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  1.  26
    Residuated Fuzzy Logics with an Involutive Negation.Francesc Esteva, Lluís Godo, Petr Hájek & Mirko Navara - 2000 - Archive for Mathematical Logic 39 (2):103-124.
    Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...)
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  2.  15
    Residuated Logics Based on Strict Triangular Norms with an Involutive Negation.Petr Cintula, Erich Peter Klement, Radko Mesiar & Mirko Navara - 2006 - Mathematical Logic Quarterly 52 (3):269-282.
    In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t-norms and their dual t-conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t-norms which are different from the product logic.
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  3.  19
    Uncertainty and Dependence in Classical and Quantum Logic—the Role of Triangular Norms.Mirko Navara & Pavel Pták - 1999 - In Maria Luisa Dalla Chiara (ed.), Language, Quantum, Music. pp. 249--261.
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  4.  23
    Sufficient Triangular Norms in Many-Valued Logics with Standard Negation.Dan Butnariu, Erich Peter Klement, Radko Mesiar & Mirko Navara - 2005 - Archive for Mathematical Logic 44 (7):829-849.
    In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem, together with convenient sufficient conditions. We list several families of strict t-norms having this property and provide (...)
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  5.  3
    Generalised Kochen–Specker Theorem in Three Dimensions.Mirko Navara & Václav Voráček - 2021 - Foundations of Physics 51 (3):1-7.
    We show that there is no non-constant assignment of zeros and ones to points of a unit sphere in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^3$$\end{document} such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell–Kochen–Specker theorem, which proves the non-existence of hidden variables in quantum theories.
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