Equivalence Between Answer-Set Programs Under (Partially) Fixed Input

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9616)

Abstract

Answer Set Programming (ASP) has become an increasingly popular formalism for declarative problem solving. Among the huge body of theoretical results, investigations of different equivalence notions between logic programs play a fundamental role for understanding modularity and optimization. While strong equivalence between two programs holds if they can be faithfully replaced by each other in any context (facts and rules), uniform equivalence amounts to equivalent behavior of programs under any set of facts. Both notions (as well as several variants thereof) have been extensively studied. However, the somewhat reverse notion of equivalence which holds if two programs are equivalent under the addition of any set of proper rules (i.e., all rules except facts) has not been investigated yet. In this paper, we close this gap and give a thorough study of this notion, which we call rule equivalence (RE), and its parameterized version where we allow facts over a given restricted alphabet to appear in the context. RE is thus a relationship between two programs whose input is (partially) fixed but where additional proper rules might still be added. Such a notion might be helpful in debugging of programs. We give full characterization results and a complexity analysis for the propositional case of RE. Moreover, we show that RE is decidable in the non-ground case.

References

  1. 1.
    Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Communications of the ACM 54(12), 92–103 (2011)CrossRefGoogle Scholar
  2. 2.
    Eiter, T., Fink, M., Tompits, H., Woltran, S.: Simplifying Logic Programs Under Uniform and Strong Equivalence. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 87–99. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Eiter, T., Fink, M.: Uniform Equivalence of Logic Programs under the Stable Model Semantics. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 224–238. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Eiter, T., Fink, M., Pührer, J., Tompits, H., Woltran, S.: Model-based recasting in answer-set programming. J. Appl. Non-Classical Logics 23(1–2), 75–104 (2013). http://dx.org/10.1080/11663081.2013.799318 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Eiter, T., Fink, M., Tompits, H., Woltran, S.: Strong and uniform equivalence in answer-set programming: characterizations and complexity results for the non-ground case. In: Proceedings of the 20th National Conference on Artificial Intelligence (AAAI 2005), pp. 695–700. AAAI Press (2005)Google Scholar
  6. 6.
    Eiter, T., Fink, M., Woltran, S.: Semantical characterizations and complexity of equivalences in answer set programming. ACM Trans. Comput. Log. 8(3), 1–53 (2007). http://doi.acm.org/10.1145/1243996.1244000 MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fink, M.: A general framework for equivalences in answer-set programming by countermodels in the logic of here-and-there. Theory Pract. Logic Programm. 11(2–3), 171–202 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Inoue, K., Sakama, C.: Equivalence of logic programs under updates. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 174–186. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Janhunen, T., Oikarinen, E., Tompits, H., Woltran, S.: Modularity aspects of disjunctive stable models. J. Artif. Intell. Res. (JAIR) 35, 813–857 (2009). http://dx.org/10.1613/jair.2810 MathSciNetMATHGoogle 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 Trans. Comput. Log. 7(3), 499–562 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lifschitz, V., Tang, L., Turner, H.: Nested expressions in logic programs. Ann. Math. Artif. Intell. 25(3–4), 369–389 (1999)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Trans. Comput. Logic 2(4), 526–541 (2001)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Oikarinen, E., Janhunen, T.: Modular equivalence for normal logic programs. In: Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), pp. 412–416. IOS Press (2006)Google Scholar
  14. 14.
    Pearce, D.J., Valverde, A.: Uniform equivalence for equilibrium logic and logic programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 194–206. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Sagiv, Y.: Optimizing datalog programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 659–698. Morgan Kaufmann, USA (1988)Google Scholar
  16. 16.
    Truszczynski, M., Woltran, S.: Relativized hyperequivalence of logic programs for modular programming. TPLP 9(6), 781–819 (2009). http://dx.org/10.1017/S1471068409990159 MathSciNetMATHGoogle Scholar
  17. 17.
    Turner, H.: Strong equivalence made easy: nested expressions and weight constraints. Theor. Pract. Logic Program. 3(4–5), 602–622 (2003)MathSciNetMATHGoogle Scholar
  18. 18.
    Woltran, S.: Characterizations for relativized notions of equivalence in answer set programming. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 161–173. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Woltran, S.: A common view on strong, uniform, and other notions of equivalence in answer-set programming. TPLP 8(2), 217–234 (2008). http://dx.org/10.1017/S1471068407003250 MathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Information SystemsTU WienViennaAustria

Personalised recommendations