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Rules of Inference 1 - Natural Deduction 7.1 2006 Kevin J...

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Natural Deduction Natural Deduction 7.1 © 2006 Kevin J. Browne
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Rules of InferenceI Modus Ponens Modus Tollens Disjunctive Syllogism Hypothetical Syllogism
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Modus Ponens Modus Ponens p q p _________ q
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Modus Tollens Modus Tollens p q ~q _________ ~p
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DisjunctiveSyllogism DisjunctiveSyllogism p v q ~p _________ q
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Hypothetical Syllogism Hypothetical Syllogism p q q r _________ p r
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Solving proofs in natural deduction is based on pattern recognition. Think of it as using the rules to crack a code!
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Example One Example One 1. F v (D T) 2. ~F 3. D /T
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Example One Example One 1. F v (D T) 2. ~F 3. D /T Using oneof the rules find a pattern in thesepremises. Thepattern hereis DS.
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Example One Example One 1. F v (D T) 2. ~F 1. D /T 2. D T 1,2 DS So we draw theconclusion from DS on line4.
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Example One Example One 1. F v (D T) 2. ~F 1. D /T 2. D T 1,2 DS Now use therules to find another pattern with what we’vejust derived. This timetherule we useto “crack the code” is MP.
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Example One Example One 1. F v (D T) 2. ~F 1. D /T 2. D T 1,2 DS 3. T 3,4 MP Oncewe reach thefinal conclusion we’vesolved theproof!
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