A New Fixed Point Theorem for Logic Programming Semantics

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 anal yse the denotational semantics of certain logic programs The theorem is obtained by generaliz ing 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 con ventional programming language semantics The class of programs to which we apply our theo rem was de ned previously by us in terms of op erators using three valued logics However the new treatment we provide here is short and intu itive and provides further evidence that metric like structures are an appropriate setting for the study of logic programming semantics