lec03-first-order-logic - EECS 203 Winter 2007 Discrete...

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EECS 203, Winter 2007 Discrete Mathematics Lecture 3 First-order logic continued January 11 Reading: Rosen [1.3, 1.4] January 11 First-order logic continued, Page 1
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3.1 Review Vocabulary of a first-order logic: constants, variables, functions , predicates (or relations ), connectives, quantifier , parenthesis, a special predicate =. Terms : a constant, variable, or f ( t 1 , · · · , t n ) for some function f and terms t 1 , · · · , t n . Well-formed formulas : 1. atomic formulas: P ( t 1 , · · · , t n ) for some predicate P and terms t 1 , · · · , t n . 2. constructed from wffs using connectives. 3. constructed from wffs using quantifiers: ( ), ( ). Free and bound variables : an occurrence of a variable x is free if it is not in the scope of a quantifier x or x . If not free, a variable is bound. A sentence is a wff if all variables are bound. January 11 First-order logic continued, Page 2
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3.2 Models of a first-order logic A model (or interpretation ) M for a first order logic L is a universe U together with an assignment of actual objects in U
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