absence of various disease agents studied by medical students

to learn diagnostic rules of inference.

Another reason for investigating how rule acquisition influences subsequent

reasoning is that it may inform educational practice in terms of instructional strategies for

4

enhancing reasoning performance. As was pointed out above, despite the central role of

conditional reasoning in many cognitive tasks ranging from inferences about causes and

effects in scientific research to problem solving and decision making in applied fields such

as medicine, law, and engineering, conditional reasoning performance is generally poor,

and inconsistent (e.g. Evans, 1982; Evans, Barston & Pollard, 1983; Markovits et al.,

1989; Wason, 1966). While the reasons for this vary depending on which of the three

theoretical perspectives one holds, it is generally agreed that in order to reason effectively

with a conditional rule, one must have an appropriate rule structure in memory (Braine &

O’Brien, 1991; Lee, 1985).

Just how conditional rule knowledge is acquired is not clear. What is clear is that

teaching the logical form of a conditional rule by direct instruction alone is not effective

(Cheng, Holyoak, Nisbett, & Oliver, 1986). On the other hand, Lee (1985) was able to

significantly improve conditional reasoning performance through training that contained,

as a key component, inductive rule learning from a set of instances with a conditional

structure. However, Lee did not manipulate the parameters of the inductive rule learning

task and therefore it is unclear whether different inductive learning conditions are equally

effective in building an appropriate conditional rule structure. If it could be shown that

different rule learning conditions do result in differential reasoning performance, it would

offer educators more options for designing learning conditions to enhance this

fundamental reasoning process. The rationale for this study is therefore based on both

theoretical, as well as practical, instructional considerations.

Acquiring and Reasoning With Conditional Rules

5

An overview of research issues and problems:-As was afready alluded to in the

introduction, virtually all previous research on reasoning with logical rules in general, and

conditional (IF.. THEN..) rules in particular, with the exception ofLee (1985), has been

carried out independently either from the perspective of rule acquisition (inductive

reasoning research tradition), or rule application (deductive reasoning research tradition).

Before developing hypotheses about transfer between the two modes of reasoning in the

case of the conditional, a review of relevant findings from each of the two research

traditions is necessary.

Whenever any findings from the separate traditions imply something about transfer

from rule acquisition to rule application, such implications will be pointed out. In addition,

relevant assumptions underlying cognitive processing and knowledge representation in the

learning and usage of logical rules will be identified. It will then be possible to propose

specific hypotheses about the influence of different acquisition conditions on transfer of an

acquired rule to conditional reasoning. This chapter will conclude with a summary of the

hypotheses along with a set of testable predictions derived from them.

C. Research On Inductive Rule Acquisition

Rule acquisition as concept learning: Concept learning studies have traditionally

investigated two learning processes involved in the acquisition of concepts defined by

logical rules: attribute learning and rule learning (Bourne 1970; Haygood & Bourne, 1965;

Lee, 1984). Within this research paradigm, the assumption has been that most concrete as

well as most abstract concepts can be defined in terms of criterial attributes (or features)

and some rule-like relationship between them:

C=R(x,y...)

6

where C stands for a concept, R is a rule, and x, y... are the defining attributes (Bourne,

1970). The kinds of rules that have been investigated in this research tradition have been

rules derived from propositional calculus of formal logic. The conditional rule is one of

four basic relationships (rules) that represent the full calculus. The others are the

conjunction (and), disjunction (or), and the biconditional (1ff). Experimental tasks used in

this concept learning paradigm include:

1. Attribute Identzjlcation:-Under this paradigm, subjects are given a rule (e.g. a conjunction of twoattributes), and their task is to learn the relevant attributes (e.g. red, circle) from a set of instancescontaining both relevant and irrelevant attributes.

2. Rule Learning:-In rule learning subjects are told what the relevant attributes are and their task is tolearn the relationship (rule) between them.

3. Rule Identiflcation:-Within this paradigm subjects are informed what the relevant attributes are, andpreviously they have learned two or more rules. Their task is to identify how the previously learned rulesapplies to the present set of instances.

4. Complete Learning:-In this learning paradigm subjects are simply introduced to various attributes(colors, shapes, types of events), are told that the concept involves a certain number of these, and theirtask is to learn both the relevant attributes as well as the appropriate rule.

The process of rule acquisition:-How do people acquire concepts defined by

logical rules? Bout-ne (1970) proposed that people utilize “an intuitive version of the

logical truth table”. A formal truth table for the conditional “IF X THEN Y” (usually

written as “X ——> Y”) is shown below:

x y

T T +

T F -

F T +

F F +

According to Bourne, rule acquisition involves building a mental representation

that reflects this kind of truth table structure. This is accomplished by two component

processes referred to as attribute coding and rule mapping (Lee, 1984). During attribute

7

coding, the relevant stimulus features, (e.g. X and Y), are collapsed into the four truth

table classes XY, —XY, X-Y, and -X--Y. This is followed by mapping each of these

classes onto the two response categories of the rule (+ or -), that is, positive or negative

instances.

One source of evidence cited in support of this assumed mechanism is the

observation that with increased experience on a concept learning task, subjects begin to

categorize all instances of a particular truth table class in the same manner (Bourne, 1970;

1974). Lee (1984) subsequently established the sufficiency of the two component

processes by demonstrating that training subjects on each component can lead to

improved rule acquisition. With respect to attribute coding, Lee argued that since this

process comprises affirmation/negation and combinatory operations, attribute coding

difficulty should in turn depend on the difficulty of these two operations. But since the

number of combinatory operations is the same for all truth table classes, attribute coding

difficulty should be a ifinction of the negation operations that are involved or, in Lee’s

words, “the number of attributes requiring negations”. What Lee is referring to here is the

number of implicit references to the negation of the target attributes - which is essentially

the notion of contrast sets to be discussed later in the section reviewing research on

deductive reasoning.

With binary dimensions, the number of negations is 0,1,1,1 for TT,TF,FT, and FF

classes respectively, while with trinary dimensions the numbers are 0,2,2,4. Indeed Lee

(1984) found that error patterns for the four classes, during rule acquisition, were

consistent with these theoretical difficulty indices.

The encoding issue is relevant to this study. It suggests that transfer of a rule may

be influenced by the number of instances from which the rule is acquired. Because a small

number of dimensions is easier to encode, transfer to deductive reasoning that is based on

8

recall of specific instances should be facilitated by sets of instances with few dimensions.

Situations where access to specific instances in deductive reasoning is possible are

situations where the rule content is the same during acquisition and application. “Rule

content” refers to the specific semantic propositions, the “X’s” and the “Y’s”, referenced by

the rule “IF X THEN Y”. This situation is referred to as “near-transfer” condition.

In contrast to instance-based models of reasoning, rule-based accounts would not

predict differences in near-transfer as a function of dimension size. However, according to

rule-based accounts, deductive reasoning with content that is different from the acquisition

phase (referred to as “far-transfer” condition) should be better with rules induced from

sets of instances with widely varying attribute dimensions because the increased variability

of training set is likely to induce a more generalizable, content-independent knowledge

structure. Studies of far-transfer have shown that increasing the number of different

training examples from which new knowledge (such as a problem schema, for example) is

induced, makes that knowledge more applicable (i.e. generalizable) to new situations (e.g.

Gick & Holyoak, 1987; Holyoak & Koh, 1989). The implications regarding near and far-

transfer are developed more systematically later; they were introduced here only because

they arise naturally from the discussion of rule acquisition and concept learning.

Pragmatic constraints in rule acquisition:-As Lee (1985) noted, we cannot assume

that a conditional rule structure, induced in a traditional concept learning task, is

automatically associated with a conditional proposition “IF X THEN Y”. This is because

the set of instances (e.g. cause-effect pairs such as cl-el, c2-el, c2-e2,...) corresponding

to a target rule (e.g. “IF cause = ci, THEN effect = el”) warrants many valid propositions

such as “when ci occurs then ci follows”, or “when c2 occurs then ci follows”, etc.

Clearly, the reasoner must rely on some other principle or method to arrive at the target

rule expressed in the appropriate causal language.

9

One way to accomplish this is to employ a prediction task using explicit linguistic

expressions of the form “IF cause = ci THEN effect = ?“ and guiding the learner, through

prompts and appropriate feedback, toward the correct formulation of the conditional rule

(Lee, 1985). However, this may not be the only, or the best method available, particularly

in naturalistic settings where such explicit and structured guidance is unlikely to occur.

What other principle might be invoked?

Recent work on inductive rule-based mechanisms points to pragmatic

considerations as likely candidates (Holland, Holyoak, Nisbett & Thagard, 1986). Holland

et al. note that in natural contexts such as scientific or medical research, pragmatic

considerations, typically the goals of the researchers, can constrain inductive inferences.

In this context, this means that some pragmatic considerations may constrain the number

of possible propositions that can be made about a set of observed relations.

Specifically, one pragmatic and fi.indamental goal of research is to derive

parsimonious and general statements about a set of observations. In fact, such statements

are often elevated to the status of scientific laws. If the pragmatic principle of generality

and parsimony is applied to a set of observations with a conditional structure, it constrains

the possible valid propositions to one that optimally summarizes the observed set relations.

That proposition is precisely the material conditional: “Whenever cause ci occurs, effect

el follows”, or equivalently, “IF cause = ci, THEN effect = el”.

In other words, pragmatic constraints such as goals enable the construction of

appropriate lexical entries to the underlying rules. Furthermore, if the traditional concept

learning task incorporates a pragmatic context such as a predictive or diagnostic context,

which utilizes the IF.. THEN.. language naturally, not only the target rule, but also its

associated causal language should be readily acquired.

10

To conclude then, the evidence presented suggests that conditional knowledge

may be induced from appropriately selected sets of instances using traditional concept

learning tasks. Furthermore, pragmatic constraints may be utilized to associate a

conditional (IF.. THEN...) statement with the induced knowledge representation.

D. Research on Deductive Reasoning With a Conditional Rule

The specific objectives of the present study are to assess transfer effects of rule

acquisition variables on deductive reasoning performances. Since the transfer criterion task

is a deductive reasoning task, it is useful to first describe the two most commonly used

tasks in deductive reasoning research. An overview of these tasks may also facilitate the

interpretation of research findings reviewed in this section.

The Wason Selection Task:-Most conditional reasoning studies have utilized some

variants of the now classic Wason’s Selection Task (Wason, 1966). In a typical version of

this task, a subject is shown a pack of cards and is told that each card has a letter on one

side and a number on the other. The subject is then told that the letters and numbers are

related by a rule which states that: ‘Tf There is a vowel on one side, then there is an even

number on the other side “. The subject is then presented with four cards laid down in

front of her (e.g. A, K, 2, 7). The subject’s task is to select those cards, and only those

cards, that would be necessary to turn over in order to determine if the stated rule does

indeed hold. The correct selection is Card A and Card 7. In other words, the task involves

the verification of a falsifying claim with a set of data (instances). The problem with this

task is that it assesses only one of several forms of deductive inferences. A more complete

test ofconditional reasoning is the syllogism task (e.g. Aristotle; Marcus & Rips, 1979;

11

Lee & Lee, 1985, 1992; Woodworth & Sells, 1935). This is the task used in the present

study.

The Conditional Syllogism Task: This task requires subjects to either derive or

validate conclusions to arguments which have a conditional rule as their first premise.

There are actually four distinct forms of deductive arguments with conditional

propositions:

Modus Ponens (MP) First premise: ifC Then ESecondpremise: C

Conclusion: E

Modus Tollens (MT) First premise: If C Then ESecondpremise: not E

Conclusion: not C

Denying the Antecedent (DA) First premise: if C Then ESecondpremise: not C

Conclusion: Indeterminate

Affirming the Conseiuent (AC) First premise: if C Then ESecondpremise: E

Conclusion: Indeterminate

Virtually all data on conditional reasoning have been obtained using some form of

these two tasks. Each of the following four sections presents critical analyses of the

research findings and identifies research issues that are investigated in this study. The

sections conclude with statements of specific research hypotheses.

12

1. Analysis of Research Issues Related to Rule Transfer as a Function of ContentSimilarity.

Effect of “familiar” rule content (semantics) on conditional reasoning:-Both the

Wason task and the syllogism task have been tried with abstract rules such as “IF A

THEN 2”, as well as with rules that refer to familiar world knowledge such as “IF a metal

bar is heated THEN it expands”. Reasoning performance with familiar rule content is

always different from abstract content, and often it is better, particularly on the Wason

task (Pollard & Evans, 1987; Evans, 1982; Griggs & Cox, 1982; Markovits, 1986; Wason

& Shapiro, 1971). It should be noted here that rule content means the objects or events

referenced by the conditional rule.

In the syllogism tasks, familiar content gives rise to what has been called the

“BeliefBias” effect (Evans, Barston, & Pollard, 1983). It is manifested by subjects tending

to confirm conclusions which they believe to be true, and discon±irming conclusions

believed to be false, regardless of the argument structure from which the conclusion was

deduced.

Clement & Falmagne (1986) have shown that reasoning with conditional rules

improves when the “semantic relatedness” between the antecedent and the consequent is

high, or when the “imagery value” of the conditional statement is high. This suggest that

reasoning may be facilitated by access to particular instances or events in memory -

instances that constitute relevant information to the inferencing process.

The above research findings suggest that access to specific instances of

antecedent-consequent relations stored in memory may influence conditional reasoning

13

performance. More specifically, better access to rule instances should lead to improved

reasoning performance with the rule.

