day41 - First Order Predicate Calculus Undecidability and...

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Click to edit Master subtitle style 10/4/11 First Order Predicate Calculus Undecidability and Reduction Classes
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10/4/11 Dec 2, © UCF (Charles E. 22 First Order Primitive Symbols Universe of discourse: U Variables: x, x1, x2, …, y, y1, y2, …, etc. over U Functions: f, f1, …, g, g1, …, etc. from Un to U, where n is the arity of the given function A set of constants denoted a, a1, …, etc. These can be viewed as 0-ary functions. Predicates: P, P1, …, etc. from Un to {T,F}. The logical constants T and F. These can be viewed as 0–ary predicates. Boolean operators: Braces ([,]) to disambiguate bindings
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10/4/11 Dec 2, © UCF (Charles E. 33 First Order Terms Any constant is a term (with no free variables). Any variable is a term (whose only free variable is itself). Any expression f ( t 1,. .., tn ) of n ≥1 arguments (where each argument ti is a term and f is a function symbol of arity n ) is a term. Its free variables are the free variables of any of the terms ti .
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10/4/11 Dec 2, © UCF (Charles E. 44 Well-Formed Formulas (WFFs) If P is a relation of valence n ≥ 1 and the ti are terms then P ( t 1,. .., tn ) is well-formed. Its free variables are the free variables of any of the terms ti . All such formulas are said to be
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This note was uploaded on 10/03/2011 for the course COT 5310 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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day41 - First Order Predicate Calculus Undecidability and...

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