Antitonic logic programs

Abstract

In a previous work we have defined Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truth-values with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3, 4]. However, none of these semantics define a form of non-monotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Well-founded Model alike semantics. We also apply and illustrate our theory to logic programs with costs, extending the original presentation of [17] with a class of negations. © Springer-Verlag Berlin Heidelberg 2001.