01329nas a2200205 4500008004100000245006400041210006400105300001200169520071800181653002700899653002500926653002200951653001700973653002000990653001301010653001801023100002201041700002001063856004001083 2010 eng d00aGeneralized Distance Functions in the Theory of Computation0 aGeneralized Distance Functions in the Theory of Computation a443-4643 aWe 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.10adenotational semantics10afixed-point theorems10alogic programming10astable model10asupported model10atopology10aultra-metrics1 aSeda, Anthony, K.1 aHitzler, Pascal uhttp://knoesis.wright.edu/node/161901406nas a2200157 4500008004100000245013100041210006900172300001200241520083200253653001701085653003901102653002501141100002201166700002001188856004001208 1999 eng d00aSome Issues Concerning Fixed-Points in Computational Logic: Quasi-Metrics, Multivalued Mappings and the Knaster-Tarski Theorem0 aSome Issues Concerning FixedPoints in Computational Logic QuasiM a223-2503 aMany 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.10afixed points10aKnaster Tarski and Kleene theorems10amultivalued mappings1 aSeda, Anthony, K.1 aHitzler, Pascal uhttp://knoesis.wright.edu/node/1629