An Unfolding-Based Semantics for Logic Programming with Aggregates

The paper presents two equivalent de nitions of answer sets for logic programs with aggregates. These de nitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with aggregates to normal logic programs or positive programs, whose answer set semantics can be used to de ned the semantics of the original programs. The rst de nition provides an alternative view of the semantics for logic programming with aggregates described in [32, 34]. In particular, the unfolding employed by the rst de nition in this paper coincides with the translation of programs with aggregates into normal logic programs described in [33]. This indicates that the approach proposed in this paper captures the same meaning as the semantics discussed in [32, 34]. The second de nition is similar to the traditional answer set de nition for normal logic programs, in that, given a logic program with aggregates and an interpretation, the unfolding process produces a positive program. The paper shows how this de nition can be extended to consider aggregates in the head of the rules. These two approaches are very intuitive, general, and do not impose any syntactic restrictions on the use of aggregates, including support for use of aggregates as heads of program rules. The proposed views of logic programming with aggregates are simple and coincide with the ultimate stable model semantics [32, 34], and with other semantic characterizations for large classes of program (e.g., programs with monotone aggregates and programs that are aggregate-strati ed). Moreover, it can be directly employed to support an implementation using available answer set solvers. The paper describes a system, called ASP, that is capable of computing answer sets of programs with arbitrary (e.g., recursively de ned) aggregates. The paper also presents an experimental comparison of ASP with another system for computing answer sets of programs with aggregates, DLVA.