A New Fixed-point Theorem for Logic Programming Semantics

TitleA New Fixed-point Theorem for Logic Programming Semantics
Publication TypeConference Paper
Year of Publication2000
AuthorsAnthony K. Seda, Pascal Hitzler
Conference NameSCI2000 and ISAS2000
Conference LocationOrlando, Florida, USA

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.

Full Text

Anthony K. Seda and Pascal Hitzler, 'A New Fixed-point Theorem for Logic Programming Semantics,' the joint IIIS & IEEE meeting of the 4th World Multiconference on Systemics, Cybernetics and Informatics (SCI2000) and the 6th International Conference on Information Systems Analysis and Synthesis (ISAS2000), Orlando, Florida, USA, July, 2000, pp. 418-423.