Abstract
Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise way, where the encoding reflects the typical “guess and check” nature of NP problems: The property is encoded in a way such that polynomial size certificates for it correspond to stable models of a program. However, the problem-solving capacity of full disjunctive logic programs (DLPs) is beyond NP at the second level of the polynomial hierarchy. While problems there also have a “guess and check” structure, an encoding in a DLP is often non-obvious, in particular if the “check” itself is coNP-complete; usually, such problems are solved by interleaving separate “guess” and “check” programs, where the check is expressed by inconsistency of the check program. We present general transformations of head-cycle free (extended) logic programs into stratified disjunctive logic programs which enable one to integrate such “guess” and “check” programs automatically into a single disjunctive logic program. Our results complement recent results on meta-interpretation in ASP, and extend methods and techniques for a declarative “guess and check” problem solving paradigm through ASP.
The major part of this work has been conducted at TU Wien, supported by FWF (Austrian Science Funds) projects P14781and Z29-N04and European Commission grants FET-2001-37004 WASP and IST-2001-33570 INFOMIX.
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References
Eiter, T., Faber, W., Leone, N., Pfeifer, G.: Declarative problem-solving using the DLV system. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 79–103. Kluwer Academic Publishers, Dordrecht (2000)
Erdem, E., Lifschitz, V.: Tight logic programs. Theory and Practice of Logic Programming 3, 499–518 (2003)
Ferraris, P., Lifschitz, V.: Weight constraints as nested expressions. Theory and Practice of Logic Programming (2003), to appear, http://www.ca.utexas.edu/ueers/vl/papers/weight.ps
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Logic Programming: Proc. Fifth Int’l Conf. and Symp., pp. 1070–1080 (1988)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)
Ge1fond, M., Przymusinska, H.: Definitions in epistemic specifications. In: Nerode, A., Marek, V., Subramanian, V.S. (eds.) Logic Programming and Non-monotonie Reasoning: Proceedings of the First Int’l Workshop, pp. 245–259 (1991)
Lifschitz, V., Turner, H.: Splitting a logic program. In: Van Hentenryck, P. (ed.) Proc. Eleventh Int’l Conf. on Logic Progromming, pp. 23–37 (1994)
Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 369–389 (1999)
Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 375–398. Springer, Heidelberg (1999)
Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273 (1999)
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Eiter, T., Polleres, A. (2003). Towards Automated Integration of Guess and Check Programs in Answer Set Programming. In: Lifschitz, V., Niemelä, I. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2004. Lecture Notes in Computer Science(), vol 2923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24609-1_12
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DOI: https://doi.org/10.1007/978-3-540-24609-1_12
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