Equivalence Classes Ps625 Concept Formation Dr. Ken Reeve Caldwell College Grad ABA Programs

Equivalence ClassesEquivalence Classes

Ps625 Concept FormationPs625 Concept Formation

Dr. Ken ReeveDr. Ken Reeve

Caldwell College Grad ABA Caldwell College Grad ABA ProgramsPrograms

DefinitionDefinition a finite group of physically disparate stimuli (no a finite group of physically disparate stimuli (no

perceptual similarity)perceptual similarity) stimuli become related as a function of training stimuli become related as a function of training

(Fields, Adams, Buffington, Yang, & Verhave, 1996; (Fields, Adams, Buffington, Yang, & Verhave, 1996; Fields & Verhave, 1987; Sidman & Tailby, 1982; Fields & Verhave, 1987; Sidman & Tailby, 1982; Sidman, 1990)Sidman, 1990)

An equivalence class must contain at least three An equivalence class must contain at least three stimulistimuli

To establish a class of To establish a class of NN stimuli, stimuli, NN-1 stimulus--1 stimulus-stimulus relations are trained such that each stimulus relations are trained such that each stimulus in the potential class is used in at least stimulus in the potential class is used in at least one relationone relation

ExampleExample

Written word DOGWritten word DOG The spoken word The spoken word

“DOG”“DOG” A picture of a dogA picture of a dog

DOG

DOG

Another ExampleAnother Example

Written word CATWritten word CAT The spoken word The spoken word

“CAT”“CAT” A picture of a catA picture of a cat

CAT

CAT

Training & Testing Training & Testing ProceduresProcedures

Usually with conditional discrimination or Usually with conditional discrimination or match-to-sample (but other methods will match-to-sample (but other methods will also be discussed)also be discussed)

Symbolic notation is often used to outline Symbolic notation is often used to outline training/testing procedures:training/testing procedures: A, B, C, …N represent each of the disparate A, B, C, …N represent each of the disparate

stimuli that will make up the classstimuli that will make up the class 1, 2, 3, etc. notate the number of classes to be 1, 2, 3, etc. notate the number of classes to be

establishedestablished Thus, A1 = first stimulus in class 1; B3 = third Thus, A1 = first stimulus in class 1; B3 = third

stimulus in class 2; etc.stimulus in class 2; etc.


To establish equivalence classes, at To establish equivalence classes, at least two potential classes must be least two potential classes must be trained concurrentlytrained concurrently

training establishes both training establishes both substitutability of all stimuli within a substitutability of all stimuli within a particular equivalence class in particular equivalence class in addition to discrimination between addition to discrimination between classesclasses


To establish equivalence classes with three To establish equivalence classes with three members, at least two relations must be trained members, at least two relations must be trained for each potential class (remember the for each potential class (remember the NN-1 rule)-1 rule)

Let’s consider our DOG and CAT potential Let’s consider our DOG and CAT potential equivalence classesequivalence classes

First train the AB relation (given stimulus A select First train the AB relation (given stimulus A select stimulus B)stimulus B) the word DOG (A1) is presented as a samplethe word DOG (A1) is presented as a sample The positive comparison (Co+) would be the spoken The positive comparison (Co+) would be the spoken

word dog (B1) (Selection would result in positive word dog (B1) (Selection would result in positive feedback or reinforcement)feedback or reinforcement)

the negative comparison (Co-) would be the spoken the negative comparison (Co-) would be the spoken word cat (B2) (Selection would result in corrective word cat (B2) (Selection would result in corrective feedback or extinction) feedback or extinction)

DOG

DOGCAT

Training AB relation

A1

B2 B1


In addition, to train the AB relationIn addition, to train the AB relation the word CAT (A2) is presented as a samplethe word CAT (A2) is presented as a sample The positive comparison (Co+) would be the spoken The positive comparison (Co+) would be the spoken

word cat (B2) (Selection would result in positive word cat (B2) (Selection would result in positive feedback or reinforcement)feedback or reinforcement)

the negative comparison (Co-) would be the spoken the negative comparison (Co-) would be the spoken word dog (B2) (Selection would result in corrective word dog (B2) (Selection would result in corrective feedback or extinction) feedback or extinction)

