The Semantics of Evidence

The usual meaning of a sentence in the predicate calculus is its truth value. In this paper we show that there is associated with every statement a set of elements comprising evidence for it. A statement is true in a model exactly when there is evidence for it. Proofs can be regarded as expressions which denote evidence. A statement is constructively true when the evidence can be computed from its proofs. Proofs are useful in practical computations when evidence for statements is needed. They are especially valuable in relating computations to the problems they solve