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On elementary equivalence in fuzzy predicate logics

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Abstract

Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863–880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and Cintula (J Symb Log 71(3):863–880, 2006) and of Section 4 of Cerami and Esteva (Arch Math Log 50(5/6):625–641, 2011) to non-exhaustive models.

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Authors and Affiliations

  1. Universitat Autònoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Pilar Dellunde

  2. Artificial Intelligence Research Institute, Campus Universitat Autònoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Francesc Esteva

Authors
  1. Pilar Dellunde
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  2. Francesc Esteva
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Correspondence to Pilar Dellunde.

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Dellunde, P., Esteva, F. On elementary equivalence in fuzzy predicate logics. Arch. Math. Logic 52, 1–17 (2013). https://doi.org/10.1007/s00153-012-0303-x

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