Lecture 9 - Inductive and Deductive Reasoning

8/17/2019 Lecture 9 - Inductive and Deductive Reasoning

1/50

Inductive and Deductive

Reasoning

Lecture 9

Prof. Storbeck


2/50

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.


3/50

Problem

• Problem &as ' parts – (oal state

– Initial state

– )perations


4/50

Problems

• $ell de*ned problem

• Ill de*ned problem


5/50

Insig&t

Insig&t invokes activit! int&e rig&t anterior superiortemporal g!rus and isassociated wit& increased

gamma bursts.+ounios , -eeman//9


6/50

Problem Space "&eor!


7/50

Strategies and 0euristics

• 1lgorit&m

• 0euristics


8/50

0euristic

• 0euristic contrar! to moving towardgoal state.


9/50


• 1lgorit&m

• 0euristics – Random searc&

• "rial and error

• -e&aviorist approac&


10/50


• 1lgorit&m


• "rial and error

• -e&aviorist approac&

– 0ill2climbing•

$ater 3ug Problem• Left2prefrontal

4 /

/

5 5/

Initial State

(oal State


11/50


12/506olvin et al. //7


13/50


• 1lgorit&m


– 0ill2climbing• $ater 3ug Problem

• Left2prefrontal

– #eans2ends anal!sis• -reak down problem into

subgoals8subproblems

• "ower of 0anoi


14/50

%perts vs. ovices

• Di;erences in organizing problems:

• ovices < surface features

•

%perts < abstract or deeper levelconcepts


15/50

1nalogical Reasoning


16/50

• 6ognitive Science relied on t&ecomputer model to understandmemor!

• -iological viruses &elped computerscientists solve computer viruses.


17/50

1nalogical Reasoning

• 7. Retrieval

• . #apping

•

'. valuation• 5. 1bstraction

• =. Predictions


18/50

• #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.


19/50

"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@


20/50

• 7A Solve Problem

• A Read8remember stor! of oneproblem Bmilitar!A later solveproblem BradiationA

• 'A Read8remember militar! get &intsolve radiation problem.


21/50

• 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'


22/50

"&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


23/50

"&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


24/50

"&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!


25/50

-e!ond $orking #emor!@

+roger et al. //


26/50


27/50


28/50

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


29/50

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.


30/50

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


31/50

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


32/50

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.


33/50

6ategor!2-ased Inductions

• Induction based on categor! andrelated features.

• Similarit!

• "!picalit!

•

(roup &omogeneit!


34/50

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.


35/50

Inductive Reasoning in t&e-rainJ


36/50

• $6S" , f#RI

• #onc&i et al. //7


37/50

• 1ctivation includes: mid2DLPK6 mid2LPK6 posterior )K6 mid2LPK6


38/50

• Seger et al. ///


39/50

Inductive Reasoning

• Implausible arguments activate areasnoted for error detectionJ


40/50

Deductive Reasoning

• S!llogism


41/50

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#


42/50

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.


43/50

6ategorical S!llogisms

• Relations between two categories

• Premise 7: 1ll 1 are -

• Premise : 6 is an 1.

• 6onclusion: 6 is -.


44/50

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.


45/50

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.


46/50

$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.


47/50

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.


48/50

-elief2bias ;ect

• Premise 7: o cigarettes areine%pensive

• Premise : Some addictive t&ings are

ine%pensive

• 6onclusion: Some additive t&ings arenot cigarettes.


49/50

-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


50/50

"&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.

Documents

Lecture 9 - Inductive and Deductive Reasoning