Disjunctive Programs with Set Constraints
We study an extension of disjunctive logic programs called set constraint disjunctive (SCD) programs where the clauses of the program are allowed to have a disjunction of monotone set constraints in their head and arbitrary monotone and antimonotone set constraints in their body. We introduce new class of models called selector stable models which represent all models which can be computed by an analogue the Gelfond-Lifschitz transform. We show that the stable models of disjunctive logic programs can be defined in terms of selector stable models and then extend this result to SCD logic programs. Finally we show that there is a natural proof theory associated with selector stable models.
KeywordsLogic Program Minimal Model Stable Model Horn Clause Proof Scheme
Unable to display preview. Download preview PDF.
- 1.Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press (2003)Google Scholar
- 2.Brik, A., Remmel, J.B.: Computing Stable Models of Logic Programs Using Metropolis Type Algorithms. In: Proceedings of Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP) 2011, paper no. 6, 15 pgs (2011)Google Scholar
- 4.Eiter, T., Faber, W., Leone, N., Pfeifer, G.: Declarative Problem-solving in DLV. In: Minker, J. (ed.) Logic-based Artificial Intelligence, pp. 79–103 (2000)Google Scholar
- 6.Gelfond, M., Lifschitz, V.: The stable semantics for logic programs. In: Proceedings 5th Int’l. Symp. Logic Programming, pp. 1070–1080. MIT Press (1988)Google Scholar
- 11.Lobo, J., Minker, J., Rajasekar, A.: Foundations of Disjunctive Logic Programming. MIT Press (1992)Google Scholar
- 12.Marek, V.W.: Introduction to Mathematics of Satisfiability. CRC Press (2009)Google Scholar
- 14.Marek, V.W., Remmel, J.B.: Effective Set Constraints (in preparation)Google Scholar