Partial stable models for logic programs with aggregates

We introduce a family of partial stable model semantics for logic programs with arbitrary aggregate relations. The semantics are parametrized by the interpretation of aggregate relations in three-valued logic. Any semantics in this family satisfies two important properties: (i) it extends the partial stable semantics for normal logic programs and (ii) total stable models are always minimal. We also give a specific instance of the semantics and show that it has several attractive features.status: publishe