Training AB relation

CAT

DOGCAT

A2

B2 B1


Once responding is 100% correct, we can conclude that Once responding is 100% correct, we can conclude that the learner has formed the AB conditional relationthe learner has formed the AB conditional relation

also demonstrates that learner can discriminate also demonstrates that learner can discriminate between the two different “A” stimuli, the two different between the two different “A” stimuli, the two different “B” stimuli, and the A stimuli from the B stimuli“B” stimuli, and the A stimuli from the B stimuli

At this point we can either continue training more At this point we can either continue training more conditional discriminations conditional discriminations oror we can do our first test we can do our first test for an EMERGENT (DERIVED) RELATION (a conditional for an EMERGENT (DERIVED) RELATION (a conditional discrimination that emerges with no direct training discrimination that emerges with no direct training history)history)

If the learner “knows” that A goes with B, can they If the learner “knows” that A goes with B, can they demonstrate the reverse? (B goes with A)demonstrate the reverse? (B goes with A)

This emergent relation shows SYMMETRY This emergent relation shows SYMMETRY

TESTING BA symmetry relation

CAT

CAT B2

A2 A1

DOG

TESTING BA symmetry relation

CAT

DOG B1

A2 A1

DOG


If BA TESTING is 100% correct, we can conclude If BA TESTING is 100% correct, we can conclude that the learner has formed the BA conditional that the learner has formed the BA conditional symmetry relation with no direct trainingsymmetry relation with no direct training

It is called “symmetry” because the relation is a It is called “symmetry” because the relation is a mirror image or reversal of the one directly mirror image or reversal of the one directly trainedtrained

At this point, we can continue training more At this point, we can continue training more conditional discriminationsconditional discriminations

Let’s train the BC conditional relationLet’s train the BC conditional relation

Training BC relation

DOG B1

C2 C1

Training BC relation

CAT B2

C2 C1


Once responding is 100% correct, we can Once responding is 100% correct, we can conclude that the learner has formed the conclude that the learner has formed the BCBC conditional relationconditional relation

Now we can either continue training more Now we can either continue training more conditional discriminations conditional discriminations oror we can do our 2 we can do our 2ndnd test for an EMERGENT (DERIVED) RELATIONtest for an EMERGENT (DERIVED) RELATION

If the learner “knows” that B goes with C, can If the learner “knows” that B goes with C, can they demonstrate the reverse? (C goes with B)they demonstrate the reverse? (C goes with B)

This emergent relation would show a SECOND This emergent relation would show a SECOND SYMMETRY relationSYMMETRY relation

TESTING CB symmetry relation

DOG

C1

B1 B2

CAT

TESTING CB symmetry relation

DOG

C2

B1 B2

CAT


If TEST responding is 100% correct, we can If TEST responding is 100% correct, we can conclude that the learner has formed the conclude that the learner has formed the CBCB symmetry conditional relationsymmetry conditional relation

At this point, we have trained our N-1 relations (3 At this point, we have trained our N-1 relations (3 members subtract 1 equals 2!)members subtract 1 equals 2!)

Now we can continue testing for another Now we can continue testing for another EMERGENT (DERIVED) RELATIONEMERGENT (DERIVED) RELATION

If the learner “knows” that A goes with B, and B If the learner “knows” that A goes with B, and B goes with C, can they demonstrate that A goes goes with C, can they demonstrate that A goes with C?with C?

This emergent relation would show a TRANSITIVE This emergent relation would show a TRANSITIVE relationrelation

TESTING AC transitive relation

A1

C2 C1

DOG

TESTING AC transitive relation

A2

C2 C1

CAT


If TEST responding is 100% correct, we can If TEST responding is 100% correct, we can conclude that the learner has formed the conclude that the learner has formed the ACAC transitive conditional relationtransitive conditional relation

We have one last test for another EMERGENT We have one last test for another EMERGENT (DERIVED) RELATION(DERIVED) RELATION

If the learner “knows” that A goes with B, and B If the learner “knows” that A goes with B, and B goes with C, can they demonstrate that C goes goes with C, can they demonstrate that C goes with A?with A?

