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Quantifier Elimination in Fuzzy Logic

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Computer Science Logic (CSL 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1584))

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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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Author information

Authors and Affiliations

  1. Institut fär Algebra und Diskrete Mathematik, Technische Universität Wien, A-1040, Austria

    Matthias Baaz

  2. Institut fär Informationssysteme, Technische Universität Wien, A-1040, Austria

    Helmut Veith

Authors
  1. Matthias Baaz
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  2. Helmut Veith
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building Parks Road Oxford,, OX1 3QD, United Kingdom

    Georg Gottlob

  2. GREYC, Université de Caen, CNRS, Campus 2, F-14032, Caen cedex, France

    Etienne Grandjean

  3.  ,  

    Katrin Seyr

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© 1999 Springer-Verlag Berlin Heidelberg

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Baaz, M., Veith, H. (1999). Quantifier Elimination in Fuzzy Logic. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_27

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  • DOI: https://doi.org/10.1007/10703163_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65922-8

  • Online ISBN: 978-3-540-48855-2

  • eBook Packages: Springer Book Archive

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