Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms

Cao Son Tran, Enrico Pontelli, Phan Huy Tu

We present two equivalent approaches for defining answer sets for logic programs with arbitrary abstract constraint atoms (c-atoms). The first approach uses an immediate consequence operator for answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The second approach generalizes the notion of well-supported models of normal logic programs to programs with c-atoms. We prove that the newly defined semantics coincides with previously introduced semantics for logic programs with monotone c-atoms and extends the original answer set semantics for normal logic programs. We discuss different possibilities for treating negation-as-failure c-atoms and characterize situations in which they yield the same answer sets. We study some properties of answer sets of programs with c-atoms and relate our definition to several semantics for logic programs with aggregates.

Subjects: 11. Knowledge Representation; 3.3 Nonmonotonic Reasoning