Lecture6 _Predicate Logic_

Lecture6 _Predicate Logic_ - Ling 726: Mathematical...

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Ling 726: Mathematical Linguistics, Logic, Section 2: Predicate Logic V. Borschev and B. Partee, October 7, 2004 p. 1 Lecture 6. Logic. Section 2: Predicate Logic. 1. Predicate Logic. .......................................................................................................................................... 1 1.0. Informal introduction. .......................................................................................................................... 1 1.1. Syntax. ................................................................................................................................................. 4 1.2. Semantics. ............................................................................................................................................ 5 2. Axioms and theories. ................................................................................................................................. 8 2.1. Tautologies, contradictions and contingencies . ................................................................................... 8 2.2. Logical equivalence and laws of Predicate Logic. ............................................................................... 8 2.3. Axioms and theories. ........................................................................................................................... 8 Homework 7. for Thurs October 14 . ........................................................................................................... 10 Reading: Predicate Logic: Chapter 7: 7.1 – 7.2, Chapter13: 13.1.2 of PMW, pp. 135 – 152, 321-331. Axioms and theories: Chapter 8: 8.1 (179-183), 8.5.1-8.5.4 (198 – 205). 1. Predicate Logic 1.0. Informal introduction Predicate Logic (or Predicate Calculus) is the most well known and in a sense the prototypical example of a formal language. On the other hand, Predicate Logic (PL) was not just invented by logicians. It was in a way extracted from the natural language as some special and important part of it. But for a long time it was used mostly for purposes of mathematics (and metamathematics) and was elaborated as a formal language. In studying Predicate Logic we would like to demonstrate features of formal languages which are most important for us: the notions of model and model-theoretic semantics, and the Principle of Compositionality (which we used already in Statement Logic). We begin with some examples and remarks. More exact definitions are given below. The sentences John loves Mary and Everyone whom Mary loves is happy can be represented as formulas of PL: John loves Mary l o v e ( John, Mary ) Everyone whom Mary loves is happy x ( love ( Mary, x ) happy ( x )) The formula x ( even ( x x >
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This note was uploaded on 02/22/2012 for the course LINGUIST 726 taught by Professor Partee during the Spring '07 term at UMass (Amherst).

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Lecture6 _Predicate Logic_ - Ling 726: Mathematical...

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