Abstract
Current Answer Set Programming systems are built on non-monotonic logic programs without function symbols; as well-known, they lead to high undecidability in general. However, function symbols are highly desirable for various applications, which challenges to find meaningful and decidable fragments of this setting. We present the class \(\mathbb{FDNC}\) of logic programs which allows for function symbols, disjunction, non-monotonic negation under answer set semantics, and constraints, while still retaining the decidability of the standard reasoning tasks. Thanks to these features, they are a powerful formalism for rule-based modeling of applications with potentially infinite processes and objects, which allows also for common-sense reasoning. We show that consistency checking and brave reasoning are ExpTime-complete in general, but have lower complexity for restricted fragments, and outline worst-case optimal reasoning procedures for these tasks. Furthermore, we present a finite representation of the possibly infinitely many infinite stable models of an \(\mathbb{FDNC}\) program, which may be exploited for knowledge compilation purposes.
Work partially supported by the Austrian Science Funds (FWF) project P17212 and the EC project REWERSE (IST-2003-506779).
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References
Baselice, S., Bonatti, P.A., Criscuolo, G.: On Finitely Recursive Programs. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007, September 8-13. LNCS, vol. 4670, pp. 89–103. Springer, Heidelberg (2007) http://dx.doi.org/10.1007/978-3-540-74610-2_7
Bonatti, P.A.: Reasoning with infinite stable models. Artif. Intell. 156(1), 75–111 (2004)
Eiter, T., Faber, W., Leone, N., Pfeifer, G., Polleres, A.: A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity. ACM Transactions on Computational Logic 5(2), 206–263 (2004)
Eiter, T., Gottlob, G.: On the Computational Cost of Disjunctive Logic Programming: Propositional Case. Annals of Mathematics and Artificial Intelligence 15(3/4), 289–323 (1995)
Eiter, T., Gottlob, G.: Expressiveness of stable model semantics for disjuncitve logic programs with functions. J. Log. Program. 33(2), 167–178 (1997)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Comput. 9(3/4), 365–386 (1991)
Giunchiglia, E., Lifschitz, V.: An Action Language Based on Causal Explanation: Preliminary Report. In: AAAI 1998. Proceedings of the Fifteenth National Conference on Artificial Intelligence, pp. 623–630 (1998)
Heymans, S.: Decidable Open Answer Set Programming. PhD thesis, Theoretical Computer Science Lab (TINF), Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, B1050 Brussel, Belgium (February 2006)
Heymans, S., Nieuwenborgh, D.V., Vermeir, D.: Nonmonotonic ontological and rule-based reasoning with extended conceptual logic programs. In: Gómez-Pérez, A., Euzenat, J. (eds.) ESWC 2005. LNCS, vol. 3532, pp. 392–407. Springer, Heidelberg (2005)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7(3), 499–562 (2006)
Marek, V.W., Remmel, J.B.: On the expressibility of stable logic programming. In: LPNMR, pp. 107–120 (2001)
Marek, W., Nerode, A., Remmel, J.: How Complicated is the Set of Stable Models of a Recursive Logic Program? Annals of Pure and Applied Logic 56, 119–135 (1992)
Minker, J. (ed.): Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Francisco (1988)
Motik, B., Horrocks, I., Sattler, U.: Bridging the Gap Between OWL and Relational Databases. In: Proc. of WWW 2007, pp. 807–816 (2007)
Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138, 181–234 (2002)
Woltran, S.: Answer Set Programming: Model Applications and Proofs-of-Concept. Technical Report WP5, Working Group on Answer Set Programming (WASP, IST-FET-2001-37004) (July 2005), available at http://www.kr.tuwien.ac.at/projects/WASP/report.html
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Šimkus, M., Eiter, T. (2007). \(\mathbb{FDNC}\): Decidable Non-monotonic Disjunctive Logic Programs with Function Symbols. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_37
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DOI: https://doi.org/10.1007/978-3-540-75560-9_37
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