Logic Programs With Abstract Constraint Atoms: The Role of Computations

The authors provide new perspectives on the semantics of logic programs with constraints. To this end they introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. They discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the paper.