Generalized Metrics and Uniquely Determined Logic Programs

TitleGeneralized Metrics and Uniquely Determined Logic Programs
Publication TypeJournal Article
Year of Publication2003
AuthorsAnthony K. Seda, Pascal Hitzler
JournalTheoretical Computer Science
KeywordsPriess-Crampe and Ribenboim Fixed-Point Theorem, Ultrametrics

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 tot eh 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, and acceptable programs amongst others, and draw on fixed-point theorems which apply to generalized ultrametric spaces and to partial metric spaces.

Full Text

Pascal Hitzler and Anthony K. Seda. 'Generalized Metrics and Uniquely Determined Logic Programs.' Theoretical Computer Science Volume: 305.(1-3) 2003: 187-219
research center: Knowledge Engineering Lab