A Well-Founded Semantics for Basic Logic Programs with Arbitrary Abstract Constraint Atoms

Abstract

Logic programs with abstract constraint atoms proposed by Marek and Truszczynski are very general logic programs. They are general enough to capture aggregate logic programs as well as recently proposed description logic programs. In this paper, we propose a well-founded semantics for basic logic programs with arbitrary abstract constraint atoms, which are sets of rules whose heads have exactly one atom. We show that similar to the well-founded semantics of normal logic programs, it has many desirable properties such as that it can be computed in polynomial time, and is always correct with respect to the answer set semantics. This paves the way for using our well-founded semantics to simplify these logic programs. We also show how our semantics can be applied to aggregate logic programs and description logic programs, and compare it to the well-founded semantics already proposed for these logic programs.