Logic programs with monotone cardinality atoms

TL;DR

This paper introduces mca-programs, a new class of logic programs using monotone cardinality atoms, unifying several existing logic programming frameworks and extending their semantics.

Contribution

It develops a formal theory for mca-programs, generalizing normal, cardinality, and disjunctive logic programming semantics.

Findings

Operational one-step provability operator generalizes to mca-programs with nondeterminism.

Mca-programs unify semantics of normal, cardinality, and disjunctive logic programming.

Formalism extends existing logic programming semantics to a broader class.

Abstract

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.