A model theory for paraconsistent logic programming

  • Carlos Viegas Damásio
  • Luís Moniz Pereira
Posters Theory of Computation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 990)


We provide a nine-valued logic to characterize the models of logic programs under a paraconsistent well-founded semantics with explicit negation WFSXp. We define a truth-functional logic, \(\mathcal{N}\mathcal{I}\mathcal{N}\mathcal{E}\), based on the bilattice construction of Ginsberg and Fitting. The models identified by WFSXp are models of logic \(\mathcal{N}\mathcal{I}\mathcal{N}\mathcal{E}\). We conclude with a discussion on the conditions to obtain an isomorphism between the two definitions, and thereby characterizing WFSXp model-theoretically.


Logic Program Logic Programming Complete Lattice Belief Revision Paraconsistent Logic 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. J. Alferes, C. V. Damásio, and L. M. Pereira. A logic programming system for non-monotonic reasoning. Journal of Automated Reasoning, Special Issue on Implementation of NonMonotonic Reasoning(14):93–147,1995.Google Scholar
  2. 2.
    J. J. Alferes and L. M. Pereira. Reasoning with Logic Programming. Springer-Verlag, 1995. In print.Google Scholar
  3. 3.
    N. D. Belnap. A useful four-valued logic. In G. Epstein and J. M. Dunn, editors, Modern Uses of Many-valued Logic, pages 8–37. Reidel, 1977.Google Scholar
  4. 4.
    H. A. Blair and V. S. Subrahmanian. Paraconsistent logic programming. Theoretical Computer Science, 68:135–154, 1989.CrossRefGoogle Scholar
  5. 5.
    S. Brass and J. Dix. A disjunctive semantics based on unfolding and bottom-up evaluation. In Proc. IFIP '94-Congress, Workshop FG2: Disjunctive Logic Programming and Disjunctive Databases, pages 83–91. Springer, 1994.Google Scholar
  6. 6.
    M. Fitting. Bilattices and the semantics of logic programming. Journal of Logic Programming, 11:91–116,1991.CrossRefGoogle Scholar
  7. 7.
    A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, 1991.Google Scholar
  8. 8.
    M. Gelfond and V. Lifschitz. Logic programs with classical negation. In Warren and Szeredi, editors, 7th ICLP, pages 579–597. MIT Press, 1990.Google Scholar
  9. 9.
    M. L. Ginsberg. Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence, 4:265–316, 1988.Google Scholar
  10. 10.
    C. M. Jonker and C. Witteveen. Revision by expansion. In G. Lakemeyer and B. Nebel, editors, Proceedings ECAI'92 Workshop on Theoretical Foundations of Knowledge Representation, pages 40–44. ECAI'92 Press, 1992.Google Scholar
  11. 11.
    R. Kowalski and F. Sadri. Logic programs with exceptions. In Warren and Szeredi, editors, 7th ICLP. MIT Press, 1990.Google Scholar
  12. 12.
    D. Pearce and G. Wagner. Reasoning with negative information I: Strong negation in logic programs. In Language, Knowledge and Intentionality, pages 430–453. Acta Philosophica Fennica 49, 1990.Google Scholar
  13. 13.
    L. M. Pereira and J. J. Alferes. Well founded semantics for logic programs with explicit negation. In B. Neumann, editor, Proc. ECAI, pages 102–106. John Wiley & Sons, 1992.Google Scholar
  14. 14.
    L. M. Pereira, J. J. Alferes, and J. N. Aparício. Contradiction Removal within Well Founded Semantics. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LPNMR'91, pages 105–119. MIT Press, 1991.Google Scholar
  15. 15.
    L. M. Pereira, J. J. Alferes, and J. N. Aparício. Contradiction removal semantics with explicit negation. In M. Masuch and L. Pólos, editors, Knowledge Representation and Reasoning Under Uncertainty, volume 808 of LNAI, pages 91–106. Springer-Verlag, 1994.Google Scholar
  16. 16.
    L. M. Pereira, J. N. Aparício, and J. J. Alferes. Non-monotonic reasoning with logic programming. Journal of Logic Programming. Special issue on Nonmonotonic reasoning, 17(2, 3 & 4):227–263,1993.Google Scholar
  17. 17.
    S. G. Pimentel and W. L. Rodi. Belief revision and paraconsistency in a logic programming framework. In A. Nerode, W. Marek, and V. S. Subrahmanian, editors, LPNMR'91, pages 228–242. MIT Press, 1991.Google Scholar
  18. 18.
    T. Przymusinski. Extended stable semantics for normal and disjunctive programs. In Warren and Szeredi, editors, 7th ICLP, pages 459–477. MIT Press, 1990.Google Scholar
  19. 19.
    C. Sakama. Extended well-founded semantics for paraconsistent logic programs. In Fifth Generation Computer Systems, pages 592–599. ICOT, 1992.Google Scholar
  20. 20.
    C. Sakama and K. Inoue. Paraconsistent stable semantics for extended disjunctive programs. Journal of Logic and Computation, 5(3), 1995.Google Scholar
  21. 21.
    G. Wagner. A database needs two kinds of negation. In B. Thalheim, J. Demetrovics, and H.-D. Gerhardt, editors, Mathematical Foundations of Database Systems, pages 357–371. LNCS 495, Springer-Verlag, 1991.Google Scholar
  22. 22.
    G. Wagner. Vivid logic: Knowledge-based reasoning with two kinds of negation. LNAI, 764, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Carlos Viegas Damásio
    • 1
  • Luís Moniz Pereira
    • 1
  1. 1.CRIA, Uninova and DCS, U. Nova de LisboaMonte da CaparicaPortugal

Personalised recommendations