Logic programs with monotone abstract constraint atoms

We introduce and study logic programs whose clauses are buil t out of monotone constraint atoms . We show that the operational concept of the one-step provab ility operator generalizes to programs with monotone constraint atoms, bu t the generalization involves nondeterminism. Our main results demonstrate that our form alism is a common generalization of (1) normal logic programming with its semantics o f models, supported models and stable models, (2) logic programming with weight atoms ( lparse programs) with the semantics of stable models, as defined by Niemel a, Simons an d Soininen, and (3) of disjunctive logic programming with the possible-model semant ics of Sakama and Inoue. To appear in Theory and Practice of Logic Programming (TPLP).