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  1. 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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  • A basic quasi-Boolean logic of intuitionistic character.Gemma Robles - 2020 - Journal of Applied Non-Classical Logics 30 (4):291-311.
    The logic B M is Sylvan and Plumwood's minimal De Morgan logic. The aim of this paper is to investigate extensions of B M endowed with a quasi-Boolean negation of intuitionistic character included...
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  • A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3DH.Gemma Robles & José M. Méndez - 2020 - Journal of Logic, Language and Information 30 (1):117-138.
    The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic BM with a dual intuitionistic negation of the type Sylvan defined for the extension CCω of da Costa’s paraconsistent logic Cω. We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3DH, the expansion of G3+ with a dual intuitionistic negation of the kind considered by Sylvan (G3+ is the positive fragment of Gödelian (...)
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  • A Lindström-style theorem for finitary propositional weak entailment languages with absurdity.Guillermo Badia - 2016 - Logic Journal of the IGPL 24 (2):115-137.
    Following a result by De Rijke for modal logic, it is shown that the basic weak entailment model-theoretic language with absurdity is the maximal model-theoretic language having the finite occurrence property, preservation under relevant directed bisimulations and the finite depth property. This can be seen as a generalized preservation theorem characterizing propositional weak entailment formulas among formulas of other model-theoretic languages.
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  • A Note on Gödel-Dummet Logic LC.Gemma Robles & José M. Méndez - 2021 - Bulletin of the Section of Logic 50 (3):325-335.
    Let \ be distintict wffs, \ being an odd number equal to or greater than 1. Intuitionistic Propositional Logic IPC plus the axiom \\vee...\vee \vee \) is equivalent to Gödel-Dummett logic LC. However, if \ is an even number equal to or greater than 2, IPC plus the said axiom is a sublogic of LC.
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  • Equivalence among RC-type paraconsistent logics.Mauricio Osorio & José Abel Castellanos Joo - 2017 - Logic Journal of the IGPL 25 (2):239-252.
    In this article we review several paraconsistent logics from different authors to ‘close the gaps’ between them. Since paraconsistent logics is a broad area of research, it is possible that equivalent paraconsistent logics have different names. What we meant is that we provide connections between the logics studied comparing their different semantical approaches for a near future be able to obtain missing semantical characterization of different logics. We are introducing the term RC-type logics to denote a class of logics that (...)
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  • A 2 Set-Up Binary Routley Semantics for Gödelian 3-Valued Logic G3 and Its Paraconsistent Counterpart G3\(_\text{Ł}^\leq\). [REVIEW]Gemma Robles & José M. Méndez - 2022 - Bulletin of the Section of Logic 51 (4):487-505.
    G3 is Gödelian 3-valued logic, G3\(_\text{Ł}^\leq\) is its paraconsistent counterpart and G3\(_\text{Ł}^1\) is a strong extension of G3\(_\text{Ł}^\leq\). The aim of this paper is to endow each one of the logics just mentioned with a 2 set-up binary Routley semantics.
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