A Constructive semantic characterization of aggregates in answer set programming

Abstract

AbstractThis technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion ofaggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator ΦaggrPfor aggregate programs, independently proposed in Pelov (2004) and Pelovet al.(2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.