Predicate Logic

The Average Person's Axioms of First Order Predicate Logic:

1. (A -> B) -> (B -> A)

2. (There exists) x A(x) -> (For all) x A(x)

3. (A -> C) AND (B -> C) -> (A -> B)

Predicate logic is the study of why the above is funny.

Actually, predicate logic is a mathematical model for reasoning with predicates (just as propositional logic is an algebra for reasoning about the truth of logical expressions).

As in propositional logic, we can create logical expressions containing predicates, manipulate those expressions according to the algebraic laws of predicate logic, and construct proofs using rules of inference to deduce new facts from axioms. In fact, proofs in predicate logic (based on unification) are a form of computation used in the programming language Prolog.

Although predicate logic is more powerful than propositional logic, it too has its limits.