Content familiarity and rule transfer:-Consider the following two transfer

situations. In the first situation, a conditional rule used in a deductive task references the

same entities or events that the reasoner encountered when initially learning the rule. A

typical example is the case of medical training where students learn the relationship

between specific disease agents and disease symptoms. The agents and symptoms are

typically the same ones the students will encounter later in their practice. So although the

reasoning process changes from induction (learning the relationships) to deduction

(inferring a diagnosis based on presented symptoms and applying the learned rule), the

actual entities involved in the reasoning (the specific symptoms and agents) are the same.

This is what is meant by the term near-transfer.

In a second type of transfer, the entities and events encountered during rule

acquisition are different from the entities or events contained in the premises of deductive

arguments. This situation represents afar-transfer condition. Here the availability and

access to specific instances will not be helpful and deductive reasoning performance may

suffer.

On the basis of the effects of content familiarity reviewed above, it is

therefore hypothesized that content similarity inherent in near-transfer conditions

would facilitate more effectively access to the conditional rule structure, and to

apply it to deductive inference, than that prevailing in far-transfer conditions.

14

2. Analysis ofResearch Issues Related to the Effects of Attribute Dimension Size on Far-Transfer of an Acquired Rule.

The basic question posed here is whether rules induced from a wider variety of

instances are more generalizable, and thus more applicable to a wider range of deductive

reasoning situations than smaller sets in inductive rule acquisition. It is a ubiquitous

observation that when limited human memory capacity is overloaded, one has to bring into

order (pattern) an array of complex stimuli (contents). Similarly in the reasoning task

situation. The reasoner must rely on more general reasoning rule structures to reach

correct conclusions. These are discussed next.

The Role of Content-free Inference Schemas in Deductive Reasoning:-In addition

to the evidence of content effects on deductive reasoning reviewed in the preceding

section, there is also evidence that some forms of deductive reasoning are not affected to

any significant degree by rule content (Braine & O’Brien, 1991; Braine, Reiser, & Rumain,

1984). For example, when subjects are confronted with the following argument:

Major premise: Either P or QMinor premise: Not P

Conclusion?

most correctly conclude that “Q” must be the case, regardless of what P and Q stand for.

In other words, in this case, reasoning performance does not depend on specific

propositional content in the argument premises.

15

The example illustrates what Braine et al. call an “inference schema”. An inference

schema refers to an abstract form of the rule structure concerned, and determines what

conclusion can be inferred from the general form of a given argument or a rule, rather than

their particular content. According to Braine et al., inference schemas play an important

role in human deductive reasoning because they can be used to derive new inferences from

a given set of premises.

Examples such as the above have been cited in defense of the view that formal

logical rules underlie much of human reasoning. According to this view, people can

acquire generalizable rule structures, such as inference schemas, which they apply in their

deductive inferencing. Because these rule structures are sensitive to the form rather than

the particular content of rules, they can be applied across a wide range of reasoning

situations (Rips, 1990).

Rule transfer and schema induction:-The question of where generalized inference

schemas originate has received little attention. In fact, as Lee (1985) pointed out, the

existence of such logic structures is usually just assumed. It was noted earlier that using an

inductive rule learning paradigm, Lee (1985) was able to induce a generalizable, content-

free conditional logic structure in a significant proportion of his subjects. However, in his

study, Lee did not vary the number of instances (examples) from which the logic structure

was induced, although trinary dimensions were used.

Researchers interested in transfer of cognitive skill (e.g. Singley and Anderson,

1989) have repeatedly found that the generalizability of a rule or a cluster of rules (a

schema) increases with exposure to a wider variety of examples (e.g. Catrambone &

Holyoak, 1989; Gick & Holyoak, 1987). Their research suggests that the degree to which

a conditional rule is independent of particular content (i.e. is more generalizable) may be a

16

function of the number of rule instances provided in the acquisition phase. More instances

should lead to the induction of more content-free rules.

The examination of related literature clearly indicates the merit of investigating the

issue surrounding the usefulness of content-free rules. More specifically, it is

hypothesized that under the conditions where the rule content does not match the

acquisition content, and cueing of specific relevant instances is unlikely,

generalizable, content-free rules, if available, need to be activated to meet the task

demand of deductive inferences. In this context, such rules are hypothesized to be

more readily acquired from exposure to large rather than small sets of exemplars.

3. Analysis ofResearch Issues Related to the Interaction Effects Between AttributeDimension Size and Deductive Argument Types in Near-Transfer of an Acquired Rule.

Awareness of alternatives in conditional reasoning:-Although a conditional rule

such as ‘IF cause THEN effect” explicitly refers to only one cause and one effect, it

implicitly references other, alternative causes and effects (e.g. “IF we eat candy THEN we

get cavities” but drinking Coke will also do the job). These alternatives are in fact essential

components of the conditional logic structure and they play a key role in conditional

reasoning. Consider the conditional rule “IF cause = ci, THEN effect = el”. A number of

researchers have shown that awareness of or familiarity with alternative causes (c2,c3) of

a given effect (el) improves reasoning with indeterminate forms of the conditional

syllogism, namely the DA and AC forms (Cummins, Lubart, Alksnis & Rist, 1991;

Markovits, 1984). The central idea here is the availability ofalternatives along a given

attribute dimension (e.g. the number of alternative causes of a particular disease

symptom). This notion is captured in the concept of contrast set which is discussed

below.

17

Several studies investigated reasoning with arguments and rules containing negated

propositions (e.g. ‘IF NOT A THEN 2”) and found that performance is more error-prone

and time-consuming when negations are present (Evans, 1982; Oaksford & Stenning,

1992). Lee et al.(1992) ranked the four basic syllogisms according to a hypothesized

difficulty level where one of the difficulty parameters was the number of negations that

needed processing. For example, the Modus Tollens (MT) type was one level above the

Modus Ponens (MP) type because it involved two more negation operations. Overall, the

results supported the contention that higher levels were more difficult to process.

Why is reasoning with negated propositions more error-prone? According to one

influential account, the reason is that our natural language-understanding mechanism

contains a “NOT-heuristic” which focuses attention only on the named proposition that is

negated, and not on all the propositions implied by the negation. Since the implied

information is often critical for correct deductions, more errors occur (Evans, 1982,

1984). Another hypothesis is that negations increase processing load because they involve

an extra mental operation, similar to a NOT operator in a computer implementation of

Boolean logic (e.g. Lee et al., 1992).

However, neither of these accounts can explain why some negated propositions

are more error-prone than others, as was discovered in a recent study that investigated the

effect of negated constituents more systematically than had previously been done

(Oaksford et al., 1992). These authors claim that negated propositions which are easier to

process are ones that facilitate mental construction of contrast sets.

Contrast Sets and Conditional Reasoning:-According to Oaksford et al., premises

that contain negated arguments cannot be directly represented as specific instances in

18

memory because it is not clear what instances the negated argument actually represents.

To see why, consider the following deductive task:

Major premise: If X is on one side of a card, then Y is onthe other side.

Minor premise: Xis not on one side.

Conclusion:

Clearly, the minor premise can represent an infinite variety of potential instances

(any letter, any number, in fact anything at all). As a result, a reasoning program will be

difficult to implement.

Now, according to this account, before a premise containing a negated argument

can be processed, the reasoner must first determine the contrast set implied by the

proposition. A contrast set is a set of all objects or events implicitly referenced by a

negated proposition. The difficulty of some negated propositions, like the abstract one

above, is that they reference large, ambiguous contrast sets, whereas other propositions

like “NOT AN EVEN NUMBER” imply a smaller, better defined contrast set, namely the

set of “ODD NUMBERS”. According to Oaksford et al., ambiguous contrast sets

increase cognitive load and consequently reasoning performance suffers. The problem with

the Oaksford et al. study, however, is that the relationship between negated propositions

and their implied contrast sets was only assumed. A more direct empirical test of this

hypothesis is needed.

Contrast set size and rule transfer:-How might contrast set size influence transfer

of an acquired rule to conditional reasoning? The findings suggest that the size of the

contrast set might interact with argument form to influence reasoning performance. Large

contrast sets increase cognitive load because more elements need to be processed.

19

However, large contrast sets also contain more alternative antecedents and consequents

associated with a rule. As was discussed earlier, awareness of these alternatives improves

reasoning on indeterminate argument types, namely the Denying the Antecedent (DA) and

the Accepting the Consequent (AC) type. It seems reasonable to propose, therefore, that

reasoning with indeterminate argument forms should be more accurate with rules

inductively acquired from large contrast sets. On the other hand, reasoning with

deterministic argument forms that also contain a negation, namely the MT type, should be

more difficult with rules acquired from large contrast sets. This is because in this case

awareness of alternatives is irrelevant, and so the only impact of the large set size is to

increase cognitive load, which will hinder the reasoning process.

To illustrate this line of reasoning more clearly, consider a conditional rule such as

“IF cause = ci THEN effect = e 1” learned from exposure to either one of two sets of

instances: one having binary attribute dimensions (e.g. two causes, ci & c2 and two

effects e i & e2), and another having trinary dimensions (e.g. three causes ci, c2 & c3 and

three effects el, e2 & e3).

Consider the DA argument type first. In this type of syllogism, the minor premise

“NOT ci” references the contrast set {c2} in the case of binary dimensions, and {c2, c3 }

in the case of trinary attribute dimensions. Since each cause is presumed to be associated

with an effect, ei, e2 and el, e2, e3 become activated in memory in the case of the binary

and trinary dimensions, respectively. Since a greater number of different effects is

activated with trinary dimensions, correspondingly larger number of conclusions is

possible. As a result, an indeterminate response, which is the correct response for the DA

type, becomes more probable with the larger dimension size.

20

Next consider the AC type. Here, affirming the consequent proposition “ci”

activates { ci, c2) and { ci, c2, c3 } for the binary and trinary dimensions, respectively.

Since more alternative causes become activated in the trinary case, the correct

indeterminate conclusion should be reached more likely in this case, as compared to the

smaller dimension case.

Finally, consider the MT type. Here the negated consequent “NOT e 1” references

{e2}, and {e2, e3 } in the binary and trinary dimensions, respectively. The associated

causes that become activated are {c2} for the binary, and {c2, c3 } for the trinary case.

Both of these activated sets represent contrast sets for the proposition “NOT ci”, which

happens to be the correct conclusion for this argument type. However, since the contrast

set for the binary condition contains only one element { c2 }, it should be processed more

easily than the larger set { c2, c3 }. Therefore, the smaller dimension size should lead to

better performance on the MT argument type.

The foregoing analysis leads to a hypothesis that increased availability of

alternative antecedents and consequents associated with larger sets of induced rule

exemplars should be particularly helpful in reasoning on the two indeterminate

argument types, DA and AC. On the other hand, a determinate type that requires

processing of a negated proposition (MT) should be easier with rules acquired from

smaller sets because cognitive load is reduced, and because the availability of

alternatives is not a factor with determinate forms.

4. Analysis of Research Issues Related to the Effects of Inductive Acquisition Mode inNear-Transfer of an Acquired Rule.

21

Another question concerning inductive rule transfer is whether the rule was

induced in predictive or diagnostic contexts. A brief review and an analysis of relevant

research findings, and an articulation of relevant theoretical assumptions is in order.

The central idea in this regard is the ability of a reasoner to access instances of a

rule during deductive reasoning. The argument put forward here is that if instance-based

accounts of reasoning are correct, then conditional reasoning should be facilitated by

access to specific instances of an acquired rule. In turn, memory access should be

facilitated by transfer-appropriate processing. Two processing modes explored here are

the predictive and the diagnostic modes. What follows is an attempt to apply the principle

of “Transfer Appropriate Processing” to the transfer of a conditional rule, where

“processing” refers to the directionality of reasoning involved in predictive and diagnostic

modes of reasoning.

The problem is to identif,’ specific parameters of the inductive rule learning task

that might affect the ease with which rule instances can be accessed during the deductive

reasoning phase. First, it is necessary to state some assumptions about representational

and processing aspects of memory implied by instance-based accounts of reasoning.

Assumed representation of instances in memory:-What might a memory

representation of rule instance look like? Anderson & Bower (1973) and Hinton and

Anderson (1981) proposed a simple model of verbal associative memory where objects or

events, which may include conditional rule knowledge of antecedents and consequents, are

connected by bidirectional associational links where activation can spread from

antecedents to consequents or visa versa. An important feature of this representation is

22

that the strength of the activation is not assumed to be symmetrical. In other words, the

strength of association between X and Y is not necessarily the same as the strength of

association between Y and X. Below is one example of such a knowledge representation

acquired from exposure to a set of cause-effect relations with a conditional structure:

ci >>> cic2 >>> elc2 >>> e2

It should be noted that all factors found to influence conditional reasoning

performance, including clause relatedness, imagery, and generation of alternatives, are all

factors that motivated the development of associative models of memory. Put another

way, these content effects are consistent with memory models based on spreading of

activation and strength of association between objects or events stored in memory (Ross

&Bower, 1981).

Instance-based accounts suggest that conditional rule knowledge may be acquired

from exposure to specific instances (e.g. causes and their associated effects) and that the

instances are associated via spread of activation along asymmetrical links from one to the

other (e.g. links from causes to effects, or from effects to causes). Given this type of

associational memory structure, the next question concerns the retrieval of specific

instances of antecedents and consequents.

Retrieval of instances from memory and transfer-appropriate processing:

According to Tulving’s Principle of Encoding Specificity, “remembering of events always

depends on the interaction between encoding and retrieval conditions” (Tulving, 1984,

p.242). A similar position is expressed in the principle of Transfer Appropriate Processing

put forward by Morris, Bransford, & Franks (1977). They stress that “the value of

23

particular types of acquisition activities must be defined relative to the types of activities

to be performed at the time of the test” (p.53 1). The principles of Transfer Appropriate

Processing and Encoding Specificity do not restrict the nature or the types of processes

involved during acquisition and retrieval. The principles only require that the processes be

“similar”. What is meant by the term “similar”, at least within the present study, will be

addressed shortly. What implications do these principles have for a study of rule transfer?

