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  1. The Class of All Natural Implicative Expansions of Kleene’s Strong Logic Functionally Equivalent to Łkasiewicz’s 3-Valued Logic Ł3.Gemma Robles & José M. Méndez - 2020 - Journal of Logic, Language and Information 29 (3):349-374.
    We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova.
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  • A Remark on Functional Completeness of Binary Expansions of Kleene’s Strong 3-Valued Logic.Gemma Robles & José M. Méndez - forthcoming - Logic Journal of the IGPL.
    A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.
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  • Bochvar's Three-Valued Logic and Literal Paralogics: Their Lattice and Functional Equivalence.Alexander Karpenko & Natalya Tomova - 2017 - Logic and Logical Philosophy 26 (2):207-235.
    In the present paper, various features of the class of propositional literal paralogics are considered. Literal paralogics are logics in which the paraproperties such as paraconsistence, paracompleteness and paranormality, occur only at the level of literals; that is, formulas that are propositional letters or their iterated negations. We begin by analyzing Bochvar’s three-valued nonsense logic B3, which includes two isomorphs of the propositional classical logic CPC. The combination of these two ‘strong’ isomorphs leads to the construction of two famous paralogics (...)
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  • Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix with Two Designated Values.Gemma Robles & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (1):37-63.
    ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two (...)
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  • Paraconsistency and Sette’s Calculus P1.Janusz Ciuciura - 2015 - Logic and Logical Philosophy 24 (2).
  • A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes.José M. Méndez & Gemma Robles - 2015 - Logica Universalis 9 (4):501-522.
    The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 (...)
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