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Strong Negation in Well-Founded and Partial Stable Semantics for Logic Programs

  • Pedro Cabalar
  • Sergei Odintsov
  • David Pearce
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4140)

Abstract

A formalism called partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. In PEL one defines a class of minimal models, called partial equilibrium models, in a non-classical logic, HT 2. On logic programs partial equilibrium models coincide with Przymusinski’s partial stable (p-stable) models, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories. We study several extensions of PEL with strong negation and compare these with previous systems extending WFS with explicit negation, notably WSFX [10] and p-stable models with “classical” negation [11].

Keywords

Logic Program Conservative Extension Strong Negation Partial Equilibrium Model Valuation Versus 
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.
    Alcântara, J., Damásio, C., Pereira, L.M.: A Frame-based Characterisation of the Paraconsistent Well-founded Semantics with Explicit Negation. Unpublished draft, available at http://centria.di.fct.unl.pt/~jfla/publications/
  2. 2.
    Alferes, J.J., Pereira, L.M.: On logic programs semantics with two kinds of negation. In: Proc. of the 5th Intl. Joint Conf. and Symposium on Logic Programming, pp. 574–588. MIT Press, Cambridge (1992)Google Scholar
  3. 3.
    Alferes, J.J., Pereira, L.M.: Reasoning with Logic Programming. Springer, Heidelberg (1996)Google Scholar
  4. 4.
    Cabalar, P., Pearce, D., Valverde, A.: Reducing propositional Theories in Equilibrium Logic to Logic Programs. In: Proc. EPIA 2005. LNCS (LNAI), vol. 3803, Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. of ICLP 1988, pp. 1070–1080. The MIT Press, Cambridge (1988)Google Scholar
  6. 6.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)CrossRefGoogle Scholar
  7. 7.
    Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Nelson, D.: Constructible falsity. Journal of Symbolic Logic 14(2), 16–26 (1949)MATHMathSciNetGoogle Scholar
  9. 9.
    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, vol. 1216, pp. 57–70. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  10. 10.
    Pereira, L.M., Alferes, J.J.: Well Founded Semantics for Logic Programs with Explicit Negation. In: Neumann, B. (ed.) European Conference on Artificial Intelligence, pp. 102–106. John Wiley & Sons, Chichester (1992)Google Scholar
  11. 11.
    Przymusinski, T.: Stable semantics for disjunctive programs. New Generation Computing 9, 401–424 (1991)CrossRefGoogle Scholar
  12. 12.
    Routley, R., Routley, V.: The Semantics of First Degree Entailment. Noûs 6, 335–359 (1972)CrossRefMathSciNetGoogle Scholar
  13. 13.
    van Gelder, A., Ross, K.A., Schlipf, J.S.: Unfounded sets and well-founded semantics for general logic programs. JACM 38(3), 620–650 (1991)MATHGoogle Scholar
  14. 14.
    Vorob’ev, N.N.: A constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR 85, 465–468 (1952)MathSciNetGoogle Scholar
  15. 15.
    Vorob’ev, N.N.: The problem of deducibility in constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR 85, 689–692 (1952)Google Scholar
  16. 16.
    Vorob’ev, N.N.: Constructive propositional calculus with strong negation (in Russian). Transactions of Steklov’s Institute 72, 195–227 (1964)MATHMathSciNetGoogle Scholar
  17. 17.
    Wansing, H.: Negation. In: Goble, L. (ed.) The Blackwell Guide to Philosophical Logic, pp. 415–436. Basil Blackwell Publishers, Cambridge (2001)Google Scholar
  18. 18.
    Logical Foundations of Well-Founded Semantics (2006) (to appear) Google Scholar
  19. 19.
    Analysing and Extending Well-Founded and Partial Stable Semantics using Partial Equilibrium Logic. Technical Report (February 2006) (submitted for publication)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Pedro Cabalar
    • 1
  • Sergei Odintsov
    • 2
  • David Pearce
    • 3
  1. 1.Corunna UniversityCorunnaSpain
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.Universidad Rey Juan CarlosMadridSpain

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