On the Notions of Residuated-Based Coherence and Bilattice-Based Consistence

  • Carlos V. Damásio
  • Nicolás Madrid
  • M. Ojeda-Aciego
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6857)


Different notions of coherence and consistence have been proposed in the literature on fuzzy systems. In this work we focus on the relationship between some of the approaches developed, on the one hand, based on residuated lattices and, on the other hand, based on the theory of bilattices.


Fuzzy System Logic Program Logic Programming Residuated Lattice Negation Operator 
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  1. 1.
    Alcântara, J., Damásio, C.V., Pereira, L.M.: An encompassing framework for paraconsistent logic programs. J. Applied Logic 3(1), 67–95 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Balduccini, M., Gelfond, M.: Logic programs with consistency-restoring rules. In: International Symposium on Logical Formalization of Commonsense Reasoning. AAAI 2003 Spring Symposium Series, pp. 9–18 (2003)Google Scholar
  3. 3.
    Barceló, P., Bertossi, L.: Logic programs for querying inconsistent databases. In: Dahl, V. (ed.) PADL 2003. LNCS, vol. 2562, pp. 208–222. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Cornelis, C., Arieli, O., Deschrijver, G., Kerre, E.E.: Uncertainty modeling by bilattice-based squares and triangles. IEEE T. Fuzzy Systems 15(2), 161–175 (2007)CrossRefzbMATHGoogle Scholar
  5. 5.
    Damásio, C.V., Pereira, L.M.: Monotonic and residuated logic programs. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 748–759. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Deschrijver, G., Arieli, O., Cornelis, C., Kerre, E.E.: A bilattice-based framework for handling graded truth and imprecision. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15(1), 13–41 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dubois, D., Prade, H., Ughetto, L.: Checking the coherence and redundancy of fuzzy knowledge bases. IEEE T. Fuzzy Systems 5(3), 398–417 (2002)CrossRefGoogle Scholar
  8. 8.
    Fitting, M.: Bilattices and the semantics of logic programming. Journal of Logic Programming 11, 91–116 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Fitting, M.: Fixpoint semantics for logic programming - a survey. Theoretical Computer Science 278, 25–51 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ginsberg, M.: Multivalued logics: A uniform approach to inference in artificial intelligence. Computational Intelligence 4, 265–316 (1988)CrossRefGoogle Scholar
  11. 11.
    Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. Journal of Intelligent Information Systems 27(2), 159–184 (2006)CrossRefGoogle Scholar
  12. 12.
    Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic. Kluwer Academic, Dordrecht (1998)CrossRefzbMATHGoogle Scholar
  13. 13.
    Madrid, N., Ojeda-Aciego, M.: Towards a fuzzy answer set semantics for residuated logic programs. In: Proc. of WI-IAT 2008 Workshop on Fuzzy Logic in the Web, pp. 260–264 (2008)Google Scholar
  14. 14.
    Madrid, N., Ojeda-Aciego, M.: On coherence and consistence in fuzzy answer set semantics for residuated logic programs. In: Di Gesù, V., Pal, S.K., Petrosino, A. (eds.) WILF 2009. LNCS, vol. 5571, pp. 60–67. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Madrid, N., Ojeda-Aciego, M.: Measuring inconsistency in fuzzy answer set semantics. IEEE Transactions on Fuzzy Systems (2011) (accepted)Google Scholar
  16. 16.
    Yuan, L., You, J.: Coherence approach to logic program revision. IEEE Tr. Knowledge and Data Engineering 10(1), 108–119 (2002)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Carlos V. Damásio
    • 1
  • Nicolás Madrid
    • 2
  • M. Ojeda-Aciego
    • 2
  1. 1.CENTRIAUniversidade Nova de LisboaPortugal
  2. 2.Dept. Matemática AplicadaUniversidad de MálagaSpain

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