Scientific Thinking - 1Scientific Thinking - 1

A.A. It is not It is not whatwhat the man of science believes the man of science believes that distinguishes him, but that distinguishes him, but howhow and and whywhy he he believes it.believes it.

B.B. A A hypothesishypothesis is scientific only if it is is scientific only if it is testabletestable, , that is, only if it that is, only if it predictspredicts something other something other than what it was introduced to explain. A than what it was introduced to explain. A hypothesis should state the test conditions hypothesis should state the test conditions that could render it false – that could render it false – falsifiabilityfalsifiability..

Scientific Thinking - 2Scientific Thinking - 2

C.C. Other things being equal, the Other things being equal, the best best hypothesishypothesis is the one that is the most is the one that is the most fruitful, that is, makes the most fruitful, that is, makes the most novel novel predictionspredictions..

D.D. Other things being equal, the Other things being equal, the best best hypothesishypothesis is the one that has the is the one that has the greatest scope, that is, that explains and greatest scope, that is, that explains and predictspredicts the the mostmost diversediverse phenomena. phenomena.

Scientific Thinking - 3Scientific Thinking - 3

E.E. Other things being equal, the Other things being equal, the best best hypothesishypothesis is the is the simplestsimplest one, that is, one, that is, the one that makes the the one that makes the fewest fewest assumptionsassumptions..

F.F. Other things being equal, the Other things being equal, the best best hypothesishypothesis is the most is the most conservativeconservative, that , that is, the one that is, the one that fitsfits best with best with established established beliefsbeliefs..

Scientific Thinking - 4Scientific Thinking - 4

G.G. We should We should acceptaccept an an extraordinaryextraordinary

hypothesishypothesis only only if no ordinaryif no ordinary one will do. one will do.

H.H. When two or more When two or more hypotheses competehypotheses compete, ,

we should make a we should make a new observationnew observation, the , the

result of which shall result of which shall eliminateeliminate some of some of

them.them.

Occam's razor – 1Occam's razor – 1

The The Occam's razorOccam's razor principle principle (of William of Ockham)(of William of Ockham)

states that the explanation of any phenomenon states that the explanation of any phenomenon

should should makemake as as few assumptionsfew assumptions as possible. as possible.

The The goalgoal is that of is that of eliminatingeliminating, or "shaving off", , or "shaving off",

the number of observable the number of observable predictionspredictions of the of the

explanatory assumptions or theory. A simpler explanatory assumptions or theory. A simpler

set of assumptions has set of assumptions has less consequencesless consequences..

(see Wikipedia)(see Wikipedia)

Occam's razor – 2Occam's razor – 2

Given twoGiven two equally valid equally valid explanationsexplanations for a for a

phenomenon, one should phenomenon, one should embrace the less embrace the less

complicatedcomplicated formulation. formulation.

And, when multiple And, when multiple competing theoriescompeting theories have have

equal predictive powers, equal predictive powers, selectselect those that those that

introduce the introduce the fewest assumptionsfewest assumptions andand the the

fewest hypothetical fewest hypothetical entitiesentities..

Abduction - 1Abduction - 1

AbductionAbduction, or abductive reasoning, is the , or abductive reasoning, is the

process of reasoning to the process of reasoning to the best explanationsbest explanations..

It is the It is the reasoningreasoning process that process that starts fromstarts from a a

set of set of observationsobservations or or conclusionsconclusions and derives and derives

their most likely explanations.their most likely explanations.

The term The term abductionabduction is sometimes used to mean is sometimes used to mean

just the just the generation of hypothesesgeneration of hypotheses to explain to explain

observations or conclusions, given a observations or conclusions, given a theorytheory..

Abduction - 2Abduction - 2

DeductionDeduction and and abductionabduction differ in the differ in the

direction in which a rule like direction in which a rule like ""aa entails entails b b "" is is

used for inference:used for inference:

DeductionDeduction allows deriving allows deriving bb as a as a

consequence of consequence of a a ; i.e., deduction is the ; i.e., deduction is the

process of process of derivingderiving the the consequencesconsequences of of

what is known. what is known.

AbductionAbduction allows  allows derivingderiving aa as an as an

hypothetical hypothetical explanationexplanation of of bb..

Abduction - 3Abduction - 3

AbductionAbduction works in reverse to deductionworks in reverse to deduction, by , by

allowing the precondition allowing the precondition aa of of ""aa entailsentails b b "" to be to be

derived from the consequence derived from the consequence bb. I.e. abduction is . I.e. abduction is

the the process ofprocess of explainingexplaining what is what is knownknown..

Charles Peirce introduced Charles Peirce introduced abductionabduction into logic, to into logic, to

mean the mean the use of a rule or hypothetical factuse of a rule or hypothetical fact to to

explainexplain an an observationobservation, e.g. , e.g. "if it rains the grass is "if it rains the grass is

wet"wet" is used to is used to explain whyexplain why the grass is wet, the grass is wet,

given that it has rained, or vice-versa.given that it has rained, or vice-versa.

Abduction - 4Abduction - 4

In logic, In logic, abductionabduction is done is done from a logicalfrom a logical

theorytheory TT representing a domain representing a domain andand a set a set

of of observationsobservations OO..

AbductionAbduction is the process of is the process of derivingderiving a set a set

of of explanationsexplanations of of OO according to according to TT. For . For EE

to be an explanation of to be an explanation of OO according to according to TT, it , it

should should satisfysatisfy two two conditionsconditions::

– OO follows fromfollows from EE andand TT; ;

– EE is consistent with is consistent with TT. .