According to an instance-based account, conditional reasoning should be

facilitated by access to rule-related instances in memory, where memory access in turn

depends on the similarity between encoding conditions and retrieval conditions. If the

type of processing during rule acquisition is in some respect similar to the type of

processing required during rule application, then access to rule instances should be

facilitated and reasoning performance should improve. This is a general statement of the

last hypothesis. To develop it further it is necessary to explain what is meant by “similar

type of processing”.

Predictive and diagnostic inductive reasoning in rule transfer:-There are two

principal modes of reasoning associated with conditional rules of the form IF X THEN Y:

predictive and diagnostic. Predictions typically require reasoning from causes to effects.

Diagnoses, on the other hand, involve reasoning in the opposite direction, from effects to

causes. In a naturalistic setting, a conditional (or any other) relationship between causes

and effects may be learned in either one of these modes by being exposed to causes linked

to effects, or effects linked to causes (Bjorkman & Nilsson, 1982; Waldman & Holyoak,

1992).

Predictive and diagnostic modes of reasoning are important not only in learning

logical rules but also in using the rules in deductive reasoning tasks (Evans & Beck, 1981).

24

To see why, consider the conditional syllogisms presented earlier. Note that the only

difference between the four types of syllogisms can be found in the minor premise and in

the conclusion (the major premise is the same for all of them). In the MP and DA forms,

the minor premise refers to an antecedent (a cause), while the conclusion refers to a

consequent (an effect). In other words, here a cause is given and an inference has to be

made regarding an effect. This is precisely the direction of reasoning required when

making a prediction - from cause to effect. In contrast, the MT and AC argument forms

contain a minor premise that references a consequent (an effect), and a conclusion that

references an antecedent (a cause). Here the effect is given, and an inference has to be

made regarding a cause. The direction of reasoning in these two cases thus corresponds to

making a diagnosis - from an effect to a cause.

On the basis of the foregoing analyses, the last hypothesis can now be stated more

specifically. It is hypothesized that when the reasoning mode (predictive / diagnostic)

under which a conditional rule is acquired matches the reasoning mode required in

the deductive task, memory access to specific rule instances - particularly

alternative causes and effects - is facilitated, resulting in improved reasoning

performance as compared to conditions where the modes of reasoning do not

match.

E. Summary of Hypotheses and Experimental Predictions

First, it is hypothesized that familiarity (in terms of lexical attributes) enhances the

application of the acquired rule. In other words, familiarity with rule attributes facilitates

transfer of rule knowledge. Consequently, it is predicted that near-transfer deductive

25

performance (i.e. where the rule content in the deductive task matches the content

encountered during inductive rule acquisition) should be better than deductive

performance on far-transfer (i.e. where the rule content on the deductive task is different

from the content encountered during rule acquisition). Specifically, it is predicted that

there will be fewer reasoning errors on the deductive transfer task with rules that have

content which matches the content used in the inductive rule acquisition task, as compared

to rules with content that does not match the inductive task content.

Second, some situations can arise where the rule content does not match the

acquisition content, and cueing of specific relevant instances is unlikely. When that

happens, it is hypothesized that accurate deductive inferencing presumably relies on

generalized, content-free rules. Such rules are more readily acquired from exposure to

large rather than small sets of exemplars. It is predicted, therefore, that rules acquired

from larger sets of training examples should transfer more readily to inferencing situations

with different propositional content as compared to rules acquired from small exemplar

sets. If this is the case, there will be fewer reasoning errors with content that is different

from the acquisition content with rules induced from instances with trinary, as compared

to binary attribute dimensions.

Third, it is hypothesized that increased availability of alternative antecedents and

consequents associated with larger sets of rule exemplars during inductive training can be

particularly helpful in reasoning on the two indeterminate argument types, DA and AC. In

contrast, a determinate type that requires processing of a negated proposition (MT) should

be easier with rules acquired from smaller sets because cognitive load is reduced, and

because the availability of alternatives is not a factor with deterministic types.

26

More specifically, as compared to rules acquired from sets of instances with binary

attribute dimensions, there will be fewer reasoning errors with rules acquired from sets of

instances with trinary attribute dimensions on the DA and AC forms. Also, as compared to

rules acquired from sets of instances with trinary attribute dimensions, there will be fewer

reasoning errors with rules acquired from sets of instances with binary attribute

dimensions on the MT argument form.

Finally, when the mode of reasoning (predictive vs. diagnostic) under which a

conditional rule is acquired matches the reasoning mode involved in the deductive task

(MP, DA vs. AC, MT), it is hypothesized that memory access to specific rule instances,

particularly alternative causes and effects, is facilitated, resulting in improved reasoning

performance as compared to conditions where the modes of reasoning do not match.

More specifically, compared to rules acquired in a diagnostic context (AC, MT), there will

be fewer deductive reasoning errors with rules acquired in a predictive context on the IVIP

and DA argument types.

27

II. METHOD

A. Subjects and Design

The subjects were 120 University of British Columbia undergraduates in the

Faculty of Education who were registered in the Primary Teacher Training Program.

Elementary student teachers were selected because their background knowledge is more

homogeneous than secondary students who specialize in different subject matter contents.

The aim was to minimize any potential influence of prior knowledge. The sample

comprised 42 males and 78 females, reflecting the overrepresentation of female students in

the primary program. All subjects were recruited by the experimenter from 15 sections of

a 400-level course on Evaluation in Teaching. Participation was on a volunteer basis only.

Subjects were paid $20 for their participation.

Experimental conditions:-Subjects were randomly assigned to one of three groups:

binary, trinary, and a control group. Within each group, subjects were assigned to one of

24 trial sequences as required by counterbalancing the experimental tasks.

(Counterbalancing is described in more detail below). A complete replication of the

counterbalanced task materials and task orders required 24 subjects in each group. In

order to improve the reliability of the results, and to increase the sensitivity of statistical

analyses, one more full replication of each training treatment group was completed by

assigning 48 (2x24) subjects to each of two treatment groups. However, the limited

logistics of the research program (i.e. funds, subject availability, and time) did not permit

another replication of 24 for the control group.

28

The inductive training conditions for rule acquisition were defined in terms of two

factors: (a) the size of attribute dimension (i.e., binary vs. trinary) and (b) the mode of

instance presentation (i.e., predictive vs. diagnostic). The former varied as a between-

subjects factor and the latter as a within-subjects factor. Since transfer relations between

inductive rule learning and subsequent application of this knowledge to deductive

reasoning is the primary focus of the present study, the conditions under which transfer

can occur need to be specified.

Transfer type is the first within-subjects design factor. The hypotheses require the

specification of two types of transfer: (a) near-transfer, where the content encountered

during inductive rule learning is the same as the content in the deductive reasoning task,

and (b) far-transfer, where the deductive syllogisms contain content that is unrelated to

any of the content encountered during inductive rule learning. The hypotheses also require

the specification of two modes of inductive rule learning, predictive and diagnostic. As a

result, the near-transfer condition is fi.jrther subdivided into familiar content encountered

during prediction-based rule learning, and familiar content encountered during diagnosis-

based rule learning. These factorial variations of the familiarity and the mode of induction

did not cross over the far-transfer condition. In addition, it was necessary to define

another within-subjects factor: type of deductive argument form (MP, DA, AC, and MT).

Transfer type and syllogism type were defined as within subject factors because

using a within subject design has the advantage of reducing error variance due to

individual differences. Attribute dimension size was treated as a between subject factor,

however, because of possible asymmetric carry-over effects from the trinary to the binary

rule acquisition conditions. As was noted earlier, a trinary set has more distinct instances

and as such can be expected to give rise to more generalized causal schema which is

29

hypothesized to influence subsequent learning and transfer (Gick & Holyoak, 1987). The

complete experimental design is depicted in Figure 1 below.

Deductive Transfer

Inductive Learning Near Far

— Prediction Diagnosis Unfamiliar Unfamiliar

Ss Grp Rule related related content content

induction content content Trial 1 Tnal 2

mode MPDAACMT MPDAACMT MPDAACMT MPDAACMT

1 BIN PredlDiag48 BIN Diag/Pred

49 TRI Pred/Diag96 TRJ DiagfPred

97CTRLl2 CTRL

Figure 1. Experimental Design Layout

As can be seen in Figure 1, the design required three groups of subjects, two

experimental and one control. Including a control group provided an opportunity to assess

the overall effect of the inductive acquisition phase. The performance of the treatment

groups may be similar but better than if no rule learning took place. On the other hand, the

treatment groups may perform differently, but the level of performance for both groups

may actually be lower as compared to a no-treatment condition (i.e. negative transfer).

Using a control group enabled a more precise assessment of these potential outcomes.

The design layout also shows two trials under the far-transfer condition. This

decision was justified on the grounds that having an extra replication would increase the

30

reliability of the data and, more importantly, the extra trial would make it possible to

assess potentially different practice effects on far-transfer for the two treatment groups.

B. Experimental Tasks and Materials

Rule acquisition task:-This task was a modification of the traditional concept

learning paradigm where subjects learn a target rule by observing positive and negative

instances of the rule. The task was to learn a rule that reflected the relationship between

dimensional attributes of interest, which in this study were specified as causes and effects.

The rationale for this is based on the fact that reasoning about causes and effects is a

ubiquitous cognitive activity which typically requires both inductive and deductive

thought, and often involves conditional relations (e.g. Sternberg, 1986; Carison &

Schneider, 1989; Cheng & Novick, 1992). In the binary-dimension set, two different

causes and two different effects appeared. In the trinary set, three different causes and

effects were presented. The relations between causes and effects under each rule truth

table class are summarized in Figure 2. A listing of examples of causes and effects used in

this study appear in Figure 3 below.

Set Size Rule Truth table Class

++ +— —+

Binary cl—el cl—e2 c2—el c2—e2

Trinary cl—el cl—e2 c2—el c2—e2

cl—el cl—e3 c3—el c2—e3

c3—e2

c3—e3

Figure 2. Causes and effects under different rule truth-table classes

31

Content A. Drugs and side effects

Target Rule: IF the drug Mixolin is administered TEEN purple skin rash develops

Causes and effects used for rule acquisition:

cl=Mixolin el=Purple rash

c2=Phoresin e2=Blue rash

c3=Benuvin e3=Green rash

Content B. Radiation sources and plant mutations

Target rule: IF a plant is exposed to Gamma radiation TEEN it grows square leaves

Causes and effects used for rule acquisition:

cl=Gamma radiation el=Square leaves

c2=Beta radiation e2=Triangular leaves

c3=Alpha radiation e3=Circular leaves

Content C: Chemical agents and fish

Target rule: IF agent TX is released in the water TEEN fish develop brittle scales

Causes and effects used for rule acquisition:

cl=Agent Tx el=Brittle fish scales

c2=Agent Ty e2=Enlarged fish scales

c3=Agent Tz e3=Loose fish scales

Content D: Lasers in eye surgery and retinal damage

Target rule: IF an Argon laser is used TEEN checkered spots appear on the retina

Causes and effects used for rule acquisition

cl=Argon laser el=Checkered spots on a retina

c2=Ruby laser e2=Striped spots on a retina

c3=krypton laser e3=Dotted spots on a retina

Figure 3. Types of content used in the inductive learning task

Each training set contained 36 instances comprising nine, randomly ordered

instances of each truth table class. In the first phase of the rule acquisition task, subjects

were presented with a series of predictions or diagnoses, one by one. They were asked to

look at each case (i.e. a rule instance) and decide whether the stated prediction or

diagnosis was true or false. Each case consisted of a cause followed by an effect (for the

prediction condition), or an effect followed by a cause (for the diagnostic condition).

Subjects received corrective feedback after each response, and then a new case was

presented. Each case was selected by the computer at random. The process continued

until a mastery criterion was reached. This criterion was set at two replications of nine

instances, yielding a total of 18 consecutive correct responses.

32

During this phase of the inductive rule acquisition task, subjects were able to

record previously presented instances along with their status (true/false). The rationale for

the simultaneous availability of previously presented instances was two-fold: (a) it

eliminated unnecessary working memory load which is desirable since the focus of the

study was on cognitive processes independent of working memory load; and (b) it

maximized the likelihood of task completion by reducing the time to learn the conditional

rule.

In the prediction-context condition, each trial involved a brief description of a

causal agent being investigated by a research team. The subject was told that prior to

conducting their experiment, the researchers predicted that the particular causal agent will

result in some specific effect. The subject was then asked to indicate whether the stated

prediction was correct or incorrect.

In the diagnostic-context condition, each trial started with a presentation of some

effect (or symptom). This was followed by a description of a diagnosis made by a team of

investigators. The subject was then asked to indicate whether the stated diagnosis proved

to be correct or incorrect.

Rule verbalization and selection task:-In the rule verbalization task presented in a

questionnaire, subjects were asked to write down the strategy they used to decide whether

a given prediction or diagnosis was correct. The multiple choice task was then introduced.

It was intended to assess subjects’ ability to identif’ a rule statement expressed in an

IF.. THEN. .language that best summarized the conditional relationships they encountered

in the inductive phase. The task simply required subjects to select one of four options on a

multiple choice item, which, in their opinion, represented the most appropriate expression

of the observed relationship between causes and effects. The options are listed below.

33

1. The most parsimonious and general (target rule) statement which had the generalform: IFcl THENe1

(e.g. IfMixolin is administered, then purple rash develops.)

