Lecture-07

Lecture-07 - Inference Rules and replacement Rules x. A (B...

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1. Last 3 inference rules: Dil, DI, conj 2. Examples 3. First 3 replacement rules: CE, DN, comm 4. Examples Lecture 07 Proofs: Inference & Replacement Rules Final 3 Inference Rules Dilemma (dil) ! ! " # ! v " 㱤! ! v # Final 3 Inference Rules Disjunction Introduction (DI) ! 㱤! ! v ! Final 3 Inference Rules Conjunction (conj) ! ! 㱤! ! ! ! 1. (D v G) (A v C) 3. C H / D ! (H v G) 2. D ! (A G) 4. D 2 simp 5. D v G 4, DI 6. A v C 1, 5 MP 7. A G 2 simp 8. H v G 3, 6, 7 dil 9. D ! (H v G) 4, 8 conj 1. ( ~ A ~ C) A 3. ~ A / ~ C 2. C ( ~ A ~ C) 4. ~ ( ~ A ~ C) 3, 1 MT 5. ~ C 2, 4 MT 4. C A 1, 2 HS 5. ~ C 3, 4 MT
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1. (R v G) ~ A 3. R ! S / W v X 2. A v W 4. R 3 simp 7. W 6, 2 DS 8. W v X 7 DI 5. R v G 4 DI 6. ~ A 1, 5 MP 1. M D 4. G D 1, 2 HS 5. D v M 2, 3, 4 dil 2. G M 3. G v G / D v M First Three Replacement Rules Conditional Exchange (CE) ! ! :: ~ ! v ! First Three Replacement Rules Double Negation (DN) ! :: ~~ ! First Three Replacement Rules Commutation (comm) ! v ! :: ! v ! ! ! ! :: ! ! ! Can be used on part of a line Differences between
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Unformatted text preview: Inference Rules and replacement Rules x. A (B C) y. A ( ~ B v C) x CE z. ~ A v ( ~ B v C) y CE Can go in either direction Differences between Inference Rules and replacement Rules z. A (B C) y CE y. A ( ~ B v C) x CE x. ~ A v ( ~ B v C) 1. C v (D ! E) 2. A ~ C 4. ~ C (D ! E) 1 CE 5. A ! (D ! E) 2, 4 HS 6. ~~ A (D ! E) 5 DN 8. R 3, 7 MP 9. ~~ R 8 DN 3. { ~~ A (E ! D)} R / ~~ R 7. ~~ A (E ! D) 6 comm 1. A v B 2. C v D 3. B ~ D / ~ A ~~ C 4. ~ A B 1 CE 5. D v C 2 comm 6. ~ D C 5 CE 7. ~ A ~ D 3, 4 HS 8. ~ A C 6, 7 HS 9. ~ A ~~ C 8 DN 1. (P Q) K 2. K (P ! Q) / ( ~ Q ~ P) (Q ! P) 3. ( ~ P v Q) K 1 CE 4. (Q v ~ P) K 3 comm 5. ( ~ Q ~ P) K 4 CE 6. ( ~ Q ~ P) (P ! Q) 5, 2 HS 7. ( ~ Q ~ P) (Q ! P) 6 comm...
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Lecture-07 - Inference Rules and replacement Rules x. A (B...

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