A New Fixed - Point Theorem for Logic

We present a new xed-point theorem akin to the Banach contraction mapping theorem, but in the context of a novel notion of generalized metric space, and show how it can be applied to analyse the denotational semantics of certain logic programs. The theorem is obtained by generalizing a theorem of Priess-Crampe and Ribenboim, which grew out of applications within valuation theory, but is also inspired by a theorem of S.G. Matthews which grew out of applications to conventional programming language semantics. The class of programs to which we apply our theorem was deened previously by us in terms of operators using three-valued logics. However, the new treatment we provide here is short and intuitive , and provides further evidence that metric-like structures are an appropriate setting for the study of logic programming semantics.