A logical system is presented that tolerates partial or total contradictions or incomplete information. Every set of formulas in such a system has a model. Other theoretical properties were also investigated concerning the generalization of the notion of contradiction from classical logic. Applications to knowledge representation were considered and a way was proposed to represent generic and explicit information while providing monotonic inference.


Classical Logic Valuation Function Truth Degree Human Lifespan Valuation Versus 
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  1. 1.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  2. 2.
    Baader, F., Sattler, U.: Description Logics with Symbolic Number Restrictions. In: Proceedings of the 12th European Conference on Artificial Intelligence, Budapest, Hungary (1996)Google Scholar
  3. 3.
    Barwise, J., Moss, L.S.: Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena. CSLI Lecture Notes. CSLI Publications, Stanford University (1996)zbMATHGoogle Scholar
  4. 4.
    Belnap, N.: A useful four-valued logic. In: Epstein, G., Dunn, J.M. (eds.) Modern Uses of Multiple-Valued Logic, pp. 7–37. Reidel Publishing Company, Dordrecht (1977)Google Scholar
  5. 5.
    Cercone, N.: The ECO Family. In: Lehmann, F. (ed.) Semantic Networks (1993)Google Scholar
  6. 6.
    Dubois, D., Lang, J., Prade, H.: Possibilistic Logic. In: Gabbay, D.M., et al. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)Google Scholar
  7. 7.
    Faust, D.: The Concept of Evidence. Int. Journal of Intelligent Systems 15, 477–493 (2000)zbMATHCrossRefGoogle Scholar
  8. 8.
    Fortemps, P., Slowinski, R.: A graded quadrivalent logic for ordinal preference modelling: Loyola-like approach. Fuzzy Optimization and Decision Making 1, 93–111 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ginsberg, M.: Bilattices and Modal Operators. Journal of Logic and Computation 1(1), 41–69 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Iwanska, L., Shapiro, S. (eds.): Language for Knowledge and Knowledge for language. AAAI Press/The MIT Press (2000)Google Scholar
  11. 11.
    Rasiowa, H., Sikorski, R.: The mathematics of metamathematics. Polish Academic Publisher (1963)Google Scholar
  12. 12.
    Reiter, R.: A logic for default reasoning. Artificial Intelligence 13(1,2), 81–132 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Smarandache, F.: Neutrosophy. American Research Press (1998)Google Scholar
  14. 14.
    Zadeh, L.: A new direction in AI: Towards a computational theory of perceptions. AI magazine 22, 73–84 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nikolai G. Nikolov
    • 1
  1. 1.CLBME-Bulgarian Academy of SciencesSofiaBulgaria

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