Advertisement

The Inference Problem for Propositional Circumscription of Afine Formulas Is coNP-Complete

  • Arnaud Durand
  • Miki Hermann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2607)

Abstract

We prove that the inference problem of propositional circumscription for afine formulas is coNP-complete, settling this way a longstanding open question in the complexity of nonmonotonic reasoning. We also show that the considered problem becomes polynomial-time decidable if only a single literal has to be inferred from an afine formula.

Keywords

Minimal Model Minimal Solution Conjunctive Normal Form Truth Assignment Inference Problem 
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. [BMvT78]
    E. R. Berlekamp, R. J. McEliece, and H. C. A. van Tilborg. On the inherent intractability of certain coding problems. IEEE Trans. on Inf. Theory, IT-24(3):384–386, 1978.zbMATHCrossRefGoogle Scholar
  2. [Cad92]
    M. Cadoli. The complexity of model checking for circumscriptive formulae. Inf. Proc. Letters, 44(3):113–118, 1992.Google Scholar
  3. [CL94]
    M. Cadoli and M. Lenzerini. The complexity of propositional closed world reasoning and circumscription. JCSS, 48(2):255–310, 1994.zbMATHMathSciNetGoogle Scholar
  4. [CMM01]
    S. Coste-Marquis and P. Marquis. Knowledge compilation for closed world reasoning and circumscription. J. Logic and Comp., 11(4):579–607, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [EG93]
    T. Eiter and G. Gottlob. Propositional circumscription and extended closed-world reasoning are IIp 2-complete. TCS, 114(2):231–245, 1993.Google Scholar
  6. [GPP89]
    M. Gelfond, H. Przymusinska, and T. C. Przymusinski. On the relationship between circumscription and negation as failure. Artificial Intelligence, 38(1):75–94, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [KK01a]
    L. M. Kirousis and P. G. Kolaitis. The complexity of minimal satisfiability problems. In A. Ferreira and H. Reichel, (eds), Proc. 18th STACS, Dresden (Germany), LNCS 2010, pp 407–418. Springer, 2001.Google Scholar
  8. [KK01b]
    L. M. Kirousis and P. G. Kolaitis. A dichotomy in the complexity of propositional circumscription. In Proc. 16th LICS, Boston (MA), pp 71–80. 2001.Google Scholar
  9. [KSS00]
    D. J. Kavvadias, M. Sideri, and E. C. Stavropoulos. Generating all maximal models of a boolean expression. Inf. Proc. Letters, 74(3–4):157–162, 2000.Google Scholar
  10. [McC80]
    J. McCarthy. Circumscription-A form of non-monotonic reasoning. Artificial Intelligence, 13(1–2):27–39, 1980.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Arnaud Durand
    • 1
  • Miki Hermann
    • 2
  1. 1.Dept. of Computer ScienceLACL Paris 12 and LAMSADE Paris 9 (CNRS UMR 7024)CréteilFrance
  2. 2.École PolytechniqueLIX (CNRS, UMR 7650)Palaiseau cedexFrance

Personalised recommendations