Inductive and Deductive Methods

8/6/2019 Inductive and Deductive Methods

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INDUCTIVE & DEDUCTIVEINDUCTIVE & DEDUCTIVE

RESEARCH APPROACHRESEARCH APPROACHMeritorious Prof. Dr. S. M. Aqil BurneyMeritorious Prof. Dr. S. M. Aqil Burney

Director UBITDirector UBITChairmanChairman

Department of Computer ScienceDepartment of Computer Science

University of KarachiUniversity of Karachi

[email protected]@computer.orgwww.drburney.netwww.drburney.net

Designed and Assisted byDesigned and Assisted by

HussainHussain [email protected]@uok.edu.pk

0606thth March 2008March 2008


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"Well begun is half done"--Aristotle, quoting an old proverb


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Research MethodsResearch Methods

Research

Types

DeductiveApproach

InductiveApproach

In research, we often refer to the two broad methods of reasoningas the deductiveand inductiveapproaches.


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Deductive Research ApproachDeductive Research Approach Deductive reasoning worksDeductive reasoning works

from the more general tofrom the more general tothe more specific.the more specific.

Sometimes this isSometimes this is

informally called ainformally called a

"top"top--down" approach.down" approach.

Conclusion followsConclusion follows

logically from premiseslogically from premises

(available facts)(available facts)Waterfall

CONFIRMATION

OBSERVATION

HYPOTHESIS

THEORY


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Inductive Research ApproachInductive Research Approach Inductive reasoning worksInductive reasoning works

the other way, movingthe other way, movingfrom specific observationsfrom specific observationsto broader generalizationsto broader generalizationsand theories.and theories.

Informally, we sometimesInformally, we sometimescall this a "bottom up"call this a "bottom up"approachapproach

Conclusion is likely basedConclusion is likely based

on premises.on premises. Involves a degree ofInvolves a degree of

uncertaintyuncertainty

Hill

Climbing

THEORY

TENTATIVE

HYPOTHESIS

PATTERN

OBSERVATION


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Deductive Vs. InductiveDeductive Vs. Inductive

CONFIRMATION

OBSERVATION

HYPOTHESIS

THEORY THEORY

TENTATIVE

HYPOTHESIS

PATTERN

OBSERVATION


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Deductive Vs. InductiveDeductive Vs. Inductive

Induction is usually described as moving fromInduction is usually described as moving from

the specific to the general, while deductionthe specific to the general, while deductionbegins with the general and ends with thebegins with the general and ends with the

specific.specific.

Arguments based on laws, rules and acceptedArguments based on laws, rules and accepted

principles are generally used for Deductiveprinciples are generally used for DeductiveReasoning. Observations tend to be used forReasoning. Observations tend to be used for

Inductive Arguments.Inductive Arguments.


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Logical Reasoning and Human NatureLogical Reasoning and Human Nature

Historically, many researchers believed thatHistorically, many researchers believed that

logical reasoning is an essential part of humanlogical reasoning is an essential part of humanthought process and this dominates in scientificthought process and this dominates in scientific

& Technological research and Development.& Technological research and Development.

However, humans are not natural logicalHowever, humans are not natural logical

reasonersreasoners

REFERENCE:REFERENCE:

S. M. Aqil Burney;S. M. Aqil Burney; NadeemNadeem MahmoodMahmood,, A Brief History of Mathematical LogicA Brief History of Mathematical Logic

and Applications of Logic in CS/ITand Applications of Logic in CS/IT,, Karachi University Journal of Science Vol.34 (1) July 2006. PP 6Karachi University Journal of Science Vol.34 (1) July 2006. PP 611--7575


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Reasoning methods andReasoning methods and

ArgumentationArgumentation

The main division between forms of reasoning that isThe main division between forms of reasoning that is

made in philosophy is betweenmade in philosophy is between deductive reasoningdeductive reasoningandandinductive reasoninginductive reasoning..

Formal logicFormal logic has been described as 'the science ofhas been described as 'the science ofdeduction'.deduction'.

The study of inductive reasoning is generally carried outThe study of inductive reasoning is generally carried outwithin the field known aswithin the field known as informal logicinformal logic oror criticalcriticalthinkingthinking..


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http://www.phac-aspc.gc.ca/publicat/cdic-mcc/18-3/d_e.html


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Automated Reasoning

Logic lends itself to automation.

A variety of problems can be attacked by

representing the problem description andrelevant background information as logical

axioms and treating problem instances astheorems to be proved.

