Lecture5 _Statement Logic_

# Lecture5 _Statement Logic_ - Ling 726 Mathematical...

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Ling 726: Mathematical Linguistics, Logic, Section 1: Statement Logic V. Borschev and B. Partee, October 5, 2004 p. 1 Lecture 5. Logic. Section1: Statement Logic. 1. Statement Logic. ......................................................................................................................................... 1 1.0. Goals. ................................................................................................................................................... 1 1.1. Syntax of Statement Logic . ................................................................................................................. 1 1.2. Semantics of Statement Logic . ............................................................................................................ 2 1.2.1. Negation . ...................................................................................................................................... 3 1.2.2. Conjunction . ................................................................................................................................. 3 1.2.3. Disjunction. .................................................................................................................................. 3 1.2.4. The Conditional. ........................................................................................................................... 4 1.2.5.The Biconditional. ......................................................................................................................... 4 1.2.6. Truth value of complex formula. .................................................................................................. 4 1.3. Tautologies, contradictions and contingencies . ................................................................................... 5 1.4. Logical equivalence and laws of statement logic . ............................................................................... 6 2. Compositionality and a compositional account of statement logic: Semantics as a homomorphism. ........ 7 2.0. The principle of Compositionality. ...................................................................................................... 7 2.1. Formulas as Algebra. ........................................................................................................................... 7 2.2. Semantics as a homomorphism . .......................................................................................................... 8 Supplementary Reading. ................................................................................................................................. 9 Homework 6. ................................................................................................................................................ 10 Reading: Chapter 5, Chapter 6: 6.1 – 6.4, Chapter13: 13.1, 13.1.1 of PTMW, pp. 87 – 134, 315-321. 1. Statement Logic.

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Lecture5 _Statement Logic_ - Ling 726 Mathematical...

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