Axiomatization of Aggregates in Answer Set Programming

The paper presents a characterization of logic programs with aggregates based on a many-sorted generalization of operator SM that refers neither to grounding nor to fixpoints. This characterization introduces new function symbols for aggregate operations and aggregate elements, whose meaning can be fixed by adding appropriate axioms to the result of the SM transformation. We prove that for programs without positive recursion through aggregates our semantics coincides with the semantics of the answer set solver clingo.