72/98


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Logic and ReasoningLogic and Reasoning

Reasoning

Logical

Reasoning

Probabilistic

Reasoning

Using given knowledge andUsing given knowledge andtruth value help us to solve,truth value help us to solve,understand real life problems.understand real life problems.

Bayesian

Networks

Subjective Objective


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EXAMPLEEXAMPLE

p: All mathematicians wear glassesp: All mathematicians wear glasses

q: Anyone who wears glasses is an algebraistq: Anyone who wears glasses is an algebraist

r: All mathematicians are algebraistr: All mathematicians are algebraist

pp

qq

rr

((

((pp

qq))

r)r)


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TRUTH TABLE

Truth Table for the formulae built with the Logical Operators

p q r pq ~(pq) ~(pq)Vr

T T T T F T

T T F T F F

T F T F T T

T F F F T T

F T T F T T

F T F F T T

F F T F T T

F F F F T T


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If r is the conclusion, and we know that p and qIf r is the conclusion, and we know that p and q

are true simultaneously then r is valid statement.are true simultaneously then r is valid statement.

In real life, the statements are true or false, hereIn real life, the statements are true or false, herestatement means an atomic statement, thusstatement means an atomic statement, thus

statements may be simple (atomic) orstatements may be simple (atomic) or

component. If p, q and r are independentcomponent. If p, q and r are independentstatements, then we need to prove:statements, then we need to prove: ppqq rr


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CommitmentCommitmentOntological CommitmentOntological Commitment::

What exists in the world: Language of reasoning (Formal).What exists in the world: Language of reasoning (Formal).

Epistemological CommitmentEpistemological Commitment

What an intelligent entity believes about the fact.What an intelligent entity believes about the fact.

Believe System: True, False, Unknown, degree of believe,Believe System: True, False, Unknown, degree of believe,

degree believe with ranks (known values)degree believe with ranks (known values)


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True/FalseTrue/False/Unknown/Unknown

Facts, objects,Facts, objects,relation and timerelation and time

TemporalTemporalLogicLogic

Degree of believeDegree of believe

on [0,1]on [0,1]Facts with changeFacts with changeProbabilityProbability

TheoryTheory

True/FalseTrue/False

/Unknown/UnknownFacts, objects,Facts, objects,

relationsrelationsPredicatePredicate

LogicLogic


/Unknown/Unknown

factsfactsPropositionalPropositional

LogicLogic

EpistemologyEpistemologyOntologyOntologyWhat exists)What exists)

FormalFormalLanguageLanguage


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/Unknown/Unknown

Facts, objects,Facts, objects,

relation, time &relation, time &SpaceSpace

Spatial LogicSpatial Logic

Known intervalKnown interval

values withvalues with

improvement inimprovement in

believebelieve

Facts with degreeFacts with degree

of believe withof believe with

learninglearning

ANNANN--FLFL

Known intervalKnown intervalvaluevalue

Facts with degreeFacts with degreeof believeof believe

Fuzzy LogicFuzzy Logic


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Evolution ofEvolution ofNeuroNeuro--Fuzzy LogicFuzzy Logic

Neuro-Fuzzy

Systems

Neural

Networks

Approximate Reasoning

Fuzzy Logic

Functional Approximation/

Randomized Search


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The whole of science is nothing

more thana refinement of everyday thinking.

- Albert Einstein


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References:References: William M.K.William M.K.TrochimTrochim,, Research Methods Knowledge BaseResearch Methods Knowledge Base

2006.2006.

S. M. Aqil Burney;S. M. Aqil Burney; NadeemNadeem MahmoodMahmood,, A Brief History ofA Brief History of

Mathematical Logic and Applications of Logic in CS/ITMathematical Logic and Applications of Logic in CS/IT,,

Karachi University Journal of Science Vol.34 (1) July 2006. PP 6Karachi University Journal of Science Vol.34 (1) July 2006. PP 611--7575

Syed Muhammad Aqil Burney;Syed Muhammad Aqil Burney;TahseenTahseenAhmedAhmedJilaniJilani,, A refinedA refined

fuzzy time series model for stock market forecastingfuzzy time series model for stock market forecastingElsevierElsevierScience Direct,Science Direct, PhysicaPhysica--A, January 2008 (in press).A, January 2008 (in press).

www.elsevier.com/locate/physawww.elsevier.com/locate/physa

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Inductive and Deductive Methods