This emergent relation would shows a This emergent relation would shows a combination of symmetry and transitivity; it is combination of symmetry and transitivity; it is called an EQUIVALENCE relationcalled an EQUIVALENCE relation

TESTING CA equivalence relation

A1A2

C1

CAT DOG

TESTING CA equivalence relation

A1A2

C2

CAT DOG

Training & Testing SummaryTraining & Testing Summary If TEST responding is 100% correct, we can conclude that the If TEST responding is 100% correct, we can conclude that the

learner has formed two equivalence classes (one for dogs and learner has formed two equivalence classes (one for dogs and one for cats)one for cats)

We TRAINED 2 relations:We TRAINED 2 relations: A A B B B B C C

We TESTED 4 EMERGENT (DERIVED) relations:We TESTED 4 EMERGENT (DERIVED) relations: B B A symmetry A symmetry C C B symmetry B symmetry A A C transitivity C transitivity C C A equivalence A equivalence

Another set of tests for REFLEXIVITY (IDENTITY) is usually Another set of tests for REFLEXIVITY (IDENTITY) is usually omitted unless the learner is less skilled:omitted unless the learner is less skilled: A A A A B B B B C C C C

Training & Testing SummaryTraining & Testing Summary Now each member of each class occasions the Now each member of each class occasions the

selection of all the other members of the classselection of all the other members of the class This occurs for all combinations even though we This occurs for all combinations even though we

only directly trained a subset of all possible only directly trained a subset of all possible relationsrelations

Equivalence Class Equivalence Class ExpansionsExpansions

Once we have 3-member equivalence Once we have 3-member equivalence classes, we can continue to expand them classes, we can continue to expand them in a number of waysin a number of ways

One way is by training additional One way is by training additional conditional relations and testing for conditional relations and testing for additional emergent conditional relationsadditional emergent conditional relations

For example, train the relation CD in which For example, train the relation CD in which stimulus D is the Spanish word PERRO for stimulus D is the Spanish word PERRO for the dog class and GATO for the cat classthe dog class and GATO for the cat class

Training CD relation

D1D2

C2

GATO PERRO

Training CD relation

D1D2

C1

GATO PERRO

Training & Testing SummaryTraining & Testing Summary Then we would test for all possible new emergent Then we would test for all possible new emergent

relationsrelations D D C symmetry C symmetry A A D transitivity D transitivity B B D transitivity D transitivity D D A equivalence A equivalence D D B equivalence B equivalence

If test results are 100%, then we can now If test results are 100%, then we can now conclude that we have two 4-member conclude that we have two 4-member equivalence classesequivalence classes

And so on…And so on…

More Equivalence Class More Equivalence Class ExpansionsExpansions

Once we have equivalence classes, we can Once we have equivalence classes, we can also expand them by using them as “transfer also expand them by using them as “transfer networks”networks”

This means that we train an operant response This means that we train an operant response (different from the previous selection (different from the previous selection response) in the presence of only 1 member response) in the presence of only 1 member of each equivalence classof each equivalence class

For example, train a child to say WOOF in the For example, train a child to say WOOF in the presence of A1 and MEOW in the presence of presence of A1 and MEOW in the presence of A2A2

DOG

WOOF!

Training response transfer

A1

MEOW!

Training response transfer

A2CAT


If we now present stimuli B, C, or D, If we now present stimuli B, C, or D, the child should also say WOOF (in the child should also say WOOF (in the presence of the dog class the presence of the dog class members) and MEOW (in the members) and MEOW (in the presence of the cat class members)presence of the cat class members)

This should occur without direct This should occur without direct trainingtraining

As such, it demonstrates another As such, it demonstrates another type of emergent behaviortype of emergent behavior

MEOW!

TESTING response transfer

GATO CAT

WOOF!

TESTING response transfer

PERRO DOG

And…um, victory is mine!