2. A correct, but less parsimonious rule statement in the form: IF c2 THEN el or e2(e.g. If Phoresin is administered, then either purple or blue rash develops.)

3. A rule statement based on an incorrect, reversed inference: IF el THEN ci(e.g. If purple rash develops, then Mixolin was administered.)

4. An incorrect rule statement related to a biconditional interpretation:(IFcl THENe1)AND(IFel THENc1)(e.g. If Mixolin is administered then purple rash develops, and if purple rash developsthen Mixolin was administered.)

The task was also designed to help subjects learn to associate the appropriate

IF.. THEN.. language with the knowledge structure they induced from the corresponding

set of instances. This was accomplished by cueing pragmatic constraints of generality and

parsimony discussed earlier. Accordingly, subjects were asked to choose the simplest,

most concise, yet general proposition that held true for the set of cases (instances) as a

whole.

Conditional syllogism reasoning as transfer task:-In the deductive task, the four

syllogistic types were presented one by one in random order. Each argument form was

presented with both an affirmative and negated conclusion, yielding a total of 8 distinct

syllogism items.

In order to facilitate a naturally-occurring reasoning context for the subjects while

not altering the traditional format of the task, subjects were told that each syllogism was a

summary of an argument made by a particular student in a high school science class.

Subjects were told that each student in the science class had been exposed to the same set

34

of cases (instances) as they themselves just encountered. They were asked to put

themselves in the role of a teacher who is marking the validity (correctness) of each

conclusion students arrived at. A validation response to a given syllogism therefore

became equivalent to a decision on whether a particular “student’s conclusion” held true

always, sometimes or never. No feedback was given, and each response as well as

response latency were automatically recorded.

C. Apparatus

All the tasks were programmed in Turbo Pascal and were presented on an IBM

386 microcomputer. Response-time (in millisecond accuracy) was recorded for every

response required in each task. Time data were collected using Assembly Language timing

subroutines interfaced with Pascal code.

D. Procedure

Trial sequence counterbalancing:-Four different content areas were necessary for

the conditional rule used in the deductive transfer tasks, two for near-transfer (prediction-

related, and diagnosis-related contents), and two for far-transfer (unfamiliar content trials

1 and 2). Four types of content taken four at a time yielded 4! = 24 distinct transfer trial

sequences counterbalanced for content effects.

The inductive task required that two of the four available content types be

presented in two different acquisition contexts. This yielded 4!/(4-2)! = 12 induction

sequences counterbalanced for content. Counterbalancing to control for sequence effects

on the induction tasks then resulted in a total of (2)12=24 unique induction trial

35

sequences. The complete set of 24 induction sequences followed by 24 deductive transfer

sequences is shown in Figure 4. This arrangement also ensured that each type of content is

equally represented in each type of transfer.

Figure 4. Task sequences used for each group

The experiment was carried out in a laboratory setting. Two subjects were run

simultaneously, each seated at one of two computer work stations located in the lab.

Subjects were given an individualized 16 page booklet which explained the purpose of the

study, provided an overview of the tasks, and gave step-by-step instructions on how to

proceed with each task. The booklet also contained space for subjects to record any

computer feedback, if they wished (see Appendix B).

Exp. Rule InductionSequence Trials

Deductive Rule TransferTrials

1 pA dB2 pA dC3 pA dD4 pB dA5 pB dC6 pB dD7 pC dA8 pC dB9 pC dD10 pD dA11 pD dB12 pD dC13 dA pB14 dA pC15 dA pD16 dB pA17 dB pC18 dB pD19 dC pA20 dC pB21 dC pD22 dD pA23 dD pB24 dD pC

A B C DB A C DC A B DD A B CA B B CB A B CC A B BD A C BA C B BB C A BC B D AB B A CA C B BB C B AC B A BD B C AA D B CB D A CC B A BD C A SA B C BB B C AC D B AB C B A

p = predictiond = diagnosticA = Content A:B = Content B:C Content C:D = Content B:

modemodeDrugs and side effectsRadiation and plant mutationsChemical agents and fish scalesLasers and retinal damage

36

In order to ensure that subjects read all instructions carefully, the computer

keyboard was disabled between tasks and required subjects to enter a code to reactivate it.

A different code was embedded at the end of each block of instructions corresponding to a

particular task.

Following the completion of each inductive task, subjects were asked (in the

booklet) to write down their strategy for deciding whether a given prediction or diagnosis

was correct or not. They then completed the multiple choice, rule-selection task. This

completed the inductive phase.

Subjects then proceeded to the sequence of deductive tasks. A brief introduction

to each transfer task was given. For the near-transfer tasks, it was pointed out to the

subjects that the content they were about to deal with was related to the content on one of

their inductive tasks. Far-transfer tasks were introduced by stating that although the

content they were about to see was unfamiliar to them, their responses were nevertheless

of great interest to the experimenters. Each subject completed four (2 near and 2 far

transfer) sets of eight deductive problems. At the end of the computer session, subjects

filled out a brief questionnaire containing basic demographic items, including gender, age,

and educational background.

37

ifi. RESULTS

The data analysis plan is as follows. First, the training data is analyzed to determine

whether meaningful learning did in fact occur. This is followed by a detailed analysis of the

response data on the deductive transfer tasks, and tests of the relevant hypotheses.

A. Analysis of Inductive Rule Training Performance

An analysis of the inductive rule learning phase of the experiment was carried out

first to establish the validity of the design by verifying: (a) that rule acquisition has taken

place, and (b) that the training outcomes including the total number of instances and the

total processing time required to reach criterion performance have values consistent with

the different training conditions.

Analysis of Number of Instances and Processing Time Required to Reach Criterion

Performance:-Outliers in the observed distribution of the total number of instances and

processing time were identified using Studentized residuals obtained from fitting a linear

model to the four training variables which included the total time and total instances for

the prediction and diagnostic conditions. A residual value of 2.5 was used for cutoff to

identifying the outliers (Beisley, Kuh & Welch, 1980). Four outlier values (two in each

group) were identified by this method and were replaced by the corresponding group

means based on the remaining cases. The resulting means and standard deviations of the

total processing time and total number of instances required to reach criterion

performance in each training condition appear in Table 1 (see also Figures 5 and 6 for a

38

graphical representation). It should be noted that in subsequent analyses of this data, the

degrees of freedom were reduced by the number of observations for which the mean

values were substituted.

Acquisition Mode

Training Variable Prediction Diagnosis

Binary Group (n=48)No. of instances

N 26.23 27.27SD 6.07 8.87

Total TimeM 456.02 593.33SD 255.39 352.50

Table 1. Means and standard deviations of number of instances and total processing time fordifferent inductive rule acquisition conditions

Figure 5. Number of instances for rule acquisition

Trinary Group (n=48)No. of instances

M 30.33 31.787.71 10.77

Total TimeM 577.42 615.53SD 231.83 234.58

Mean No. of Instances Required for Rule Acquisition

4O

35

• Binary Group30 rrinary Group

Z 25

20

Prediction Diagnosis

Acquisition Mode

EL

39

Mean Processing Time Required for Rule Acquisition

Figure 6. Processing time for rule acquisition

Both the instance and response time variables were transformed prior to analysis to

stabilize any departures from a normal distribution. The instance variable was transformed

with the square root transformation and the response time variable with the log transform

(Box & Cox, 1964). The correlation between the total number of instances and the total

processing time was moderate, with Pearson r =.32, (<.OO1) in the prediction condition,

and .49, (p<.000) in the diagnostic condition.

The response time and instance data were analyzed together using multivariate

repeated measures analysis of variance (MANOVA). The analysis of the response

measures revealed that the total number of instances and total processing time required to

reach the mastery criterion of 18 consecutive correct responses by the trinary group were

significantly greater and longer than those required by the binary group, H-L Trace=.25,

(s=1, m=-2, n=2), p<.000; F’s(1,94)=14.16, (MSE=1.05), and 6.32, (MSE=.60), p’s<.OOO

700

-!. 600

500

400

• Binary Group

UTrinary Group

Prediction Diagnosis

Acquisition Mode

40

and .014 respectively, as expected. The corresponding effect sizes (‘s) were .38 and .26

for the instance and time measures, respectively.

The diagnostic mode of rule induction did not require significantly more instances

but it did require significantly more processing time, as compared to the prediction mode,

‘s(1,94)=.74 and 5.91, p’s<.391 and .017, for the instance and time measures,

respectively. The corresponding effect sizes were .18 and .50 for the instance and time

measures, respectively.

These results are consistent with the expectation that rule induction from a set of

diverse instances should require more processing time compared to a set of instances that

are less variable. On the average, each new instance from a trinary set provides more

unique information about the underlying relationship than an instance from a binary set.

Processing the trinary information should therefore require more time but not necessarily

more instances, which is what the results have shown.

Subjects’ Introspection Reports of Their Inductive Learning Strategies:-In order to

learn more about subjects’ inductive learning strategies, at the end of each inductive task

subjects were asked how they were able to tell whether a particular prediction or diagnosis

was correct or not. All responses were coded, yielding the following response categories:

Category 1: No Articulated Strategy (Trial & Error)

This category contains responses which show no evidence ofany systematicstrategy. A strategy may have been used but a subject was not able to verbalize it. Atypical response was: “I don’t know, it was basically trial and error

Category 2: Memory Processing Strategies

This category includes responses characterized as memory-based enumerationstrategies since they contained lists ofvarious cause and effect relationships that subjects

41

encountered The most typical response was: “I recalled that Mixolin causes only purplerash, but Phoresin causes purple rash, and it can also cause blue rash”.

Category 3: Coding Strategies

Responses in this category revealed afocus on particular attributes within the setof instances. The attributes subjectsfocused on included either relevant or irrelevantones. The key characteristic of this category ofresponses is the reported attention tospecfic attributes. Typical responses were: “I basicallyfocused on which diagnoses wereincorrect”; “Ipaid attention to the cities where the experiments were done “.

Category 4: Rule-Related Strategies

Responses in this category reflected a systematic searchfor a rule. These subjectstypically drew a two-way or a three-way table where they systematically recorded theobserved relationships between causes and effects. They also produced a concise, generalstatement which summarized the underlying relationship. Typical response was: “Thebasic pattern was that Phoresin causes dfferent rashes but Mixolin causes only purplerash “.

Frequencies of reported strategy categories appear in Table 2.

Acquisition Mode

Self—Report Strategy Prediction Diagnosis

Binary (n=48)

1. Trial & error 6 72. Memory 28 273. coding 10 94. Rule—related 4 5

Trinary (n=48)

1. Trial & error 3 32. Memory 32 353. coding 4 24. Rule—related 9 8

Table 2. Category frequencies for reported inductive learning strategies

42

An inspection of the data in Table 2 clearly reveals that the most frequently

reported strategy under prediction as well as under diagnosis was a memory-based

strategy. Explicit rule-based strategies were infrequently reported, particularly by the

binary group. Trial and error strategies were also infrequent, particularly in the trinary

group. One thing that is clearly evident in the verbalized reports is that the subjects do not

engage in demanding cognitive operations, as shown in the frequency data (i.e. category 1

and 2 vs. category 3 and 4), although the trinary group showed a little more effort in

searching some rule or pattern.

Assessment of the Propositional Form of an Acquired Rule:-Although all subjects

reached the criterion performance level on the inductive task, their ability to identify the

appropriate rule when expressed in the standard conditional language of the form ]F x

THEN y was also assessed using a four-option, multiple choice question. The distribution

of responses for each option is given in Table 3.

43

Acquisition Mode

Option* Prediction Diagnosis

Binary (n=48)1 1 12 2 33 30 294 15 15

Trinary (n=48)1 0 32 4 83 6 84 38 29

Item;

Based on what you have observed in the set of examples just presented, which of the

following statements represents a CONCISE, GENERAL rule that BEST SUMS UP the relationship

between the type of (cause) and the type of (effect)?

*Options:

1. If (effectl) then (causel)

2. If (causel) then )effectl)

and if (effectl) then (causel)

3. If (cause2) then either

(effectl) or )effect2)

4. If (causel) then (effecti)

Table 3. Response frequencies for each option on a rule assessment item

As can be seen in Table 3, the vast majority of subjects in both groups selected one

of the two propositional statements which correctly described the conditional relationships

used for training (options 3 and 4). A test of the proportion of subjects in each group who

selected one of these two options revealed that subjects in the trinary group selected the

correct statement for the target rule (option 4) significantly more often than those in the

binary group, under the prediction mode as well as under the diagnosis mode, Chi

Sguare(1, j 96) 22.28, p<.000, and Chi-Sguare(1, = 96) = 8.22, p<.OO1, for the

prediction and diagnosis mode, respectively.

The rule selection results suggest that rule induction from a trinary set, because of

its greater variability of instances, increases the need for a more integrated, parsimonious

representation of the observed set of relations. The target rule statement exemplifies such

44

a representation, and the fact that the trinary group selected it more frequently provides

additional evidence for the validity of the inductive training task.

To see whether self-reported strategies were congruent with selection of the target

rule statement, the number of subjects who selected the target rule statement was

calculated for each self-report strategy category. The results for each group (binary and

trinary) are shown in Tables 4a and 4b.

