Computation of Non-Ground Disjunctive Well-Founded Semantics with Constraint Logic Programming

Impressive work has been done in the last years concerning the meaning of negation and disjunction in logic programs, but most of this research concentrated on propositional programs only. While it suuces to consider the propositional case for investigating general properties and the overall behaviour of a semantics, we feel that for real applications and for computational purposes an implementation should be able to handle rst-order programs without grounding them. In this paper we present a theoretical framework by deening a calculus of program transformations that apply directly to rules with variables and function symbols. Our main results are that (1) this calculus is connuent for arbitrary programs, (2) for nite ground programs it is equivalent to a terminating calculus introduced by Brass and Dix (1995), and (3) it approximates a generalisation of D-WFS for arbitrary programs. We achieve this by transforming program rules into rules with equa-tional constraints thereby using heavily methods and techniques from constraint logic programming. In particular, disconnection-methods play a crucial role. In principle, any constraint theory known from the eld of constraint logic programming can be exploited in the context of non-monotonic reasoning, not only equational constraints over the Herbrand domain. However, the respective constraint solver must be able to treat negative constraints of the considered constraint domain. In summary, this work yields the basis for a general combination of two paradigms: constraint logic programming and non-monotonic reasoning.