lec9-2010

# lec9-2010 - 1 Outline Reasoning& Problem Solving 2...

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Unformatted text preview: 1 Outline: Reasoning & Problem Solving 2 Remember some pictures we saw last month? 3 or or or 4 or or or Lewis Carroll “Contrariwise,” continued Tweedledee, “If it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.” Chapter Outline Logic and Reasoning Deductive Reasoning Modus Ponens and Modus Tollens Wason selection task Pragmatic Reasoning Schemas Inductive Reasoning Base Rate Neglect Analogy Gentner’s Structure Mapping Theory Holyoak and Thagard’s ACME Logic Deductive Reasoning Modus Ponens Modus Tollens If P, then Q If P, then Q P ~Q---------------------------------------- ∴ Q ~P • Inductive Reasoning • Reasoning from partial knowledge to more general beliefs It is likely to rain today ∴ I should carry an umbrella Logic Deductive Reasoning Modus Ponens Modus Tollens If Raining , then Grass is Wet If Raining , then Grass is Wet Raining Grass is Not Wet---------------------------------------- Grass is Wet Not Raining • Inductive Reasoning • Reasoning from partial knowledge to more general beliefs It is likely to rain today ∴ I should carry an umbrella Taxonomy of thought NO Daydream YES Calculation YES Induction NO Deduction YES Increase in Semantic Information? NO Creation NO Precise goal? YES Deterministic? Goal? Chapter Outline Logic and Reasoning Deductive Reasoning Modus Ponens and Modus Tollens Wason selection task Pragmatic Reasoning Schemas Inductive Reasoning Base Rate Neglect Analogy Gentner’s Structure Mapping Theory Holyoak and Thagard’s ACME Wason Selection Task (Wason & Johnson-Laird, 1972) Each card has a letter on one side and a number on the other. Which cards would you turn over to test if the following rule is valid: “If a vowel on one side, then there is an even number on the other.” [E] [B] [2] [7] p ~p q ~q Only 4% correct (Wason, 1966) Maybe we need to be concrete: Every time I go to Manchester, I travel by train [Manchester] [Sheffield] [Train] [Car] Every time I go to San Francisco, I travel by plane [S.F.] [Boston] [Plane] [Car] New Version: If a letter is sealed, then it has a 50-lire stamp on it. 88% of Italian subjects correct (Johnson-Laird, et al., 1972) and this was replicated in England with a 4d or 5d stamp Subjects a University of Florida failed on letter version, as well (Griggs & Cox, 1982) 50 40 ~p p q ~q If drinking beer, then you must be 21. [beer] [coke] [25] [17] p ~p q ~q 73% correct on second version, 0% correct on letter version and on the abstract version [vowel/even] (Griggs & Cox, 1982). Mental Representation & Difficulty Concrete representation External representation Mental Models Variety of reference without common usage Cluster structure for sorted terms Sowa style conceptual graph Johnson-Laird tableaus for syllogisms Functional, behaving model Gentner & models of electricity Norman & models of devices.. Etc. SYLLOGISMS: Two premises, one conclusion, for example: All A are B All B are C So, All A are C SYLLOGISMS: THE FOUR MOODS...
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## This note was uploaded on 09/28/2010 for the course SIS IS2300 taught by Professor Brianbutler during the Fall '10 term at Pittsburgh.

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lec9-2010 - 1 Outline Reasoning& Problem Solving 2...

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