Prediction (N=48)1. Trial & error 1 52. Memory 8 203. coding 3 74. Rule—related 3 1

Diagnosis (N=48)

Table 4a. Target rule selection by reported strategy for the binary group

Prediction (N=48)1. Trial & error 2 12. Memory 24 83. coding 4 04. Rule—related 8 1

Table 4b. Target rule selection by reported strategy for the tnnary group

Rule Options Selected

Strategy categoryTarget Other

(option 4) (options l,2,or3)

1. Trial & error2. Memory3. coding4. Rule—related

1941

618

54

Strategy category

Rule Options Selected

Target Other(option 4) (options l,2,or3(

1. Trial & error2. Memory3. coding4. Rule—related

220

16

Diagnosis (N=48)1

1512

45

When pooled together across the two groups, the data show only a weak

relationship between target rule selection and reported strategy in the prediction mode,

Chi-Square (3, N 96) = 6.53, R<091.and an absence of any significant relationship

between these two variables in the diagnostic mode, Chi-Square (3, N = 96) = 1.37,

p>.713. In the prediction mode, of the thirteen subjects who reported a rule-related

strategy, eleven in fact selected the target rule statement, but in the diagnostic mode only

seven out of thirteen with a rule strategy selected the target rule.

These findings suggest, although not conclusively, that subjects who relied on a

rule-based strategy in the prediction mode may have induced a representation of a rule that

more consistently matched the target rule statement as compared to the representation

induced under the diagnostic mode. This is a reasonable explanation given that the target

rule is expressed in the form of a predictive rather than a diagnostic proposition.

B. Analysis of Deductive Reasoning Performance

This section describes the analysis of transfer data collected from the deductive

reasoning performance. The main measure used in the analysis of deductive reasoning

performance was a response accuracy score on the deductive syllogisms. Each syllogism

was scored according to the normative conditional interpretation of each argument type.

The scoring key is shown in Table 5.

46

Modus Ponens P -> Q P Q AModus Ponens P -> Q P —Q NDenying Antecedent P -> Q -P Q SDenying Antecedent P -> Q -P —Q SAffirming Consequent P -> Q Q P SAffirming Consequent P -> Q Q —P SModus Tollens P -> Q -Q P NModus Tollens P —> Q -Q —P A

A = Always trueS = Sometimes trueN = Never true

Table 5. Scoring key for 8 types of conditional syllogisms

Applying the scoring protocol to each response yielded an accuracy score of 0 or 1

for each subject on each syllogism. Since each syllogism type was presented with both an

affirmative and a negated conclusion, two scores for each syllogism type were obtained.

These scores were added together, resulting in one score for each type of syllogism that

ranged from 0 to 2 for each subject. The means and standard deviations of these scores are

listed in Tables 6, 7, and 8 for the binary, trinary, and the control groups, respectively.

47

Syllogism First Second Conclusion Correcttype premise premise response

Far Transfer Near—transfer

Argument Trial 1 Trial 2 Prediction Diagnosistype

Modus Ponens

N 1.77 1.89 1.81 1.90

SD 0.55 0.31 0.49 0.43

Denying Antecedent

M 1.04 1.19 1.50 1.48

SD 0.87 0.89 0.77 0.82

Affirming Consequent

M 0.94 1.02 1.38 1.08

SD 0.83 0.93 0.82 0.85

Modus Tollens

N 1.68 1.52 1.69 1.50

SD 0.62 0.74 0.59 0.68

Table 6. Mean scores and standard deviations on deductive reasoning performance for the binarygroup (N=48)

48

Far Transfer Near—transfer

Argument Trial 1 Trial 2 Prediction Diagnosistype

Modus Ponena

M 1.70 1.83 1.83 1.71

SD 0.62 0.43 0.48 0.61

Denying Antecedent

N 1.08 1.23 1.29 1.27

SD 0.87 0.86 0.85 0.81

Affirming Consequent

M 0.81 0.92 1.27 1.10

SD 0.91 0.92 0.89 0.97

Modus Tollens

M 1.66 1.56 1.54 1.52

SD 0.61 0.58 0.62 0.65

Table 7. Mean scores and standard deviations on deductive reasoning performance for the trinarygroup (N=48)

49

Far Transfer Near—transfer

Argument Trial 1 Trial 2 Prediction Diagnosistype

Modus Ponens

N 1.63 1.58 1.58 1.50

SD 0.71 0.65 0.66 0.72

Denying Antecedent

M 1.37 1.38 1.21 1.25

SD 0.88 0.77 0.88 0.79

Affirming Consequent

N 1.16 1.00 1.04 1.17

SD 0.92 0.93 0.86 0.87

Modus Tollens

N 1.33 1.54 1.46 1.33

SD 0.76 0.83 0.83 0.75

Table 8. Mean scores and standard deviations on deductive reasoning performance for the controlgroup (N=24)

It will be recalled that the experimental design specified one between-subjects

factor, namely the Treatment Group (Binary, Trinary, and Control), and two within-

subjects repeated measures factors. The repeated measures factors were (a) Transfer Type

which included two trials of far-transfer, and two trials of near-transfer (prediction-related

/ diagnosis-related), and (b) Syllogism Type (MP,DA,AC,MT). Performance scores

obtained under this experimental design were analyzed with a multivariate analysis of

variance (MANOVA) by 1-df linear contrasts performed on the mean vectors.

It should be noted that although the basic task response unit is binary (correct/incorrect),

reasoning scores are based on multiple item responses, and multiple subjects.

50

Consequently, the deductive reasoning data can be appropriately analyzed by standard

multivariate methods (Collett, 1991).

The analysis was carried out in two steps. First, following the General Linear

Model (GLM) approach, a model was fitted to the data, model parameters were

estimated, and tests of main effects and interactions were performed. An overall Type I

error of .10 was used for the omnibus tests. Second, individual 1-df contrasts

corresponding to the predictions derived from the hypotheses were utilized to test the

specific hypotheses. To control for the pyramiding of contrast probabilities, a conventional

alpha level of .05 was used on tests of the individual contrasts (Huberty & Smith, 1982).

As a first step, the overall transfer performance was analyzed. Performance on the

four argument types was combined, yielding a total deductive performance score ranging

from 0 to 8 for each subject in each transfer condition. The data is shown in Table 9.

Far Transfer Near—transfer

Trial 1 Trial 2 Prediction Diagnosis

Binary( N=4 8)

M 5.44 5.63 6.38 5.96

SD 1.89 2.02 1.66 1.65

Trinary( N=4 8)

M 5.23 5.54 5.94 5.60

SD 1.71 1.66 1.56 1.84

Control(N=24)

M 5.50 5.50 5.29 5.25

SD 2.32 2.02 2.21 2.29

Table 9. Mean scores and standard deviations for overall deductive reasoning performance

51

The analysis revealed significant interactions between training conditions and

transfer types E(6,351)=1.84, (MSE=.32), p<O9l. In addition there was a significant main

effect for transfer type E(3 ,3 51)3.37, <.019, however the main effect of inductive

training conditions was not significant E(2,1 17)0.77, >.47. The results of the omnibus

tests warranted more detailed testing of the individual hypotheses using 1 -df multivariate

contrasts. Inspection of the data suggests that the effect of inductive training is present on

the near-transfer reasoning problems but not on the far-transfer problems. The specific

nature of this transfer can be further examined by detailed analyses.

Tests of Specific Hvpotheses:-The first hypothesis addressed rule transfer

performance as a firnction of content similarity. The verifiable prediction proposed on the

basis of this hypothesis was that the overall near-transfer performance (i.e. performance

across all argument types) would be better than the overall far-transfer performance for

both the binary and trinary groups. No such difference would be predicted for the control

group since it did not have the benefit of the inductive rule learning. Near and far-transfer

performance data are summarized in Figure 7.

52

Overall Deductive Transfer Performance

Figure 7. Overall transfer performance

The analysis was further carried out using a contrast of overall performance on

near and far-transfer deductive tasks. The analysis therefore also served as an additional

verification of the overall validity of the transfer of training design. If any meaningful

inductive learning occurred, a difference between near and far-transfer performance should

be observed for the treatment groups (but not for the control group) since the near-

transfer tasks used rule content that was related to the content in the inductive learning

phase.

Indeed, overall performance on near-transfer was significantly better than on far

transfer, (1,1 17) = 4.57, (MSE = 6.58), c035, and further, the interaction between

transfer and the three treatment groups was also significant, E(2, 117) = 3.65, p<.029.

Furthermore, this performance difference was due to the two treatment groups

outperforming the control group, E(1,117) 6.38, <.013. However, the two treatment

groups did not differ from each other significantly in their overall near versus far-transfer

performance, E(1, 117) = 0.91, >.342.

8

700

_______

Cl)C INearI

lOFar Ia,

4

ControlBinary Trinary

Treatment Group

53

Since the transfer types were varied as a within-subjects factor with nested

definitions of reasoning modes and trials, the following hypotheses were tested with each

nested factor (cf Figure 1). Thus, the second hypothesis addressed far-transfer

performance as a function of the training content of varying attribute dimension size

(binary vs. trinary). From this hypothesis, which was elaborated earlier, it was predicted

that there would be fewer reasoning errors with rule content that is different from the

acquisition content (far-transfer condition) with rules induced from instances with trinary,

as compared to binary attribute dimensions.

Results pertaining to the prediction based on the second hypothesis appear in

Figure 8. The prediction was tested with a contrast of performance scores of the three

groups on the four syllogisms with unfamiliar content. No difference in performance was

found between the binary and trinary groups F(2, 117) = .17, (MSE = 12.15), >.683. In

addition, the performance of these two treatment groups was not significantly different

from control group performance E(1,117)=.O1, >.9l’7.

Figure 8. Far transfer by dimension size

Far-Transfer Performance by Attribute Dimension Size

aU0

0

2

0

•Binary

0Trinary

ControI

MP MT DA AC

Syllogism Type

54

These results therefore falsify the second hypothesis. The inductive training with a

trinary set does not facilitate far-transfer to a greater degree than a binary set of

dimensioned materials. Furthermore, the results show that the rule knowledge the two

treatment groups acquired during the inductive phase did not transfer to completely new,

unfamiliar rule content.

The third hypothesis addressed near-transfer of an acquired rule as a ffinction of

the size of the contrast set from which the rule is induced. Two predictions arising from

this hypothesis were verified: (a) as compared to rules acquired from sets of instances with

binary attribute dimensions, there will be fewer reasoning errors with rules acquired from

sets of instances with trinary attribute dimensions on the DA and AC forms; and (b) as

compared to rules acquired from sets of instances with trinary attribute dimensions, there

will be fewer reasoning errors with rules acquired from sets of instances with binary

attribute dimensions on the MT argument form. The data pertaining to predictions based

on this hypothesis are summarized in Figure 9.

Figure 9. Near transfer by dimension size

2

Near-Transfer Performance by Attribute Dimension Size

0U

Co

0

a,

• Binary

0Trinary

MP MT DA AC

Syllogism Type

55

The predictions were verified with a contrast of near-transfer performance scores

of the binary vs. the trinary groups on the four syllogisms. No significant difference in

deductive performance was found between the binary and trinary group on the four

syllogisms, E(1,117) = 1.36, (MSE = 11.08), p>.246.

The result clearly falsified the third hypothesis. Deductive reasoning performance

with a conditional rule was not influenced by the attribute dimension size of the set of

instances from which the rule was initially induced. This result, therefore, also casts doubt

on the influence of the size of a contrast set encountered during rule induction. According

to the hypothesis, larger contrast sets with more alternative dimension values should

facilitate reasoning performance with indeterminate argument forms, but according to the

present results, this effect of the trinary inductive training set was not realized. It might be

noted at this time that this particular outcome may have been due to the binary nature of

the traditional deductive syllogism task. If so, then the trinary group may have been less

able to utilize their conditional knowledge as compared to the binary group. This point is

discussed in more detail later.

The fourth, and final hypothesis addressed near-transfer of an acquired rule as a

function of acquisition mode. Two verifiable predictions were proposed on the basis of

this hypothesis: (a) as compared to rules acquired in a diagnostic context, there would be

fewer deductive reasoning errors with rules acquired in a predictive context on the MP

and DA argument forms; and (b) as compared to rules acquired in a prediction context,

there would be fewer deductive reasoning errors with rules acquired in a diagnostic

context on the AC and MT argument forms. The data pertaining to the predictions based

on the fourth hypothesis are summarized in Figure 10.

56

The predictions were verified with a contrast of performance on the four

syllogisms with a prediction-related content versus the four syllogisms with a diagnosis-

related content. Overall deductive performance by the two treatment groups was better on

prediction-related content as compared to diagnosis-related content, but this difference

only approached statistical significance E(1,1 17) = 3.78, (MSE = 1.99), p<.055. The locus

of this difference was in performance on the AC argument type, where prediction-related

content significantly facilitated reasoning performance, (1,1 17) = 4.07, p<.O46.

Performance on the remaining argument types was not significantly different.

C. Additional Analysis of Transfer Data

After testing the hypotheses, a further analysis of transfer data was carried out to

investigate additional transfer effects that might inform the interpretation of the above

results. A response pattern analysis was canied out for each subject to determine whether

the subject’s overall response pattern to the eight syllogism types followed a

predominantly conditional or biconditional rule interpretation. The percentages of subjects

following each interpretation in near and far-transfer conditions are presented in Table 10.

Figure 10. Near transfer by acquisition mode

57

Binary Trinary Control(n=48) (n=48) (n=24)

Transfer type Near Far Near Far

Responsepattern

Conditional .68 .45 .55 .46 .51

Biconditional .20 .35 .30 .44 .28

Table 10. Proportion of subjects following either a conditional or a biconditional rule interpretation

The conditional response structure (pattern) was the most common response

structure produced by control subjects (51%), as well as subjects in the treatment groups

(68% and 55% for the binary and trinary groups, respectively, on the near-transfer

problems, and 45% and 46% for the binary and trinary groups, respectively, on the far-

transfer problems). The biconditional response structure represented the majority of non-

normative (i.e. non-conditional) responses (28% for the control and the binary groups, and

37% for the trinary group, averaged across all transfer problems).

