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  1. Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
    This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.
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  • Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz's 3-Valued Logic Ł3.Gemma Robles, Francisco Salto & José M. Méndez - 2013 - Journal of Philosophical Logic (2-3):1-30.
    Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley (...)
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  • Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
    This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.
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  • Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz’s 3-Valued Logic Ł3.Gemma Robles, Francisco Salto & José M. Méndez - 2014 - Journal of Philosophical Logic 43 (2-3):303-332.
    Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive (...)
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  • Suszko’s Problem: Mixed Consequence and Compositionality.Emmanuel Chemla & Paul Égré - 2019 - Review of Symbolic Logic 12 (4):736-767.
    Suszko’s problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two truth values. Malinowski showed that this number can equal three if some of Tarski’s structural constraints are relaxed. By so doing, Malinowski introduced a case of so-called mixed consequence, allowing the notion of a designated value to vary between the premises and the conclusions of an argument. (...)
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  • Many-Valued and Kripke Semantics.Jean-Yves Béziau - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 89--101.
  • The Critics of Paraconsistency and of Many-Valuedness and the Geometry of Oppositions.Alessio Moretti - 2010 - Logic and Logical Philosophy 19 (1-2):63-94.
    In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition (...)
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  • Suszko’s Thesis, Inferential Many-Valuedness, and the Notion of a Logical System.Heinrich Wansing & Yaroslav Shramko - 2008 - Studia Logica 88 (3):405-429.
    According to Suszko's Thesis, there are but two logical values, true and false. In this paper, R. Suszko's, G. Malinowski's, and M. Tsuji's analyses of logical two-valuedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation.
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  • Multi-Valued Semantics: Why and How.Arnon Avron - 2009 - Studia Logica 92 (2):163-182.
    According to Suszko's Thesis,any multi-valued semantics for a logical system can be replaced by an equivalent bivalent one. Moreover: bivalent semantics for families of logics can frequently be developed in a modular way. On the other hand bivalent semantics usually lacks the crucial property of analycity, a property which is guaranteed for the semantics of multi-valued matrices. We show that one can get both modularity and analycity by using the semantic framework of multi-valued non-deterministic matrices. We further show that for (...)
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  • Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.
    This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the (...)
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  • Two-Valued Weak Kleene Logics.Bruno da Ré & Damian Szmuc - 2019 - Manuscrito 42 (1):1-43.
    In the literature, Weak Kleene logics are usually taken as three-valued logics. However, Suszko has challenged the main idea of many-valued logic claiming that every logic can be presented in a two-valued fashion. In this paper, we provide two-valued semantics for the Weak Kleene logics and for a number of four-valued subsystems of them. We do the same for the so-called Logics of Nonsense, which are extensions of the Weak Kleene logics with unary operators that allow looking at them as (...)
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  • Louis Joly as a Platonist Painter?Roger Pouivet - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 337--341.
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