%0 Journal Article
%J The Computer Journal
%D 2010
%T Generalized Distance Functions in the Theory of Computation
%A Anthony K. Seda
%A Pascal Hitzler
%K denotational semantics
%K fixed-point theorems
%K logic programming
%K stable model
%K supported model
%K topology
%K ultra-metrics
%X We discuss a number of distance functions encountered in the theory of computation, including metrics, ultra-metrics, quasi-metrics, generalized ultrametrics, partial metrics, d-ultra-metrics, and generalized metrics. We consider their properties, associated fixed-point theorems, and some general applications they have within the theory of computation. We consider in detail the applications of generalized distance functions in giving a uniform treatment of several important semantics for logic programs, including acceptable programs and natural generalizations of them, and also the supported model and the stable model in the context of locally stratified extended disjunctive logic programs and databases.
%B The Computer Journal
%P 443-464
%G eng
%0 Journal Article
%J Topology Proceedings
%D 1999
%T Some Issues Concerning Fixed-Points in Computational Logic: Quasi-Metrics, Multivalued Mappings and the Knaster-Tarski Theorem
%A Anthony K. Seda
%A Pascal Hitzler
%K fixed points
%K Knaster Tarski and Kleene theorems
%K multivalued mappings
%X Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operations determined by the database or program. We discuss known versions for multivalued mappings of the Knaster-Tarski theorem and of the Banach contraction mapping theorem and formulate a version of the classical fixed point theorem (sometimes attributed to Kleene) which is new. All these results have applications to the semantics of disjunctive logic programs, and we will describe a class of programs to which the new theorem can be applied. We also show that a unification of the latter two theorems is possible, using quasi-metrics, which parallels the well-known unification of Rutten and Smyth in the case of conventional programming language semantics.
%B Topology Proceedings
%P 223-250
%G eng