Three-valued completion for abductive logic programs

There is a growing interest in ways to represent incomplete information in logic programs. It has been shown that limited forms abduction can be used quite elegantly for this purpose. In this paper, we propose a a three-valued completion semantics for abductive logic programs, which solves some problems associated with Console et al’s two-valued completion semantics. The semantics is a generalization of Kunen’s completion semantics for general logic programs, which is know to correspond very well to a class of effective proof procedures for general logic programs. Secondly, we propose a proof procedure for abductive logic programs, which is a generalization of a proof procedure for general logic programs based on constructive negation. This proof procedure is sound and complete with respect to the proposed semantics. Basically, by generalizing a number of results on general logic programs to the class of abductive logic programs, we present further evidence for the idea that limited forms of abduction can be added quite naturally to general logic programs. One problem that remains, is the occurrence of inconsistencies. We argue that there are cases in which these do not pose a problem.