\(\mathbb{FDNC}\): Decidable Non-monotonic Disjunctive Logic Programs with Function Symbols

  • Mantas Šimkus
  • Thomas Eiter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4790)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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 Google Scholar
  2. 2.
    Bonatti, P.A.: Reasoning with infinite stable models. Artif. Intell. 156(1), 75–111 (2004)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    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)CrossRefMathSciNetGoogle Scholar
  4. 4.
    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)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Eiter, T., Gottlob, G.: Expressiveness of stable model semantics for disjuncitve logic programs with functions. J. Log. Program. 33(2), 167–178 (1997)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Comput. 9(3/4), 365–386 (1991)CrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    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)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Marek, V.W., Remmel, J.B.: On the expressibility of stable logic programming. In: LPNMR, pp. 107–120 (2001)Google Scholar
  12. 12.
    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)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Minker, J. (ed.): Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Francisco (1988)Google Scholar
  14. 14.
    Motik, B., Horrocks, I., Sattler, U.: Bridging the Gap Between OWL and Relational Databases. In: Proc. of WWW 2007, pp. 807–816 (2007)Google Scholar
  15. 15.
    Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138, 181–234 (2002)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mantas Šimkus
    • 1
  • Thomas Eiter
    • 1
  1. 1.Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 ViennaAustria

Personalised recommendations