Advertisement

Model Representation over Finite and Infinite Signatures

  • Christian G. Fermüller
  • Reinhard Pichler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4160)

Abstract

Computationally adequate representation of models is a topic arising in various forms in logic and AI. Two fundamental decision problems in this area are: (1) to check whether a given clause is true in a represented model, and (2) to decide whether two representations of the same type represent the same model. ARMs, contexts and DIGs are three important examples of model representation formalisms. The complexity of the mentioned decision problems has been studied for ARMs only for finite signatures, and for contexts and DIGs only for infinite signatures, so far. We settle the remaining cases. Moreover we show that, similarly to the case for infinite signatures, contexts and DIGs allow one to represent the same classes of models also over finite signatures; however DIGs may be exponentially more succinct than all equivalent contexts.

Keywords

Function Symbol Predicate Symbol Ground Atom Ground Instance Universal Variable 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE 2003. LNCS, vol. 2741, pp. 350–364. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Baumgartner, P., Tinelli, C.: The model evolution calculus with equality. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS, vol. 3632, pp. 392–408. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Baumgartner, P., Fuchs, A., Tinelli, C.: Lemma Learning in the Model Evolution Calculus (submitted)Google Scholar
  4. 4.
    Comon, H., Delor, C.: Equational formulae with membership constraints. Information and Computation 112(2), 167–216 (1994)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Caferra, R., Zabel, N.: Extending resolution for model construction. In: van Eijck, J. (ed.) JELIA 1990. LNCS (LNAI), vol. 478, pp. 153–169. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  6. 6.
    Caferra, R., Leitsch, A., Peltier, N.: Automated Model Building. Applied Logic Series, vol. 31. Kluwer Academic Publishers, Dordrecht (2004)MATHGoogle Scholar
  7. 7.
    Eiter, T., Faber, W., Traxler, P.: Testing strong equivalence of datalog programs - implementation and examples. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS, vol. 3662, pp. 437–441. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Eiter, T., Fink, M., Tompits, H., Traxler, P., Woltran, S.: Replacements in non-ground answer set programming. In: Proc. of WLP 2006, pp. 145–153 (2006)Google Scholar
  9. 9.
    Fermüller, C.G., Leitsch, A.: Model building by resolution. In: Martini, S., Börger, E., Kleine Büning, H., Jäger, G., Richter, M.M. (eds.) CSL 1992. LNCS, vol. 702, pp. 134–148. Springer, Heidelberg (1993)Google Scholar
  10. 10.
    Fermüller, C.G., Leitsch, A.: Hyperresolution and automated model building. Journal of Logic and Computation 6(2), 173–203 (1996)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Fermüller, C., Pichler, R.: Model representation via contexts and implicit generalizations. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS, vol. 3632, pp. 409–423. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Gottlob, G., Pichler, R.: Working with ARMs: Complexity results on atomic representations of Herbrand models. Information and Computation 165, 183–207 (2001)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kapur, D., Narendran, P., Rosenkrantz, D., Zhang, H.: Sufficient-completeness, ground-reducibility and their complexity. Acta Informatica 28(4), 311–350 (1991)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kunen, K.: Answer sets and negation as failure. In: Proceedings of ICLP 1987, pp. 219–228. MIT Press, Cambridge (1987)Google Scholar
  15. 15.
    Lassez, J.-L., Marriott, K.: Explicit representation of terms defined by counter examples. Journal of Automated Reasoning 3(3), 301–317 (1987)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Martelli, A., Montanari, U.: An efficient unification algorithm. ACM Transactions on Programming Languages and Systems 4(2), 258–282 (1982)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christian G. Fermüller
    • 1
  • Reinhard Pichler
    • 1
  1. 1.Technische Universität WienViennaAustria

Personalised recommendations