Rules of Inference 2

# Rules of Inference 2 - Natural Deduction 7.2 2006 Kevin J Browne Rules of Inference II Constructive Dilemma Simplification Conjunction Addition

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Natural Deduction 7.2 © 2006 Kevin J. Browne

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Rules of Inference II Constructive Dilemma Simplification Conjunction Addition
Constructive Dilemma (p q) . (r s) p v r _________ q v s

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Simplification p . q _________ p q
Conjunction p q _________ p . q

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Addition p _________ p v q
Now we have double the rules and double the proving power.

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Example 1. N (D . W) 2. D K 3. N /N . K
Example 1. N (D . W) 2. D 3. N /N . K Using one of the rules find a pattern in these premises. The pattern here is MP.

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Example 1. N (D . W) 2. D K 3. N /N . K 4. D . W 1,3 MP So we draw the conclusion from MP on line 4.
Example 1. N (D . W) 2. D K 3. N /N . K 4. D . W Now it looks like there’s nothing else we can do with the first four rules. So, let’s consider using one of the Conjunctions can always be simplified.

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Example 1. N (D . W) 2. D K 3. N /N . K 4. D . W 1,3 MP 5. D 4 simp. Now we can use line 5 to find

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## This note was uploaded on 05/05/2008 for the course PHIL 311 taught by Professor D.c. during the Spring '07 term at University of Louisville.

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Rules of Inference 2 - Natural Deduction 7.2 2006 Kevin J Browne Rules of Inference II Constructive Dilemma Simplification Conjunction Addition

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