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Quantifier Elimination in Fuzzy Logic

  • Matthias Baaz
  • Helmut Veith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)

Abstract

We investigate quantifier elimination of first order logic over fuzzy algebras. Fuzzy algebras are defined from continuous t-norms over the unit interval, and subsume Łukasiewicz [28, 29], Gödel [16, 12] and Product [19] Logic as most prominent examples.

We show that a fuzzy algebra has quantifier elimination iff it is one of the abovementioned logics. Moreover, we show quantifier elimination for various extensions of these logics, and observe other model-theoretic properties of fuzzy algebras.

Further considerations are devoted to approximation of fuzzy logics by finite-valued logics.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Matthias Baaz
    • 1
  • Helmut Veith
    • 2
  1. 1.Institut fär Algebra und Diskrete MathematikTechnische Universität WienAustria
  2. 2.Institut fär InformationssystemeTechnische Universität WienAustria

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