Analysis of transfer performance as a function of rule selection scores:-To gain

additional insight into the relationship between inductive and deductive reasoning, overall

deductive performance on the four transfer tasks was analyzed as a function of rule

selection scores. The original rule selection score was collapsed into a new variable,

labeled RC, which was defined as follows: If the correct propositional representation of

the target rule was selected in both the prediction and the diagnostic condition, a score of

3 was assigned; if it was not selected in either condition, a score of 1 was assigned;

otherwise, a score of 2 was assigned. A high RC score therefore reflects a consistent

identification of the appropriate propositional form of the target rule. Because deductive

58

performance did not differ between the two training treatment groups (binary and trinary),

the groups were combined for the purpose of this particular analysis. Transfer scores

summed over the four argument types for each rule selection score are presented in Table

11 (see also Figure 11).

Rule Selection Score*(N 96)

1 2 3Transfer Type (N=34) (N=27) (N=35)

Far—Transfer(Trial 1)

M 5.09 5.26 5.63SD 1.78 1.93 1.72

Far—Transfer(Trial 2)

M 5.35 5.74 5.69SD 2.03 1.63 1.83

Near—Transfer(Prediction>

M 6.27 6.07 6.11SD 1.71 1.44 1.67

Near—Transfer(Diagnosis)

M 5.62 5.59 6.09SD 1.67 1.80 1.79

* If the target rule was selected in both training modes then score=3,if the target rule was selected in one of the two modes then score=2else score=l.

Table 11. Transfer scores summed over all argument types by rule selection score

59

Analysis of the data in Table 11 revealed that the overall transfer performance did

not vary as a function of the rule selection score, F(2,93) = 0.38, (MSE = 8.45), p>.684.

Apparently, subjects who selected the target rule, did not perform better than those who

did not. An inspection of the data reveals a noteworthy trend in the transfer scores, namely

that as the rule selection score increases, the difference between the prediction-related and

diagnosis-related transfer scores appears to decrease (see Figure 11). It appears that with

more reliable target rule selection, performance became more independent of the cause-

effect directionality encountered during inductive training.

The difference scores were regressed on the rule selection scores and the relationship was

tested for each group. The relationship was clearly not significant for the trinary group,

(1,94) .32, (MSE = 2.37), j>.572, however it closely approached significance for the

binary group, E(1,94) = 3.58, (MSE = 1.85), p<062. The results suggest that for the

binary group at least, near-transfer performance became more stable as the target rule was

being selected more reliably following the inductive tasks. Thus, better recognition of rule

structure as expressed in multiple choice statements appears to be related to performance.

Figure 11. Transfer performance by rule score

60

W. DISCUSSION

A. Summative Overview

The broad aim of this study was to gain a better understanding of deductive

reasoning with conditional statements, or rules, of the form IF x THEN y. The motivation

for the study was based on the broad premise that deductive reasoning with conditional

rules depends on how the rules were acquired, or induced, by the reasoner in the first

place. The purpose of the study, therefore, was to investigate how, if at all, the conditions

under which conditional rules are induced, influence rule transfer to deductive reasoning

with conditional propositions. In other words, this study was an investigation of transfer

between inductive and deductive conditional reasoning.

Four specific hypotheses pertaining to the transfer of conditional knowledge were

proposed. The first hypothesis addressed overall differences in near and far-transfer

performance. Near-transfer referred to a situation where the content from which a

conditional rule was induced matched the content on the subsequent deductive transfer

task. Far-transfer referred to a situation where the inductive and deductive content did not

match. The second hypothesis addressed far-transfer performance as a function of

attribute dimension size (binary vs. trinary). The remaining two hypotheses concerned

near-transfer performance: one addressed near-transfer as a function of attribute

dimension size, and the final one focused on near-transfer as a function of acquisition

mode (predictive vs. diagnostic).

61

The hypotheses and the testable predictions derived from them were developed by

drawing on a combination of empirical findings and theoretical claims from two competing

psychological theories of human reasoning, namely a class of theories referred to as rule-

based (Braine et al., 1991; Inhelder & Piaget, 1958; Nisbett 1993), and an other class of

theories labeled instance, or memory-based theories (Griggs et al., 1982; Pollard et al.,

1981). Rule-based theories propose that deductive reasoning is carried out by the use of

rules that are sensitive to the logical form of deductive arguments. Memory-based theories

on the other hand propose that reasoning depends primarily on the cueing of relevant

instances by the content of argument propositions or their context (Rips, 1990). The near-

transfer hypotheses were developed on the basis of the memory view, while the far-

transfer hypothesis was derived from the rule perspective. Therefore, the summary of the

findings and their implications will be discussed in the context of the theoretical

perspective from which each hypothesis evolved.

B. Implications for Theories of Conditional Reasoning

Implications for Rule-based Theories of Deductive Reasoning:-Any discussion of

rule-based theories of human reasoning runs into a difficulty as soon as it becomes

necessary to specify what rules one is talking about (Rips, 1994). The current debate over

the utility of rules in reasoning includes a wide variety of inferential rules such as logical

rules, elementary inference schemas, pragmatic reasoning schemas, and statistical rules

including the law of large numbers (Nisbett, 1993). This study focused on logical

(conditional) rules, but the results, specifically those pertaining to the second hypothesis,

have implications for other types of rules as well.

62

Rule transfer studies have repeatedly found that rules are generalized to novel

situations more consistently if they are induced from sets of instances with high compared

to low variability (Catrambone et al., 1989; Royer, 1979; Singley & Anderson, 1989).

Since the trinary training set exhibits greater variability than the binary set, rule-based

theories would predict the far-transfer performance of the trinary group to be better than

the binary group. This was not the case in this study, however. The groups did not differ

on the far-transfer tasks, and in fact no far-transfer was observed for either training group.

The lack of far-transfer in this study was not due to poor training. All subjects

reached the inductive training criterion of 18 consecutively correct predictions and

diagnoses, and the vast majority of subjects in both treatment groups selected one of the

two correct conditional rule statements. Furthermore, the analysis of the inductive training

data confirmed that the trinary group took significantly more time, and required more

instances to reach criterion compared to the binary group. Since induction of rules from

variable sets of instances would be expected to require more elaborate processing, the

present results are consistent with the claim that meaningful training did in fact occur.

Inadequate training, therefore, does not appear to be a factor responsible for lack of far-

transfer. What may have occurred instead, is that the assumed content-free rule structure

might have developed from the training materials, particularly from the trinary dimensional

sets, but such rule structure might not have been properly operative. As was already

noted, one reason may have been the inherent binary nature of the criterion propositional

reasoning task which might have mitigated the adaptive function of the content-free rule

structure.

What implications does the absence of far-transfer have for rule-based theories of

conditional reasoning? To help frame the rule debate, Smith et al.(1992) proposed eight

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criteria for deciding whether reasoning involves the use of abstract rules such as the set of

logical rules which includes the conditional. The criteria are as follows:

1. Reasoning performance is the same on familiar and unfamiliar content.2. Performance is the same with abstract and concrete material.3. Early in acquisition, a rule may be overextended.4. Performance deteriorates as a fhnction of the number of rules that are required for

solving a task.5. Performance is facilitated by prior application of the same rule.6. A rule is mentioned in a verbal protocol.7. Performance on tasks with specific content is improved by training on abstract

versions of the rule.8. Performance on problems in a particular domain is improved as much by training on

problems outside the domain as on problems within it.

Many of the criteria are not directly applicable to the present study. For example,

this study was not concerned with performance differences on abstract and concrete tasks;

the rule content on all the tasks was at a similar level of abstraction. However, the first and

last criteria are relevant here. If abstract rules are being used, then performance on familiar

(near-transfer) and novel (far-transfer) deductive tasks should be similar, and experience

with one task content should facilitate performance with others types of content. This

clearly did not happen in the present study. Overall scores on near-transfer tasks were

significantly higher than on far-transfer tasks, and experience with one type of content did

not facilitate performance with unfamiliar content since the treatment groups did not do

any better than the controls on arguments with novel rule content.

The present findings indicate that subjects who underwent inductive rule

acquisition clearly learned something, but not generalizable inference rules that they could

apply in new contexts. Subjects did not seem to rely on inferential rules or schemas that

were independent of content.

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Implications for Memory-Based Theories of Deductive Reasoning: Memory-based

transfer has been shown to be facilitated by transfer-appropriate processing (Morris et al.,

1977) where encoding and retrieval conditions match (Tulving, 1984). Therefore, if

deductive conditional reasoning is memory-based, it should also be facilitated by transfer-

appropriate processing. Thus, according to the fourth hypothesis which was derived from

the memory view, rules induced from examples of causes followed by effects (prediction

mode) should facilitate performance on deductive argument types that involve primarily

cause-to-effect reasoning, namely the MP and the DA types. On the other hand, rules

acquired by exposure to examples of effects being traced backward to causes (diagnostic

mode) should aid performance on argument forms that also involve inferences from effects

to causes, namely the AC and MT types.

The results of this study do not support the above hypothesis. The facilitative

effect of transfer-appropriate processing did not materialize. The diagnostic acquisition

mode did not enhance near-transfer performance on argument forms involving reversed,

diagnostic inferences. In fact, the opposite result occurred on the AC form, where the

predictive mode resulted in significantly better performance compared to the diagnostic

mode.

The findings cast doubt on instance-based accounts of reasoning. Reasoning on the

AC form has been shown to depend on the reasoner’s awareness of alternative antecedents

(Markovits, 1984), which in the context of this study means alternative causes of a given

effect. According to the memory-for-instances view, the recall of alternative causes of a

particular effect on the AC form should have been facilitated by the matched effect-to

cause directionality encountered on the diagnostic rule induction task. The fact that this

did not occur suggests that recall of specific instances may not be involved in deductive

reasoning. This conclusion does not contradict the fact that awareness of alternatives

65

plays a role in conditional reasoning. It may be that reasoners benefit from simply being

aware of the fact that some alternatives exist, but just what these are may not be critical

for making correct inferences.

Support for the instance-based account of reasoning is also undermined by the

results of the test of the third hypothesis. In contrast to the last hypothesis, which

addressed access to relevant instances through transfer-appropriate processing, the third

hypothesis focused on the availability of such instances. This hypothesis involved a

comparison of near-transfer performance of two treatment groups. The binary group

induced conditional rules from sets of instances that had binary attribute dimensions, the

trinary group from trinary sets. In the context of this study, the rule instances in the binary

sets were constructed from two distinct causes and two distinct effects. The trinary sets

were constructed from three causes and three effects.

Since the pooi ofunique alternatives (of antecedents and consequents) that was

available to reasoners in the trinary group was larger than the pooi of alternatives available

to the binary group, instance-based theories would predict better deductive performance

for the trinary group on the DA and AC types. This is because these two argument types

are indeterminate, and correct conditional inferences depend once again on the ability of

the reasoner to consider alternative antecedents that can lead to a given consequent

(Evans, 1982; Oaksford et al., 1992). Since the near-transfer performance did not differ

between the binary and trinary groups, there appears to be no advantage of having a larger

pooi of alternatives available for making deductive inferences. This finding, together with

the refutation of the first hypothesis, question the validity of the claim that people recall

specific instances when they reason with conditional rules.

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Implications for Theories of Reasoning by Mental Models:-Currently the most

intensely debated theory of propositional reasoning in general, and conditional reasoning

in particular is the mental model theory (Johnson-Laird, Byrne, & Schaeken, 1992; 1994).

Because the mental model view is so prominent in the literature, and because the results of

the present study have some implications for this theory, the key elements of the theory

are briefly outlined below.

The mental models approach rejects the idea that people use abstract logical rules

that are sensitive only to the logical form of sentences. Instead, Johnson-Laird et al.

propose that people reason in more concrete ways, by constructing and manipulating

mental models of argument premises. Reasoning by mental models involves the following

steps:

1. The reasoner begins by studying the premises and then forms a mental model whichrepresents a possible state of the world in which the premises hold.

2. The reasoner then proceeds to search for a proposition which is both true in the model,and also is informative in the sense that it is not a repetition of an existing premise or atrivial inference. This derived proposition represents the reasoner’s putative conclusion.

3. In the last step the reasoner looks for counter-examples to check the validity of theputative conclusion. Counter-examples are models which are consistent with the argumentpremises but inconsistent with the conclusion. If no counter-examples are found, thereasoner accepts the conclusion as valid.

According to the mental model theory, errors in conditional reasoning occur when

reasoners fail to represent some relevant information in their model. The more their

implicit model is “fleshed out” with explicit information, the better the reasoning

performance (Johnson-Laird et a!., 1992; 1994). Unfortunately, the theory does not clearly

specifr what determines the extent to which a model is fleshed out. As Evans (1993)

67

points out, the theory needs to be more specific with respect to (a) the nature of the

mental representations, and (b) what causes the initial representations to be expanded.

The results of this study can in fact inform these gaps in the mental model theory.

The theory assumes that when people encounter an IF.. THEN.. statement they

automatically construct a mental representation that has either an implicit or an explicit

conditional structure. Just where people acquire the knowledge to do this is never

addressed. Given the generally poor reasoning results reported in the literature, it would

appear that most people do not in fact have this presumed conditional knowledge.

