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
True/FalseTrue/False
/Unknown/Unknown
factsfactsPropositionalPropositional
LogicLogic
EpistemologyEpistemologyOntologyOntologyWhat exists)What exists)
FormalFormalLanguageLanguage
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True/FalseTrue/False
/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