Lecture 9 - Inductive and Deductive Reasoning

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    Inductive and Deductive

    Reasoning

    Lecture 9

    Prof. Storbeck

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    Problem Solving and Reasoning

    • Problem solving: set of cognitive processes applied to overcome obstacles to a goal

    • Reasoning: cognitive processes used to

    make inferences from knowledge and draw conclusions.

    Draw on categorization imager! decisionmaking attention L"# $# e%ecutive processes 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! in t&e rig&t anterior superior temporal g!rus and is associated 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 toward goal 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&e computer model to understand memor!

    • -iological viruses &elped computer scientists 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 one problem Bmilitar!A later solve problem BradiationA

    • 'A Read8remember militar! get &int solve radiation problem.

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    • 7A no memor! task solve radiation 7/C

    • A remember militar! solve radiation '/C

    • 'A remember militar!  &int solve radiation E=C

    (ick , 0ol!oak 794/ 794'

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     "&ree attempts to induce transfer

    • 7A subFects told to summarize stor! in abstract terms  – Gif !ou need a large force to accomplis&

    some purpose but are prevented from appl!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 1nalogical Reasoning

    • Structure #apping "&eor! BS#"A  – Searc& L"# for structural component

    similarit!

     – valuation of mapping

    • Learning and Inference wit& Sc&emas and 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 known instances to draw inferences about unknown instances

    • 6ategor!2based inductions  – (eneral induction

     – Speci*c induction

    o Inductive Process 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 been7K.

     "&erefore tomorrow t&e boiling point of water will be 7K.

     "&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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