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8/17/2019 Lecture 9 - Inductive and Deductive Reasoning
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Inductive and Deductive
Reasoning
Lecture 9
Prof. Storbeck
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Problem Solving andReasoning
• Problem solving: set of cognitive processesapplied to overcome obstacles to a goal
• Reasoning: cognitive processes used to
make inferences from knowledge and drawconclusions.
•
Draw on categorization imager! decisionmaking attention L"# $# e%ecutiveprocesses and language.
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Problem
• Problem &as ' parts – (oal state
– Initial state
– )perations
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Problems
• $ell de*ned problem
• Ill de*ned problem
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Insig&t
Insig&t invokes activit! int&e rig&t anterior superiortemporal g!rus and isassociated wit& increased
gamma bursts.+ounios , -eeman//9
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Problem Space "&eor!
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Strategies and 0euristics
• 1lgorit&m
• 0euristics
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0euristic
• 0euristic contrar! to moving towardgoal state.
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Strategies and 0euristics
• 1lgorit&m
• 0euristics – Random searc&
• "rial and error
• -e&aviorist approac&
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Strategies and 0euristics
• 1lgorit&m
• 0euristics – Random searc&
• "rial and error
• -e&aviorist approac&
– 0ill2climbing•
$ater 3ug Problem• Left2prefrontal
4 /
/
5 5/
Initial State
(oal State
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Strategies and 0euristics
• 1lgorit&m
• 0euristics – Random searc&
– 0ill2climbing• $ater 3ug Problem
• Left2prefrontal
– #eans2ends anal!sis• -reak down problem into
subgoals8subproblems
• "ower of 0anoi
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%perts vs. ovices
• Di;erences in organizing problems:
• ovices < surface features
•
%perts < abstract or deeper levelconcepts
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1nalogical Reasoning
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• 6ognitive Science relied on t&ecomputer model to understandmemor!
• -iological viruses &elped computerscientists solve computer viruses.
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1nalogical Reasoning
• 7. Retrieval
• . #apping
•
'. valuation• 5. 1bstraction
• =. Predictions
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• #ilitar! Problem
• 1 small countr! was ruled from a strong fortress b! a dictator. "&e
• fortress was situated in t&e middle of t&e countr! surrounded b! farms
• and villages. #an! roads led to t&e fortress t&roug& t&e countr!side. 1
• rebel general vowed to capture t&e fortress. "&e general knew t&at an
• attack b! &is entire arm! would capture t&e fortress. 0e gat&ered &is• arm! at t&e &ead of one of t&e roads read! to launc& a full2scale direct
• attack. 0owever t&e general t&en learned t&at t&e dictator &ad planted
• mines on eac& of t&e roads. "&e mines were set so t&at small bodies of
• men could pass over t&em safel! since t&e dictator needed to move &is
•
troops and workers to and from t&e fortress. 0owever an! large force• would detonate t&e mines. ot onl! would t&is blow up t&e road but it
• would also destro! man! neig&boring villages. It t&erefore seemed
• impossible to capture t&e fortress.
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"ransfer of Problems
• Radiation Problem
• Suppose !ou are a doctor faced wit& a patient w&o &as a malignant
• tumor in &is stomac&. It is impossible to operate on t&e patient but
• unless t&e tumor is destro!ed t&e patient will die. "&ere is a kind of
• ra! t&at can be used to destro! t&e tumor. If t&e ra!s reac& it all at
•
once at a su>cientl! &ig& intensit! t&e tumor will be destro!ed.• ?nfortunatel! at t&is intensit! t&e &ealt&! tissue t&e ra!s pass t&roug&
• on t&e wa! to t&e tumor will also be destro!ed. 1t lower intensities t&e
• ra!s are &armless to &ealt&! tissue but t&e! will not a;ect t&e tumor
• eit&er. $&at t!pe of procedure mig&t be used to destro! t&e tumor
• wit& t&e ra!s and at t&e same time avoid destro!ing t&e &ealt&! tissue@
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• 7A Solve Problem
• A Read8remember stor! of oneproblem Bmilitar!A later solveproblem BradiationA
• 'A Read8remember militar! get &intsolve radiation problem.
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• 7A no memor! task solve radiation7/C
• A remember militar! solve radiation'/C
• 'A remember militar! &int solveradiation E=C
(ick , 0ol!oak 794/ 794'
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"&ree attempts to inducetransfer
• 7A subFects told to summarize stor!in abstract terms – Gif !ou need a large force to accomplis&
some purpose but are prevented fromappl!ing suc& a force directl! man!smaller forces H
•
A general principle provided• 'A draw diagram
-everidge , Parkins
794E
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"&ree attempts to transfer
• "ransfer: – #ore transfer w&en sc&ema more
abstract
– #ore transfer w&en stories more similar
– #ore transfer wit& diagram or principle
1bstract t&inking separates%perts from ovicesJ
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"&eories of 1nalogicalReasoning
• Structure #apping "&eor! BS#"A – Searc& L"# for structural component
similarit!
– valuation of mapping
• Learning and Inference wit& Sc&emasand 1nalogies BLIS1A
– eural etworks – "arget activates features
– Keatures activates Source for analog!
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-e!ond $orking #emor!@
+roger et al. //
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Inductive Reasoning
• ?se of knowledge of speci*c knowninstances to draw inferences aboutunknown instances
• 6ategor!2based inductions – (eneral induction
– Speci*c induction
o InductiveProcess can ever
be certain
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Inductive 1rguments
I &ave seen 99 swans and all of t&em are w&ite.
