A New Fixed-Point Theorem for Logic Programming Semantics
Anthony Karel Seda, Pascal Hitzler · Journal of Bioresource Management · 2000
We present a new fixed-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 defined 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 metriclike structures are an appropriate setting for the study of logic programming semantics. Keywords: Logic Programming, Denotational Semantics, Supported Model, Generalized Metric, Fixed-point Theorem Introduction One advantage possessed by a log...