natural deduction 1 - Natural Deduction (1) 1 Besides using...

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1 Natural Deduction (1)
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2 Besides using truth-table to prove the validity of an argument, we can use another method, called “natural deduction,” to do the same. Using this method, we can deduce step-by- step the conclusion from the premises with the help of some rules.
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3 Rules of Inference There are altogether 18 rules: 8 rules of implication and 10 rules of replacement. Don’t worry: some of them you have already learnt and some are very obvious.
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4 Rules of Implication The 8 rules of implication are themselves valid argument forms.
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5 1. Modus Ponens (MP) This we have learnt, apart from the name. It simply says that given a conditional, and the premise, we can deduce the consequent or the conclusion. p q p____ q
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6 2. Modus Tollens (MT) It simply says that given a conditional and the denial of the consequent, we can deduce the denial of the antecedent/premise. p q ~q__ ~p
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7 3. Hypothetical Syllogism (HS) Given two conditionals with a common element, we can make up a new conditional without the common proposition. p q q r p r
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8 4. Disjunctive Syllogism (DS) It says given a disjunction, and the denial of either one disjunct, we can arrive at the other disjunct. p v q ~p__ q
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9 Up till now, we can see that the rules are okay because they observe the results of the 5 truth tables that we have learnt. But more importantly, the rules feel natural to us. But note that the method of natural
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This note was uploaded on 11/26/2011 for the course COMPUTER S 1003 taught by Professor Angelosstavrou during the Spring '11 term at King Saud University.

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natural deduction 1 - Natural Deduction (1) 1 Besides using...

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