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Duality via Truth for Some Fuzzy Modal Logic

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Algebraic Techniques and Their Use in Describing and Processing Uncertainty

Part of the book series: Studies in Computational Intelligence ((SCI,volume 878))

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Abstract

Duality via truth is a kind of correspondence between a class of algebras and a class of relational systems (frames, following terminology well-known in non-classical logics). The first class is viewed as an algebraic semantics of some logic, whereas the other class constitutes Kripke-style semantics of this logic. The duality principle underlying the duality via truth states that algebras and their corresponding frames provide equivalent semantics for this logic in the sense that a formula is true with respect to one semantics if and only if it is true with respect to the other semantics. Consequently, the algebras and the frames express the equivalent notions of truth and in this sense they are viewed as dual structures. In this paper we develop duality via truth for a fuzzy modal logic. The MTL logic, introduced by Esteva and Godo, is taken as a basis. Several axiomatic extensions, motivated by well-known schemas of modal logic, are also considered.

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Acknowledgements

This paper is dedicated to Prof. Elbert Walker, a passionated fuzzy mathematician with whom we could talk about universal algebra!

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Authors and Affiliations

  1. Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Anna Maria Radzikowska

  2. Faculty of Applied Mathematics, Computer Science and Statistics Ghent University, Krijgslaan 281 (S9), 9000, Gent, Belgium

    Etienne E. Kerre

Authors
  1. Anna Maria Radzikowska
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Correspondence to Anna Maria Radzikowska .

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Editors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA

    Hung T. Nguyen

  2. Department of Computer Science, The University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Radzikowska, A.M., Kerre, E.E. (2020). Duality via Truth for Some Fuzzy Modal Logic. In: Nguyen, H., Kreinovich, V. (eds) Algebraic Techniques and Their Use in Describing and Processing Uncertainty. Studies in Computational Intelligence, vol 878. Springer, Cham. https://doi.org/10.1007/978-3-030-38565-1_11

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