"&erefore all swans are w&ite.
"&e boiling point of water in t&e past &as alwa!s been7K.
"&erefore tomorrow t&e boiling point of water will be7K.
"&ere is intelligent life on #ercur!. "&ere is intelligent life on enus.
"&ere is intelligent life on 3upiter.
"&erefore t&ere is intelligent life on #ars.
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Inductive 1rguments
ot Gvalid or Ginvalid
ar! in strengt&
1 Ggrab bag of tricksot Fust particular to generalH
.g. 6&impanzees like eating onions.
"&ereforegorillas like eatingonions.
-ut if we do go from particular to
generalH
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Inductive Reasoning
• Scientist use to generate predictions
• Inductive Reasoning wit& a game – Deck of cards varied on 5 dimensions
wit& ' attributes• 6olor Bw&ite black blueA
• umber of items on card Bone two t&reeA
•
S&ape of item Bcircle cross sMuareA• umber of borders Bone two t&reeA
• ' N ' N ' N ' < 47 cards instances
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Inductive Reasoning
• Simples rules eas! to get BredA
• 6onFunctive rules ne%t easiest Bred sMuareA
• DisFunctive rules &arder Bred orsMuareA
• egative rules Bnot redA were still&arder
• DisFunctive negative rules most &ardBnot red or crossA.
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6ategor!2-ased Inductions
• Induction based on categor! andrelated features.
• Similarit!
• "!picalit!
•
(roup &omogeneit!
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Similarit!26overage #odel
• "!picalit! for categor!2based induction
• #ore t!pical more readil! feature ismapped to conclusion:
– Dogs &ave a liver. – 6ats &ave a liver.
– 6onclusion: #ammals &ave a liver.
– Dogs &ave a liver.
– $&ales &ave a liver.
– 6onclusion: #ammals &ave a liver.
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Inductive Reasoning in t&e-rainJ
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• $6S" , f#RI
• #onc&i et al. //7
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• 1ctivation includes: mid2DLPK6 mid2LPK6 posterior )K6 mid2LPK6
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• Seger et al. ///
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Inductive Reasoning
• Implausible arguments activate areasnoted for error detectionJ
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Deductive Reasoning
• S!llogism
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Deductive 1rguments
1ll men are mortal. premise
Socrates is a man. premise
"&erefore Socrates is mortal. conclusion
1ll artists are beekeepers.
1ll beekeepers are c&emists.
1ll artists are c&emists.
)" Fust general to particularH
IK PR#ISS 1R "R? "0 6)6L?SI) #?S"- "R? -O IR"? )K I"S K)R#
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Deductive vs Inductive
1ll plurbs are c&enn!. I saw 7// plurbs and all
are c&enn!.
Kred is a plurb. Kred is a plurb.6onclusion@ Kred isH 6onclusion@ Kred isH
Deductive: Inductive:
"rue b! virtue of form alone. #a! be stronger orweaker.
#eaning of words not matter.#eaning of wordsmatters.
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6ategorical S!llogisms
• Relations between two categories
• Premise 7: 1ll 1 are -
• Premise : 6 is an 1.
• 6onclusion: 6 is -.
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6ategorical S!llogisms
• ?niversal 1>rmation: 1ll 1 are -.
• ?niversal egative: o 1 are -.
• Particular 1>rmative: Some 1 are -.
• Particular egative: Some 1 are not-.
• 6an be represented as enndiagrams.
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6onditional S!llogisms
• Kirst premise If p t&en MQ
• Second premise to take one of four forms:
– 1>rmation of t&e antecedent: p is true
– Denial of t&e antecedent: p is not true – 1>rmation of t&e conseMuent: M is true
– Denial of t&e conseMuent: M is not true.
• If t&e automobile is a Porsc&e t&en it is reliable.
• "&e -o%ster is a Porsc&e.
• 6onclusion: "&e -o%ster is reliable.
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$ason Selection "ask
1 5 E D
If card &as a vowel on one sidet&en it &as an even number on t&eot&er sideQ
(oal: to determine w&et&er t&erule is true or false wit& leastnumber of cards ipped.
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rrors in Deductive "&inking
• Korm – Premise 7: o 1s are -s
– Premise : o -s are 6s
– 6onclusion: o 1s are 6s
• 6ontent – Premise 7: 1ll t&ings t&at &ave a motor
need oil. – Premise : 1utomobiles need oil.
– 6onclusion: 1utomobiles &ave motors.
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-elief2bias ;ect
• Premise 7: o cigarettes areine%pensive
• Premise : Some addictive t&ings are
ine%pensive
• 6onclusion: Some additive t&ings arenot cigarettes.
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-elief2bias ;ect
• Premise 7: o cigarettes are ine%pensive
• Premise : Some addictive t&ings areine%pensive
•
6onclusion: Some additive t&ings are notcigarettes.
• Premise 7: o addictive t&ings are ine%pensive
• Premise : Some cigarettes are ine%pensive• 6onclusion: Some cigarettes are not addictive
"& i f D d ti
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"&eories of DeductiveReasoning
• "&eor! of #ental #odels – #ental model constructed
– 1 tentative conclusion is generated
evaluated – "&e conclusion must be validated
– 1ccounts for Korm and 6ontent errors.