Logic Programs with Abstract Constraint Atoms

We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is act constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M X C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudo-boolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the one-step provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.

• Type: Conference
• Year: 2004
• Where: AAAI
• Authors: Victor W. Marek, Miroslaw Truszczynski
• Keywords: AAAI 2004, Finite Set, Intelligent Agents, Logic Programming, Monotone Constraints