{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# day41 - First Order Predicate Calculus Undecidability and...

This preview shows pages 1–5. Sign up to view the full content.

Click to edit Master subtitle style 10/4/11 First Order Predicate Calculus Undecidability and Reduction Classes

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 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: o (and), * (or), ° (not), r (implies), ° (equivalence) Quantifiers over elements of U: X (there exists), ° (for all) Braces ([,]) to disambiguate bindings
10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 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 . Nothing else is a term.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 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 atomic .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 12

day41 - First Order Predicate Calculus Undecidability and...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online