Abstract
A generalization of logic program rules is proposed where rules are built from weight constraints with type information for each predicate instead of simple literals. These kinds of constraints are useful for concisely representing different kinds of choices as well as cardinality, cost and resource constraints in combinatorial problems such as product configuration. A declarative semantics for the rules is presented which generalizes the stable model semantics of normal logic programs. It is shown that for ground rules the complexity of the relevant decision problems stays in NP. The first implementation of the language handles a decidable subset where function symbols are not allowed. It is based on a new procedure for computing stable models for ground rules extending normal programs with choice and weight constructs and a compilation technique where a weight rule with variables is transformed to a set of such simpler ground rules.
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References
G. Brewka and T. Eiter. Preferred answer sets for extended logic programs. In Principles of Knowledge Representation and Reasoning Proceedings of the Sixth International Conference, pages 86–97, 1998.
F. Buccafurri, N. Leone, and P. Rullo. Strong and weak constraints in disjunctive datalog. In Proceedings of the 4th International Conference on Logic Programming and Non-Monotonic Reasoning, pages 2–17, 1997.
M. Cadoli, L. Palopoli, A. Schaerf, and D. Vasile. NP-SPEC: An executable specification language for solving all problems in NP. In Practical Aspects of Declarative Languages, LNCS 1551, pages 16–30, 1999.
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proceedings of the 5th International Conference on Logic Programming, pages 1070–1080, 1988.
S. Greco. Dynamic programming in Datalog with aggregates. IEEE Transactions on Knowledge and Data Engineering, 11(2):265–283, 1999.
J. Lu, A. Nerode, and V. Subrahmanian. Hybrid knowledge bases. IEEE Transactions on Knowledge and Data Engineering, 8(5):773–785, 1996.
W. Marek and M. Truszczyński. Autoepistemic logic. J. ACM, 38:588–619, 1991.
W. Marek and M. Truszczyński. Logic programming with costs. Manuscript, available at http://www.cs.engr.uky.edu/~mirek/papers.html, 1999.
W. Marek and M. Truszczyński. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: a 25-Year Perspective, pages 375–398. Springer-Verlag, 1999.
R. Ng and V. Subrahmanian. Stable semantics for probabilistic deductive databases. Information and Computation, 110:42–83, 1994.
I. Niemelä. Logic programs with stable model semantics as a constraint programming paradigm. In Proceedings of the Workshop on Computational Aspects of Nonmonotonic Reasoning, pages 72–79. Available at http://www.tcs.hut.fi/pub/reports/A52abstract.html, 1998. An extended version to be published in Annals of Mathematics and Artificial Intelligence.
I. Niemelä and P. Simons. Efficient implementation of the well-founded and stable model semantics. In Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 289–303, 1996.
I. Niemelä and P. Simons. Smodels-an implementation of the stable model and well-founded semantics for normal logic programs. In Proceedings of the 4th International Conference on Logic Programming and Non-Monotonic Reasoning, pages 420–429, 1997.
D. Sabin and R. Weigel. Product configuration frameworks-a survey. IEEE Intelligent Systems & Their Applications, pages 42–49, July/August 1998.
P. Simons. Extending the stable model semantics with more expressive rules. In Proceedings of the 5th International Conference on Logic Programming and Non-Monotonic Reasoning, 1999.
T. Soininen and I. Niemelä. Developing a declarative rule language for applications in product configuration. In Practical Aspects of Declarative Languages, LNCS 1551, pages 305–319, 1999.
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Niemelá1, I., Simons, P., Soininen, T. (1999). Stable Model Semantics of Weight Constraint Rules. In: Gelfond, M., Leone, N., Pfeifer, G. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 1999. Lecture Notes in Computer Science(), vol 1730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46767-X_23
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DOI: https://doi.org/10.1007/3-540-46767-X_23
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