The issue of conditional knowledge acquisition, of course, motivated the present

study. Since subjects in this study were exposed to explicit examples of conditional

relationships during the rule induction task, their experience should improve their ability to

“flesh out” their mental models they presumably utilize on the deductive task. The present

findings provide mixed support for thefleshing out component of the model theory. The

fact that both treatment groups performed better on the near-transfer task suggests that

their exposure to the exemplar sets used in the inductive task facilitated their ability to

construct more explicit mental representations of the premises compared to the control

group.

The results also suggest that if subjects did flesh out their models, their expanded

representations were probably not constructed from specific instances. If they were, then

the trinary group should have outperformed the binary group because the trinary set

contained a greater variety of potential model building “material”. It is more likely that

people relied on representations that lie somewhere between abstract rules and concrete

models built from specific instances.

68

The fact that near-transfer performance Modus Tollens did not rise above the level

of controls for either treatment group also has implications for the mental model theory.

Performance on MT was not facilitated by inductive training and remained generally

unchanged across groups and conditions. Yet, unlike Modus Ponens, which also remained

unchanged, the MT scores do not indicate a performance ceiling which would limit any

potential improvement. The MT form is generally considered to be relatively difficult since

it contains a negation as well as a reversed inference from consequent to antecedent

(Evans, 1982). The presence ofboth of these factors may in fact tax cognitive resources to

such an extent that subjects do not even attempt to construct even implicit mental models.

The mental model theory stipulates that models are represented and manipulated in

working memory (e.g. Baddeley, 1990), therefore a significant cognitive load imposed by

particular argument structures may constrain reasoning with internally represented

models.

Summary of Major Implications From the Findings:-The results clearly rule out a

reasoning process that operates on specific instances stored in memory. The trinary group

always performed at or below the level of the binary group despite the fact that the trinary

group had equal access to and greater availability of specific instances that could be used

to generate more counterexamples or more explicit models to aid reasoning. Instance-

based processing is also ruled out by the fact that transfer-appropriate processing failed to

improve performance. Previous research has shown that access to encoded instances is

facilitated by matching the encoding and retrieval conditions. When this was done in the

present study by matching the direction of inferences between the inductive and deductive

tasks, no facilitative effect of transfer-appropriate processing was observed. Since any

reasoning program that relies on access to specific instances would be expected to benefit

from improved memory access, the present findings indicate that an instance-based

process was probably not involved.

69

At the same time, the results also do not provide evidence for a process driven

solely by abstract, general rules. If such rules were used, then far-transfer would be

expected to take place, particularly in the trinary condition. The inductive training data for

the trinary group was consistent with the expectation of more abstract rule learning (e.g.

increased processing time, and more reliable selection of the more parsimonious and

general rules summarizing the observed conditional relationships). Yet, the trinary group

performance on far-transfer was no better than either the trinary or the control group,

indicating that the reasoning process was probably not driven by abstract rules. It should

once again be noted, however, that an abstract rule structure may have developed during

training, but it may not have been operated on during the deductive task.

So far, results of this research have been used as evidence for rejecting current

accounts of conditional reasoning. However, considered together, the results suggest

alternative accounts of deductive conditional reasoning. One such account is proposed in

the sequel.

C. Proposed Account of Conditional Reasoning

Taken together, the present findings point to a reasoning process driven by rules

that are specific to a domain, but generalizable over particular instances of the domain.

This explains the superiority of the near over the far-transfer performance in conjunction

with the lack of observed performance facilitation due to improved access and availability

of particular instances in memory. But what form do these domain-specific rules take?

The verbal reports on inductive strategies suggest that these rules are not

represented in the syntactic form of IF x THEN y. The majority of subjects produced

70

statements such as “Drug x causes only symptom y, but the other drugs cause all the

observed symptoms”. All such statements formed the response category labeled “memory-

based”, which was also the largest category for both treatment groups. Such statements

can be expressed more generally as: “A member x, from the class of X’s is associated only

with one member, y, of the class of Y’s, but any of the other X’s could be associated with

any member of the set of Y’s”. A rule at this intermediate level of abstraction might be

optimal in terms of reasoning efficiency. It captures the general conditional structure of

observations, yet it provides enough detail for constructing and manipulating mental

representations in the form of mental models. The assumed associative memory structure

referenced by this linguistic expression is shown below.

Several aspects of the proposed rule representation should be noted. First, the

relationship between the C’s (e.g. antecedents) and E’s (e.g. consequents) conforms to the

material conditional. This is corroborated by the fact that the conditional response

structure (pattern) was the most common response structure in the transfer conditions.

Second, in the proposed representation the associative link connecting Cl and El

is bi-directional, and stronger than all the others. As a result, the rule representation is

biased toward biconditional reasoning errors, particularly when it is operated on under

increased processing load, involving trinary dimensions, for example. The present findings

again support this conjecture. A biconditional response structure represented the majority

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of non-normative (i.e. non-conditional) subject responses across all transfer problems,

however it was more prevalent in the trinary group as compared to either the binaiy or the

control groups.

The proposed rule structure also explains the counter-intuitive finding that

performance on the AC argument form was better in the predictive induction condition,

despite the fact that the AC form is distinguished by a diagnostic inference mode. The

reason for this is that the proposed rule structure optimally represents the one-to-one and

one-to-many mappings which define a conditional structure, but which only hold in a

predictive context. To see why, consider the proposed rule structure from a diagnostic

perspective (i.e. view it from the set of consequents, the E’ s, to the set of antecedents, the

C’s). From this perspective, all the consequents have one-to-many mappings to the

antecedents, and consequently subjects may infer a structure based on a symmetric

mapping, such as the biconditional. When the structure is viewed in a predictive context,

on the other hand, the one-to-one mapping between Cl and El is readily apparent. Since

this mapping represents the key defining feature of a conditional interpretation, subjects’

reasoning is more likely to reflect this normative conditional interpretation in the

predictive context. This is indeed what the results show. Performance on prediction

related content was better for all argument types, although it reached significance only on

the AC syllogism. This finding has instructional implications which are discussed in the

next section.

Finally, it is proposed that conditional reasoning may involve more than one level

of information processing: the underlying reasoning process may depend on the argument

type encountered. There is no a priori reason to assume that the same cognitive process

must be deployed to deal with all types of conditional reasoning arguments. In fact, the

present findings suggest otherwise. The results show that near-transfer performance was

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significantly better (compared to control levels) only on the DA and AC forms. The MP

and MT levels, however, remained essentially unchanged across conditions. Why?

Past research has shown that reasoning with Modus Ponens is essentially at a

ceiling level, with typical performance in the 85-100 percent range (e.g. Evans, 1982).

Results of this study are no different. In fact Modus Ponens is the flagship of proponents

of inference schemas (Braine et al., 1991) since performance on it is unaffected by content

and is highly accurate. When considered together, the results suggest that the reasoning

process on the MP form is likely to be based on compiled procedural knowledge

(Anderson, 1983) and as such, any further performance improvement is not likely to be

observed.

In contrast, the MT form may involve little, if any, systematic reasoning. The

rationale for this supposition is based on task analysis of Modus Tollens which suggests

that it is, in fact, the most difficult syllogistic form since it involves both a negation and a

reversed inference (Evans, 1982). Yet performance on the MT form is generally quite

good, reaching as high as 80 percent proportion correct (Evans, 1993). Again the results

of this study are consistent with previous research, with MT performance being second

only to MP. It is proposed that the reason for such a seemingly impressive performance on

the toughest syllogism form is simply due to the well documented matching bias discussed

in section Dl. (Evans, 1982). The joint presence of the two resource-taxing operations

may interfere with the retrieval of the memory-based rule representation. Because of the

relative strength of the biconditional link in the assumed representation, the biconditional

bias inherent in this rule representation would increase, thus increasing the probability of a

biconditional interpretation. Under this interpretation, the negation of the consequent

compels subjects to add a matching negation to the antecedent term, which in this

particular case yields the correct response.

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D. Implications for Education

The major implication of this research for educational practice is that conditional

reasoning, which is ubiquitous across academic and professional disciplines, can be

enhanced by appropriately designed training. Even the brief inductive training utilized in

this study resulted in significant improvement in reasoning with training-related content.

Longer training periods, which were not realistic in this experimental set-up, may have

yielded even better performance outcomes. It should also be noted that deductive

performance may have been improved by training subjects on the deductive syllogisms

directly, without the benefit of the inductive phase. However, knowledge acquired by

simply substituting different content into standard logical or other rule-based forms is

likely to be “inert”, and bound to specific application contexts. The bottom-up inductive

approach may require more time and effort, but the knowledge so constructed may be

more flexible, and adaptable to different reasoning contexts. Clearly, more research is

needed to resolve this issue.

The present results may also inform the ongoing debate (e.g. Cheng et al., 1986)

regarding the optimal method of teaching deductive reasoning skills. Given that subjects in

this study did not make inferences on the basis of content-free, generalizable rules,

induction from rule instances alone, may not be sufficient to develop such rules. Inductive

training may have to be supplemented by explicitly teaching students the syntactic

structure of conditional rules.

The results also indicate that at least for simple conditional arguments with binary

propositions such as those used in this study, inductive training sets with binary

74

dimensions appear to be equal or superior to sets with more varied instances. Another

advantage is that rule learning from binary sets also requires less time compared to larger,

trinary sets. This is a usefhl result from a practical perspective of teachers who may not

have the time to construct large rule-learning exemplar sets, and who want to minimize

instructional time.

This research also clearly established the superiority of the predictive mode of rule

acquisition over the diagnostic mode. Transfer to prediction-related content was

consistently equal to or significantly better compared to the diagnostic mode, including

transfer to deductive reasoning which emphasized the diagnostic mode. These results may

be particularly relevant for medical education where diagnostic reasoning is, of course,

critical.

E. Limitations of the Study and Suggestions for Further Research

Since the limitations of the current research often motivate additional research, the

two issues are discussed together. This study has several limitations. Subjects were

volunteers who were paid for their participation; they were not randomly selected from the

population and they lacked any intrinsic motivation on the experimental tasks. All subjects

were undergraduate students in a Teacher Training Program, which limits any

generalizations to other populations. Additional research with samples from other

populations is clearly needed.

Methodological limitations span both the inductive and deductive tasks. The

inductive task was by necessity relatively short, averaging about one hour. This length of

time may not be adequate for inducing a full blown logical rule in the form of

75

automatized, compiled, procedural knowledge that can be effortlessly applied in different

settings (Anderson, 1983). Additional research is needed to determine whether more

extensive rule induction training would result in transfer to deductive tasks with unfamiliar

content. In addition, different inductive training sets need to be tested since there is no

reason to assume that the exemplar sets used in this study were in any way exhaustive or

optimal.

In order to make the duration of the inductive task reasonable, subjects were

allowed to record their observations, responses, and corresponding feedback from the

computer during rule learning. This procedure made the task easier but it may not have

encouraged deeper processing because subjects did not have to restructure the information

they encountered in order to make it more manageable for their working memory. In turn,

their ability to reconstruct their conditional knowledge from memory may have been

reduced. Further research comparing this experimental procedure with one that forces

subjects to rely completely on their memory would be informative.

The deductive task utilized standard syllogism forms which may not represent

practical reasoning situations that generally involve more information in a less structured

format. Perhaps more importantly, in the standard deductive syllogism, the premises

present only binary propositions. In other words, each individual proposition contains only

one term or its negation (p or not p, or q or not q). This may have biased the task

difficulty in favour of the binary group since, with binary content, a negation implies a

small contrast set which is easier to represent and thus reduces cognitive load. Therefore,

future research needs to consider non-binary deductive tasks such as, for example: “Given

Ifxl then yl, together with x3 is the case, what follows?”.

76

The task content may also limit generalizations to different domains. The challenge

was to develop task content that was neutral in that it did not cue many pre-existing

semantic associations based on experience, while at the same time providing a sense of

realism and practical relevance. Every effort has been made to satisfy these conflicting

criteria, but the inevitable tradeoff may have diminished the external validity of the tasks.

Future research should investigate transfer within and between “real-world” content

domains.

The method of scoring the deductive performance may also have masked some

effects. It will be recalled that validation scores for affirmative and negated conclusions

were added together to yield an overall performance score. Validation responses are

generally not identical for these two situations (e.g. Lee, 1985; Marcus & Rips, 1979) and,

more importantly, the response patterns may interact with different inductive training

conditions. Further research is clearly needed, which may also necessitate a different

analytical approach suitable for the analysis of categorical data.

As in other experimental studies in cognitive experimental psychology, the

possibility existed that subjects may not have been fully motivated to engage all their

available cognitive resources while working on the tasks. Consequently, some

performance differences may have been attenuated if subjects did not bother to deploy

some strategy or knowledge which they may have acquired during the inductive phase.

However, since the context under which the tasks were presented (i.e. evaluating student

learning) was highly relevant to the subjects’ coursework, the vast majority of subjects

appeared highly engaged and genuinely interested in the experimental tasks. Still, future

research should investigate inductive and deductive reasoning that is motivated by realistic

goals and has real consequences.

77

One important issue raised by the present research concerns the boundaries of near

and far-transfer. In this study, the near vs. far distinction was based on the similarity, in

terms ofcontent semantics, between the acquisition and the application of rule

knowledge. Research in other areas of cognitive psychology on the transfer of cognitive

skill, most notably research on analogical reasoning is relevant here. Studies of analogical

reasoning indicate that transfer is a function of the similarity between the transfer task, and

the reasoner’s internal representation of a related situation encountered previously

(Vosniadou & Ortony, 1989). Studies of analogical reasoning have shown that internal

representations based on structural features enable far-transfer when these representations

are successfully mapped onto new situations that share the same structural features

(Gentner & Toupin, 1986). In this context, the structural features of conditional

representations are the one-to-one and one-to-many mappings between antecedent and

consequent pairs, as illustrated in the model proposed above.

