Lecture_4 - Lecture 4 Lecture 4 More Syntactic Structure...

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Unformatted text preview: Lecture 4 Lecture 4 More Syntactic Structure More Syntactic Structure Substitution Trees Polish notation SL as algebra SL as algebra 1. 2. 3. 4. 5. 6. Substitution of equivalents Basic laws: Double Negation Associativity Commutativity Idempotence Distributive De Morgan’s Exercises 2.13 Exercises 2.13 Find the law and substitution ¬(A ∨¬B) ∧ (B ∧ ≡ ¬[(A ∨¬B) ∨ ∧ ¬ C) (B C)] ¬B ∨ ∧ A) ≡ (¬B ∨ ∧ ¬B ∨¬A) (C ¬ C) ( A ∧ ∨ ∨ ∧ ≡ A ∧ ∨ ∧ ∨ (B C) A C C A (B C) Additional Equivalence Laws Additional Equivalence Laws TC, CC, CD, TD from p.64 Soundness and completeness Simplify the following from 2.17: A ∧ ∨¬B ∧ B A ¬B ∧ ∨ (B A) Duality Duality Dual of a connective Dual of a sentential expression The truth­tables of dual expressions are obtained from each other by toggling everywhere T and F. (p.70) If two expressions are equivalent, so are their duals. (p.71) ...
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This note was uploaded on 02/27/2011 for the course PHILOSOPHY 101 taught by Professor H during the Spring '11 term at Columbia College.

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