Abduction - 5Abduction - 5 In formal logic, In formal logic, OO and and EE are assumed to be are assumed to be

sets of literals. The two conditions for sets of literals. The two conditions for EE being being an explanation of an explanation of OO according to theory according to theory TT are:are:

– T T ⋃⋃ E E ⊨⊨ OO ; ;

– T T ⋃⋃ EE is consistent. is consistent.

Among the possible explanations Among the possible explanations EE satisfying satisfying these two conditions, a condition of minimality these two conditions, a condition of minimality is usually imposed to avoid irrelevant facts is usually imposed to avoid irrelevant facts (i.e. not contributing to the entailment of (i.e. not contributing to the entailment of OO ) ) to be included in the explanations.to be included in the explanations.

Abduction - 6Abduction - 6 An application of abduction is that of detecting An application of abduction is that of detecting

faults in systems: given a theory relating faults faults in systems: given a theory relating faults with their effects and a set of observed effects, with their effects and a set of observed effects, abduction can be used to derive sets of faults that abduction can be used to derive sets of faults that are likely to be the cause of the problem.are likely to be the cause of the problem.

Belief revision, the process of adapting beliefs in Belief revision, the process of adapting beliefs in view of new information, is another field in which view of new information, is another field in which abduction has been applied. The main problem of abduction has been applied. The main problem of belief revision is that the new information may be belief revision is that the new information may be inconsistent with the corpus of beliefs, while the inconsistent with the corpus of beliefs, while the result of the incorporation must result of the incorporation must notnot be be inconsistent.inconsistent.

Models -1Models -1

ScientistsScientists often describe what they do as often describe what they do as

constructing constructing modelsmodels. Understanding . Understanding

scientific reasoning requires understanding scientific reasoning requires understanding

something about models and how they are something about models and how they are

used in science.used in science.

There are at least There are at least 3 kinds3 kinds of models: of models:

– scalescale: : e.g. model airplanee.g. model airplane

– analoganalog: : e.g. conventional city mapse.g. conventional city maps

– theoreticaltheoretical: : e.g. Newtonian physics equations e.g. Newtonian physics equations

Models -2Models -2

ModelsModels need to be put in need to be put in correspondencecorrespondence with with

realityreality, through , through hypotheseshypotheses and and interpretationsinterpretations..

A model may A model may predictpredict something that is something that is notnot

confirmedconfirmed, in which case the model is , in which case the model is incorrectincorrect..

A model may A model may fail to predictfail to predict something it should something it should

be able to, in which case it is be able to, in which case it is incompleteincomplete..

Like other mal-functioning Like other mal-functioning artefactsartefacts, mistaken , mistaken

models can be models can be diagnoseddiagnosed. .

Model-based diagnosis - 1Model-based diagnosis - 1

DiagnosisDiagnosis is concerned with the development of is concerned with the development of algorithms and techniques that can determine algorithms and techniques that can determine whether the whether the behaviourbehaviour of a system (or of a system (or artefactartefact) is ) is correct. The artefact may be a correct. The artefact may be a theorytheory..

If the system is not If the system is not functioningfunctioning correctly, the correctly, the algorithm should be able to determine, as algorithm should be able to determine, as accurately as possible, which part of the system accurately as possible, which part of the system is failing, and the kind of is failing, and the kind of faultfault it is facing. it is facing.

The computation is based on The computation is based on observationsobservations which which provide information on the current behaviour. provide information on the current behaviour.

Model-based diagnosis - 2Model-based diagnosis - 2 Model-based diagnosis is an example of Model-based diagnosis is an example of

abductiveabductive reasoningreasoning using a using a modelmodel of the of the system:system:

Model-based diagnosis - 3Model-based diagnosis - 3

A A modelmodel describes the behaviour of the system, or describes the behaviour of the system, or artefact. The model can itself artefact. The model can itself bebe the artefact.the artefact.

It an abstraction of the It an abstraction of the behaviourbehaviour of the system of the system and can be incomplete. The and can be incomplete. The faulty behaviourfaulty behaviour may may be little-known, and the be little-known, and the fault modelfault model might not be might not be represented. If the model is a program: represented. If the model is a program: debuggingdebugging..

Given the Given the observationsobservations, the diagnoser, the diagnoser simulatessimulates the system using the model, and compares the the system using the model, and compares the observations actually made to the observations observations actually made to the observations predictedpredicted by the simulation. by the simulation.

Model-based diagnosis - 4Model-based diagnosis - 4 The modelling can be expressed by the rules The modelling can be expressed by the rules

(where (where AbAb is the is the AbAbnormality predicate)normality predicate)::

If the behaviour of the system is not If the behaviour of the system is not abnormal (i.e. normal), then the internal abnormal (i.e. normal), then the internal (unobservable) behaviour will be (unobservable) behaviour will be Int1Int1 and the and the observable one observable one Obs1Obs1..

Otherwise, the internal behaviour will be Otherwise, the internal behaviour will be Int2Int2 and the observable behaviour and the observable behaviour Obs2Obs2..

Given the observations Given the observations ObsObs, the problem is to , the problem is to determine whether the system behaviour is determine whether the system behaviour is normal or not (normal or not (¬ ¬ Ab(S)Ab(S) or or Ab(S)Ab(S) ). This is an ). This is an example of example of abductive reasoningabductive reasoning..