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Lecture-06

# Lecture-06 - Inference Rules Simplification(simp 㱤 Three...

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1. Introduction to the proof method 2. Two inference rules: MP, MT, examples 3. Discussion 4. DS, HS, simp, examples Lecture 06 Proofs: Inference Rules Introduction to the Proof Method 1. Representation of argument 1. (A ! B) C 2. A ! B / C Introduction to the Proof Method 2. How does it work? 1. D v (E ~ G) 2. ~ D ! G / ~ E 4. E ~ G 3, 1 DS 6. ~ E 5, 4 MT 3. ~ D 2 simp 5. G 2 simp Introduction to the Proof Method 3. Why does it work? Rules are Truth Preserving If they are applied to only true lines, they will produce only true lines First two Inference Rules Modus Ponens (MP) ! ! ! 㱤! ! First two Inference Rules Modus Tolens (MT) ! ! ~ ! 㱤! ~ !

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1. (A ! B) C 2. A ! B / C 3. C 1, 2 MP 1. P ~ Q 4. Q / A K 5. ~ P 1, 4 MT 2. ~ Q ~ P 3. ~ P (A K) 6. A K 3, 5 MP Three more Inference Rules Disjunctive Syllogism (DS) ! v ! ~ ! 㱤! ! Hypothetical Syllogism (HS) ! ! ! " 㱤! ! " Three more
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Unformatted text preview: Inference Rules Simplification (simp) ! ! ! 㱤! ! Three more Inference Rules 1. D v (E 㱭 ~ G) 2. ~ D ! G / 㱤 ~ E 3. G 2 simp 5. E 㱭 ~ G 4, 1 DS 6. ~ E 3, 5 MT 4. ~ D 2 simp 1. (B 㱭 A) ! (C 㱭 D) 4. ~ (A 㱭 D) 㱭 K / 㱤 B 㱭 D 5. ~ K 2, 3 DS 2. ~ B 3. B v ~ K 6. A 㱭 D 5, 4 MT 7. B 㱭 A 1 simp 8. B 㱭 D 6, 7 HS 1. ~ D v (H v H) 5. D / 㱤 ~ J 6. H 㱭 ~ J 2 simp 2. ~ R ! (H 㱭 ~ J) 3. (R ! D) 㱭 ~ J 4. (H 㱭 ~ J) 㱭 (H 㱭 R) 7. H v H 5, 1 DS 11. H 10, 7 DS 10. ~ H 9, 8 MT 9. ~ R 2 simp 12. ~ J 6, 11 MP 8. H 㱭 R 6, 4 MP 1. ~ (R 㱭 R) v K 5. A 㱭 (B 㱭 ~ K) / 㱤 ~ B 8. S ! A 7, 3 MT 6. R 㱭 R 2, 4 HS 2. R 㱭 (S ! K) 3. ~ (S ! A) 㱭 ~ K 4. (S ! K) 㱭 R 7. K 6, 1 DS 11. ~ B 10, 7 MT 10. B 㱭 ~ K 9, 5 MP 9. A 8 simp...
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Lecture-06 - Inference Rules Simplification(simp 㱤 Three...

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