Logic programs with monotone cardinality atoms

We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We demonstrate that the operational concept of the one-step provability operator generalizes to mca-programs, but the generalization involves nondeterminism. Our main results show that the formalism of mca-programs is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with cardinality atoms and with the semantics of stable models, as defined by Niemela, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.