UMass Amherst LINGUIST 726 - Logic. Section 2: Predicate Logic. (12 pages)

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Logic. Section 2: Predicate Logic.



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Logic. Section 2: Predicate Logic.

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Lecture Notes


Pages:
12
School:
University of Massachusetts Amherst
Course:
Linguist 726 - Mathematical Linguistics

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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 love John Mary Everyone whom Mary loves is happy x love Mary x happy x The formula x even x x 1 says that there are even numbers greater than 1 Formulas and other expressions of PL are built from individual constants or simply constants individual variables predicate constants or predicate symbols logical connectives the same as in statement logic and quantifiers Each expression belongs to a certain type The type structure of PL is very simple individuals relations of different arities and truth values In our examples we



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