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  1. Fuzzy Logic.Petr Hajek - 2008 - Stanford Encyclopedia of Philosophy.
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  • The Dual Adjunction Between MV-Algebras and Tychonoff Spaces.Vincenzo Marra & Luca Spada - 2012 - Studia Logica 100 (1-2):253-278.
    We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. (...)
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  • Three Characterizations of Strict Coherence on Infinite-Valued Events.Tommaso Flaminio - 2020 - Review of Symbolic Logic 13 (3):593-610.
    This article builds on a recent paper coauthored by the present author, H. Hosni and F. Montagna. It is meant to contribute to the logical foundations of probability theory on many-valued events and, specifically, to a deeper understanding of the notion of strict coherence. In particular, we will make use of geometrical, measure-theoretical and logical methods to provide three characterizations of strict coherence on formulas of infinite-valued Łukasiewicz logic.
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  • MV-Algebras, Infinite Dimensional Polyhedra, and Natural Dualities.Leonardo M. Cabrer & Luca Spada - 2017 - Archive for Mathematical Logic 56 (1-2):21-42.
    We connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify the aforementioned construction by observing that there is no need of using presentations of MV-algebras in order to obtain the adjunction. We also provide a description of the dual maps that is intrinsically geometric, and thus avoids the syntactic notion of definable map. Finally, we apply these results to better explain the relation (...)
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  • An Analysis of the Logic of Riesz Spaces with Strong Unit.Antonio Di Nola, Serafina Lapenta & Ioana Leuştean - 2018 - Annals of Pure and Applied Logic 169 (3):216-234.
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