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Generalized Metrics And Uniquely Determined Logic Programs, Pascal Hitzler, Anthony K. Seda
Generalized Metrics And Uniquely Determined Logic Programs, Pascal Hitzler, Anthony K. Seda
Computer Science and Engineering Faculty Publications
The introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility, but creates some semantical problems. Specifically, certain operators which are monotonic in the absence of negation become non-monotonic when it is introduced, with the result that standard approaches to denotational semantics then become inapplicable. In this paper, we show how generalized metric spaces can be used to obtain fixed-point semantics for several classes of programs relative to the supported model semantics, and investigate relationships between the underlying spaces we employ. Our methods allow the analysis of classes of programs which include the acyclic, locally hierarchical, …
Semantic Operators And Fixed-Point Theory In Logic Programming, Anthony K. Seda, Pascal Hitzler
Semantic Operators And Fixed-Point Theory In Logic Programming, Anthony K. Seda, Pascal Hitzler
Computer Science and Engineering Faculty Publications
We consider rather general operators mapping valuations to (sets of) valuations in the context of the semantics of logic programming languages. This notion generalizes several of the standard operators encountered in this subject and is inspired by earlier work of M.C. Fitting. The fixed points of such operators play a fundamental role in logic programming semantics by providing standard models of logic programs and also in determining the computability properties of these standard models. We discuss some of our recent work employing topological ideas, in conjunction with order theory, to establish methods by which one can find the fixed points …
A New Fixed-Point Theorem For Logic Programming Semantics, Anthony K. Seda, Pascal Hitzler
A New Fixed-Point Theorem For Logic Programming Semantics, Anthony K. Seda, Pascal Hitzler
Computer Science and Engineering Faculty Publications
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 …