Unfortunately, structural mappings unlike surface mappings based on semantic

relatedness, are more difficult to access since they are often less salient. One way to

facilitate access to these features is to provide contextual cues. Another way is to

explicitly focus attention on relations between objects, rather than the objects themselves.

In terms of the present research, it would be valuable to investigate transfer of conditional

knowledge using different contextual cues between the inductive and deductive phases. In

this way, the applicability of even a limited, domain-specific representation may be

stretched by cueing the reasoner to focus on the structural features that are presumable

already present in their internal knowledge representation. Using this approach, it would

be possible to test deductive transfer to other domains, that may not share any surface

features with task domains encountered during rule acquisition.

F. Final Summary and Conclusion

78

Reasoning with conditional rules represents one of the most essential and

ubiquitous forms of human reasoning. Despite the proliferation of research on conditional

reasoning, many questions regarding the knowledge representation and the processing

involved in this form of reasoning have not been fully answered. One reason is that in

virtually all studies of conditional reasoning, the existence of conditional knowledge was

simply assumed, and how the assumed knowledge was acquired in the first place has not

been addressed. In contrast, this study utilized a transfer-of-training paradigm which

made it possible to actually manipulate the learning and the application of conditional

knowledge, and consequently, to test different hypotheses about its underlying form and

function. Taken together, the present findings suggest that conditional reasoning is based

on a knowledge representation of intermediate level of abstraction, not unlike that of basic

level categories. Instead of completely generalized schemas or specific instances, subjects

appear to rely on conditional knowledge that is domain-specific and that contains the

minimum number of antecedents and consequents that captures the observed conditional

relations. This minimum number appears to include the target antecedent-consequent pair

(i.e. ci and ci), as well as an abstract representation of the respective logical complements

{ not ci, not ci). Further research is needed, however, with a non-binary version of the

deductive task to assess the full extent to which induced conditional knowledge can in fact

be generalized.

79

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APPENDICES

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APPENDIX A: An illustration of rule transfer based on the proposed hypotheses

To provide a more concrete picture of the hypothetical steps involved in the

transfer of an acquired rule according to the instance-based account of reasoning, this

section briefly, and informally, illustrates how a conditional rule might be learned, and how

it might subsequently be used in making deductive inferences.

Phase I. Acquiring a Conditional Rule (Inductive Reasoning):-Let’s assume that a

researcher wants to discover what effect, if any, certain environmental agents have on the

health of people who have been exposed to these agents. Let’s take a simple example

where she wants to investigate only two such agents known as causal agent ci and causal

agent c2. The effects she is considering are health effect labeled el, and no health effect,

labeled e2. Let’s assume that this researcher administers each agent and observes the effect

over several trials. Here is what she might observe if the agents and heath effects have a

conditional (asymmetrical) relational structure:

ci -->elc2-->elc2 --> e2

After running a number of these trials, her memory for these observations might be

represented as simple associations between the causal agents and their health effects:

ci >>> elc2 >>> e2ci >>> cic2 >>> el

Note that in this notation the symbol “>>>“ indicates the strength and direction of

the association between the cause and the effect as they are represented in memory.

Her next task is to conclude something from the data. Clearly, a number of

different conclusions, or propositional statements emerge from the results:

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a. “Agent ci causes a health effect el”b. “Agent c2 causes a health effect el on some trials but no effect on others”c. “Agent ci never results in the absence of a health effect”, etc.

Given that her goal is to come up with some general, concise statement that summarizes

the results (i.e. a general conclusion), she notes that no general conclusion can be stated

about agent c2. In fact the most appropriate general and concise statement summarizing

the results is:”Whenever agent ci is administered, effect el occurs” or, “IF ci THEN el”.

Because a statement in this general form is in effect induced from the set of observations

represented in memory,, it can serve as a pointer to her memory representation for that set

of observations.

In addition, the researcher’s search for a general rule (conclusion), and her attempt

to formulate her conclusion in a propositional form, means that the ci >>> ci pair has

been processed more elaborately (more deeply) then the other pairs. This means that the

associative link from ci to e I has actually been strengthened by the application of the

pragmatic constraints.

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Phase II. Transfer of the Acquired Rule to Conditional Reasoning:-For the sake of brevity,

the assumed reasoning process is illustrated only in the case of the DA inference form.

Step 1. Representation of the First Premise:-According to the instance view, the first

premise (the acquired rule) provides lexical access to the stored representation of the

instances from which the rule was induced:

“IFclTHENel” > cl>>>elc2 >>elc2 >>e2

Step 2. Representation of the Second Premise:-The negation of the antecedent in the

second premise activates the set of antecedents in the first premise (since both refer to the

same category of causes). To accommodate a consistent internal representation of both

premises, the inference schemaP or Qnot P

Q

is instantiated yielding the following unified representation of both premises:

c2>> elc2>> e2

Step 3. Generating a Conclusion:-Following the association links from the antecedents to

the consequents, our reasoner arrives at the conclusion that either el or e2 occurs. In

other words the reasoner concludes that ci sometimes occurs, meaning that the

conclusion “ci” is sometimes true which is the correct conclusion.

A complete account of the hypothesized reasoning process with rules acquired

under different conditions is given below.

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APPENDIX B: Instructions to subjects

Teacher Education Study

Instruction Booklet

Step 1. Please read the following section:

In this study we are interested in learning more about how teachers evaluate their students’learning. Specifically, we are exploring how teachers assess the way their students applynewly acquired knowledge about causes and effects in a variety of content areas.

The study involves two separate parts:

Part A. Discovery Learning No. 1Discovery Learning No. 2

Part B. Evaluating Students: Situation No.1Evaluating Students: Situation No.2Evaluating Students: Situation No.3Evaluating Students: Situation No.4

The purpose of the discovery learning part is to let new teachers like yourself go throughthe same learning experience that some students have actually gone through.

Generally, people take less than an hour to complete the entire study. You should expectPart A to take a little longer than part B. The evaluation situations in Part B are all veryshort. So sit back, relax, and have fun!

Step 2. Please boot-up the computer, inset the disk into drive A (or B) and do thefollowing:

i. Make drive A (or B) the active directoryby entering the command a: (or B:)

ii. When you see the A> prompt, start the program by enteringthe command go

iii. Follow the directions on the screenand please, type everything in lower case only.

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Part A. Discovery Learning: Predicting Effects of Radiation on Plants

Step 1. Please read the following section carefully:

The topic we will deal with in this part involves predicting the effects of different types ofradiation on plants. A variety of plants were exposed to several radiation sources bybiologists in different countries. Each group ofbiologists made a specific predictionconcerning the effect of their particular type of radiation on their plants. You will see eachprediction on the screen shortly.

When you begin the next computer session, you will look at each prediction beingdisplayed on the screen, and decide if the prediction is correct or not. After each response,you will receive feedback which you can use to make a more informed decision next time.The goal is to discover a simple rule which will help you decide whether each predictionis correct or not. The program will stop after you make 18 correct decisions in a row.

Step 2. Please type the lower case letter m to begin the next computer session...

You are encouraged to record relevant information about each diagnosis in the spacebelow:

Type of Radiation Predicted Effect Prediction Correct?(yin)

91

Step 1. Please answer the following question:

How were you able to tell whether a particular prediction was correct or not?

Please write your response on the line below:

Step 2. Please turn to the next page....

92

Step 1. Please answer the following question:

Based on what you have observed in the set of examples just presented, which of thefollowing statements represents a CONCISE, GENERAL rule that BEST SUMS UP therelationship between the type of radiation and the type of mutation?

Please circle your best choice, and put an X beside your second best choice, in case youhave one.

1. If a plant is exposed to Beta radiation, then it grows either square, triangular, orcircular leaves.

2. If a plant is exposed to Gamma radiation, then it grows square leaves.

3. If a plant is exposed to Gamma radiation then it grows square leaves, and if a plantgrows square leaves then it was exposed to Gamma radiation.

4. If a plant grows square leaves then it was exposed to Gamma radiation.

Step 2. Please turn to the next page....

93

Part A. Discovery Learning: Diagnosing Causes of Strange Fish Scales

Step 1. Please read the following section careflilly:

The topic we will deal with in this part involves diagnosing the causes of unusual scales offish that swim in polluted waters. The fish were diagnosed by fisheries officials in manydifferent locations. Each group of fisheries officials made a specific diagnosis concerningthe cause of the particular appearance of fish scales they observed at their location. Youwill see each diagnosis on the screen shortly.

When you begin the next computer session, you will look at each diagnosis beingdisplayed on the screen, and decide if the diagnosis is correct or not. After each response,you will receive feedback which you can use to make a more informed decision next time.The goal is to discover a simple rule which will help you decide whether each diagnosisis correct or not The program will stop after you make 18 correct decisions in a row.

Step 2. Please type the lower case letter y to begin the next computer session...

You are encouraged to record relevant information about each diagnosis in the spacebelow:

Appearance of Scales Diagnosed Cause Diagnosis Correct?(yin)

94

Step 1. Please answer the following question:

How were you able to tell whether a particular diagnosis was correct or not?

Please write your response on the line below:

Step 2. Please turn to the next page....

95

Step 1. Please answer the following question:

Based on what you have observed in the set of examples just presented, which of thefollowing statements represents a CONCISE, GENERAL rule that BEST SUMS UP therelationship between the type of chemical agent and the type of fish scales?

Please circle your best choice, and put an X beside your second best choice, in case youhave one.

1. If fish have brittle scales then agent Tx was released in the water.

2. If agent Tx is released then fish develop brittle scales, and if fish have brittle scalesthen agent Tx was released into the water.

3. If agent Tx is released in the water, then fish develop brittle scales.

4. If agent Ty is released in the water, then fish develop either enlarged, brittle, orloose scales.

Step 2. Please turn to the next page....

96

Evaluating Students: Situation No. 1

Step 1. Please read the following section:

The students you are about to evaluate went through a discovery learning exercise thatwas identical to the one you went through. It was the one involving radiation sourcesand plant mutations.

These students observed the same set ofexamples you have seen, and from theseexamples they discovered a simple rule about a type of radiation and a type of plantmutation. The rule they discovered happens to be the correct rule (You will see this rulewhen you begin to work on the computer again.)

The students used this correct rule along with some additional information to arrive atvarious conclusions. Your task is to evaluate each student’s conclusion. That is, you are todecide whether the conclusion a particular student arrived at is:

1. Always True, or2. Sometimes True or Sometimes False, or3. Always False.

There are eight students that you will evaluate.

Step 2. Please type the lower case letter c to begin your evaluation...

97

Evaluating Students: Situation No. 2

Step 1. Please read the following section:

The students you are about to evaluate went through a discovery learning exercise thatwas identical to the one you went through. It was the one involving chemical agents andfish scales.

These students observed the same set ofexamples you have seen, and from theseexamples they discovered a simple rule about a type of chemical agent and a type of fishscales. The rule they discovered happens to be the correct rule (You will see this rulewhen you begin to work on the computer again.)

The students used this correct rule along with some additional information to arrive atvarious conclusions. Your task is to evaluate each student’s conclusion. That is, you are todecide whether the conclusion a particular student arrived at is:

1. Always True, or2. Sometimes True or Sometimes False, or3. Always False.

There are eight students that you will evaluate.

Step 2. Please type the lower case letter o to begin your evaluation...

98

Evaluating Students: Situation No. 3

Step 1. Please read the following section:

The students you are about to evaluate were learning about new drugs and strange skinrashes. This material is completely different from any of the learning experiences you havegone through here, but we are still interested in your assessment of these students.

These students discovered a relationship between a type of drug and a type of skin rash.They stated this relationship in the form of a rule which you will see shortly when youstart on the computer again.

Even though you are not familiar with this content area, please suppose that the rule theydiscovered is correct.

The students used this supposedly correct rule along with some additional information toarrive at various conclusions. Your task is to evaluate each student’s conclusion. That is,you are to decide whether the conclusion a particular student arrived at is:

1. Always True, or2. Sometimes True or Sometimes False, or3. Always False.

There are eight students that you will evaluate.

Step 2. Please type the lower case letter d to begin your evaluation...

99

Evaluating Students: Situation No. 4

Step 1. Please read the following section:

The students you are about to evaluate were learning about various types of lasers used ineye surgery. This material is completely different from any of the learning experiences youhave gone through here, but we are still interested in your assessment of these students.

These students discovered a relationship between a type of surgical laser and some strangespots on the retina of the eye. They stated this relationship in the form of a rule which youwill see shortly when you start on the computer again.

Even though you are not familiar with this content area, please suppose that the rule theydiscovered is correct.

The students used this supposedly correct rule along with some additional information toarrive at various conclusions.Your task is to evaluate each student’s conclusion. That is,you are to decide whether the conclusion a particular student arrived at is:

1. Always True, or2. Sometimes True or Sometimes False, or3. Always False.

There are eight students that you will evaluate.

Step 2. Please type the lower case letter e to begin your evaluation...

100

Finally, just a few (easy) questions:

1. Age

____

2. Gender M F

3. What is your educational background?

B.A. in____________

B.Sc.in

________________

M.A. in

________________

Ph.D.in

_______________

Other

__________________

4. What program of studies are you currently registered in?

Major

______________

Minor

___________________

Year

5. Throughout your university career, approximately how many courses did you take ineach of the following, general areas?

Math

_____

Biology

_____

Chemistry____Physics

_____

Psychology

_____

Evaluation in teaching

____

Philosophy

____

Art__Special Ed

_____

That’s it! Thanks for your time and effort. It is highly appreciated.

Please return the disk and the booklet to collect your honorarium.

101