Once we have equivalence classes, we can Once we have equivalence classes, we can also expand them by testing to see whether also expand them by testing to see whether physical variations (“variants”) of each physical variations (“variants”) of each equivalence class member will still occasion equivalence class member will still occasion selection of all other membersselection of all other members

For example, what if we present emergent For example, what if we present emergent relations in which the dog or cat picture relations in which the dog or cat picture used in training (stimulus C1 and C2) is used in training (stimulus C1 and C2) is substituted with DIFFERENT pictures? substituted with DIFFERENT pictures? (notated as C’1 or C’2)(notated as C’1 or C’2)

Will these “variants” still occasion class-Will these “variants” still occasion class-consistent responding?consistent responding?

TESTING C’A “generalized” equivalence relation

A1A2

C’2

CAT DOG

A1A2

C’2

CAT DOG


A1A2

C’2

CAT DOG


A1A2

C’2

CAT DOG


Generalized Equivalence Generalized Equivalence ClassClass

Note that many cat pictures occasion selection Note that many cat pictures occasion selection of the other members of the equivalence classof the other members of the equivalence class

Thus, the class-consistent selections made by Thus, the class-consistent selections made by the learner have generalized to variants of one the learner have generalized to variants of one member of the equivalence classmember of the equivalence class

So we call this a “generalized equivalence So we call this a “generalized equivalence class”class”

It is actually a merger of an equivalence class It is actually a merger of an equivalence class with a perceptual class…with a perceptual class…

CAT

One equivalence class + one linked perceptual class =

CAT

GATO

CAT

Generalized equivalence class

CAT

GATO

Generalized Equivalence Generalized Equivalence ClassClass

We can also present variants of EACH We can also present variants of EACH equivalence class member to see if they equivalence class member to see if they occasion selection of the other members occasion selection of the other members of the equivalence classof the equivalence class

This would produce an even larger This would produce an even larger generalized equivalence classgeneralized equivalence class

It would be a merger of an equivalence It would be a merger of an equivalence class with perceptual classes linked to class with perceptual classes linked to each equivalence class member…each equivalence class member…

CAT

Generalized equivalence class (expanded further)

CAT GATO

GATO

GATO

CATCAT

CAT

CAT

Training Structures for Training Structures for Equivalence ClassEquivalence Class

Refers to how the training relations and Refers to how the training relations and derived relations are “situated” relative to derived relations are “situated” relative to one anotherone another

Can affect likelihood of class formationCan affect likelihood of class formation See nextSee next

Linear Training StructureLinear Training Structure

A A B B

B B C C

C C D D

One-to-Many Training One-to-Many Training StructureStructure

A A B B

CC

DD

Many-to-One Training Many-to-One Training StructureStructure

B B A A

C C

DD

Training/Testing VariationsTraining/Testing Variations

This refers to when you train and test for This refers to when you train and test for various conditional relationsvarious conditional relations

See next…See next…

Simultaneous ProcedureSimultaneous Procedure

First, train ALL training relations in one First, train ALL training relations in one trial block until you reach criteriontrial block until you reach criterion

Then, test ALL derived (emergent) Then, test ALL derived (emergent) relations in another trial blockrelations in another trial block

This procedure tends to produce poor This procedure tends to produce poor performanceperformance

Simple-to-Complex Simple-to-Complex ProcedureProcedure

First, train only 1 relation to criterion in a trial First, train only 1 relation to criterion in a trial block (e.g., Ablock (e.g., AB)B)

Then, test the “simplest” derived (emergent) Then, test the “simplest” derived (emergent) relation in another trial block (e.g., Brelation in another trial block (e.g., BA)A)

Then, train the next 1 relation to criterion in a trial Then, train the next 1 relation to criterion in a trial block (e.g., Bblock (e.g., BC)C)

Then, test the next “simplest” derived (emergent) Then, test the next “simplest” derived (emergent) relation in another trial block (e.g., Crelation in another trial block (e.g., CB)B)

Followed by AFollowed by AC testingC testing Followed by CFollowed by CA testingA testing

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Equivalence Classes Ps625 Concept Formation Dr. Ken Reeve Caldwell College Grad ABA Programs