Loop Formulas for Splitable Temporal Logic Programs

  • Felicidad Aguado
  • Pedro Cabalar
  • Gilberto Pérez
  • Concepción Vidal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6645)


In this paper, we study a method for computing temporal equilibrium models, a generalisation of stable models for logic programs with temporal operators, as in Linear Temporal Logic (LTL). To this aim, we focus on a syntactic subclass of these temporal logic programs called splitable and whose main property is satisfying a kind of “future projected” dependence present in most dynamic scenarios in Answer Set Programming (ASP). Informally speaking, this property can be expressed as “past does not depend on the future.” We show that for this syntactic class, temporal equilibrium models can be captured by an LTL formula, that results from the combination of two well-known techniques in ASP: splitting and loop formulas. As a result, an LTL model checker can be used to obtain the temporal equilibrium models of the program.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm, pp. 169–181. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  3. 3.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Logic Programming: Proc. of the Fifth International Conference and Symposium, vol. 2, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  4. 4.
    Cabalar, P., Pérez Vega, G.: Temporal equilibrium logic: A first approach. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds.) EUROCAST 2007. LNCS, vol. 4739, pp. 241–248. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Pearce, D.: A new logical characterisation of stable models and answer sets. In: Dix, J., Przymusinski, T.C., Moniz Pereira, L. (eds.) NMELP 1996. LNCS (LNAI), vol. 1216. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. 6.
    Pearce, D.: Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47(1-2), 3–41 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1991)zbMATHGoogle Scholar
  8. 8.
    Aguado, F., Cabalar, P., Pérez, G., Vidal, C.: Strongly equivalent temporal logic programs. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 8–20. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Cabalar, P.: A normal form for linear temporal equilibrium logic. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS, vol. 6341, pp. 64–76. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Lifschitz, V., Turner, H.: Splitting a logic program. In: Proceedings of the 11th International Conference on Logic programming (ICLP 1994), pp. 23–37 (1994)Google Scholar
  11. 11.
    Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Artificial Intelligence, pp. 112–117 (2002)Google Scholar
  12. 12.
    Ferraris, P., Lee, J., Lifschitz, V.: A generalization of the Lin-Zhao theorem. Annals of Mathematics and Artificial Intelligence 47, 79–101 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Heyting, A.: Die formalen Regeln der intuitionistischen Logik. In: Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 42–56 (1930)Google Scholar
  14. 14.
    Ferraris, P.: Answer sets for propositional theories. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 119–131. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Fages, F.: Consistency of Clark’s completion and existence of stable models. Methods of Logic in Computer Science 1, 51–60 (1994)Google Scholar
  16. 16.
    Cabalar, P., Diéguez, M.: STeLP – a tool for temporal answer set programming. In: Delgrande, J., Faber, W. (eds.) LPNMR 2011. LNCS (LNAI), vol. 6645, pp. 359–364. Springer, Heidelberg (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Felicidad Aguado
    • 1
  • Pedro Cabalar
    • 1
  • Gilberto Pérez
    • 1
  • Concepción Vidal
    • 1
  1. 1.Department of Computer ScienceUniversity of CorunnaSpain

Personalised recommendations