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Automata-Based Computation of Temporal Equilibrium Models

  • Pedro Cabalar
  • Stéphane Demri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7225)

Abstract

Temporal Equilibrium Logic (TEL) is a formalism for temporal logic programming that generalizes the paradigm of Answer Set Programming (ASP) introducing modal temporal operators from standard Linear-time Temporal Logic (LTL). In this paper we solve some problems that remained open for TEL like decidability, bounds for computational complexity as well as computation of temporal equilibrium models for arbitrary theories. We propose a method for the latter that consists in building a Büchi automaton that accepts exactly the temporal equilibrium models of a given theory, providing an automata-based decision procedure and illustrating the ω-regularity of such sets. We show that TEL satisfiability can be solved in exponential space and it is hard for polynomial space. Finally, given two theories, we provide a decision procedure to check if they have the same temporal equilibrium models.

Keywords

Logic Program Temporal Logic Logic Programming Stable Model Stable Model Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    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
  2. 2.
    Aguado, F., Cabalar, P., Pérez, G., Vidal, C.: Loop Formulas for Splitable Temporal Logic Programs. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 80–92. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Boenn, G., Brain, M., De Vos, M., Ffitch, J.: ANTON: Composing Logic and Logic Composing. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 542–547. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Büchi, R.: On a decision method in restricted second-order arithmetic. In: Intl. Congress on Logic, Method and Philosophical Science 1960, pp. 1–11 (1962)Google Scholar
  5. 5.
    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
  6. 6.
    Cabalar, P., Diéguez, M.: STeLP – A Tool for Temporal Answer Set Programming. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 370–375. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Demri, S., Gastin, P.: Specification and verification using temporal logics. In: Modern Applications of Automata Theory. IIsc Research Monographs, vol. 2. World Scientific (2011) (to appear)Google Scholar
  8. 8.
    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
  9. 9.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: ICLP 1988, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  10. 10.
    Grasso, G., Iiritano, S., Leone, N., Lio, V., Ricca, F., Scalise, F.: An ASP-Based System for Team-Building in the Gioia-Tauro Seaport. In: Carro, M., Peña, R. (eds.) PADL 2010. LNCS, vol. 5937, pp. 40–42. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 42–56 (1930)Google Scholar
  12. 12.
    Kautz, H.: The logic of persistence. In: AAAI 1986, pp. 401–405 (1986)Google Scholar
  13. 13.
    Leone, N., Eiter, T., Faber, W., Fink, M., Gottlob, G., Greco, G.: Boosting information integration: The INFOMIX system. In: Proc. of the 13th Italian Symposium on Advanced Database Systems, SEBD 2005, pp. 55–66 (2005)Google Scholar
  14. 14.
    Manna, Z., Pnueli, A.: A hierarchy of temporal properties. In: PODC 1990, pp. 377–408. ACM Press (1990)Google Scholar
  15. 15.
    Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm, pp. 169–181. Springer (1999)Google Scholar
  16. 16.
    McCarthy, J.: Elaboration tolerance. In: Proc. of the 4th Symposium on Logical Formalizations of Commonsense Reasoning (Common Sense 1998), London, UK, pp. 198–217 (1998)Google Scholar
  17. 17.
    McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence Journal 4, 463–512 (1969)zbMATHGoogle Scholar
  18. 18.
    Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Nogueira, M., Balduccini, M., Gelfond, M., Watson, R., Barry, M.: An A-Prolog Decision Support System for the Space Shuttle. In: Ramakrishnan, I.V. (ed.) PADL 2001. LNCS, vol. 1990, pp. 169–183. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  20. 20.
    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, pp. 57–70. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    Perrin, D., Pin, J.-E.: Infinite Words: Automata, Semigroups, Logic and Games. Elsevier (2004)Google Scholar
  22. 22.
    Pnueli, A.: The temporal logic of programs. In: FOCS 1977, pp. 46–57. IEEE (1977)Google Scholar
  23. 23.
    Safra, S.: Complexity of Automata on Infinite Objects. PhD thesis, The Weizmann Institute of Science, Rehovot (1989)Google Scholar
  24. 24.
    Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. JCSS 4(2), 177–192 (1970)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Sistla, A., Clarke, E.: The complexity of propositional linear temporal logic. JACM 32(3), 733–749 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Sistla, A., Vardi, M., Wolper, P.: The complementation problem for Büchi automata with applications to temporal logic. TCS 49, 217–237 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Vardi, M.: Alternating Automata: Unifying Truth and Validity Checking for Temporal Logics. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249, pp. 191–206. Springer, Heidelberg (1997)Google Scholar
  28. 28.
    Vardi, M., Wolper, P.: Automata-theoretic techniques for modal logics of programs. JCSS 32, 183–221 (1986)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Vardi, M., Wolper, P.: Reasoning about infinite computations. I & C 115, 1–37 (1994)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Černá, I., Pelánek, R.: Relating Hierarchy of Temporal Properties to Model Checking. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 318–327. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pedro Cabalar
    • 1
  • Stéphane Demri
    • 2
  1. 1.Department of Computer ScienceUniversity of CorunnaSpain
  2. 2.LSV, ENS de Cachan, CNRS, INRIAFrance

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