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  1. A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics.Natalya Tomova - 2021 - Bulletin of the Section of Logic 50 (1):35-53.
    In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two four-element lattices included in the upper semi-lattice. Functional properties and sets of tautologies of corresponding literal-paraconsistent-paracomplete matrices are investigated. Among the considered matrices there are the (...)
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  • History of logic in Latin America: the case of Ayda Ignez Arruda.Gisele Dalva Secco & Miguel Alvarez Lisboa - 2022 - British Journal for the History of Philosophy 30 (2):384-408.
    Ayda Ignez Arruda was a key figure in the development of the Brazilian school of Paraconsistent logic and the first person to write a historical survey of the field. Despite her importa...
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  • Literal‐paraconsistent and literal‐paracomplete matrices.Renato A. Lewin & Irene F. Mikenberg - 2006 - Mathematical Logic Quarterly 52 (5):478-493.
    We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples.
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  • First order theory for literal‐paraconsistent and literal‐paracomplete matrices.Renato A. Lewin & Irene F. Mikenberg - 2010 - Mathematical Logic Quarterly 56 (4):425-433.
    In this paper a first order theory for the logics defined through literal paraconsistent-paracomplete matrices is developed. These logics are intended to model situations in which the ground level information may be contradictory or incomplete, but it is treated within a classical framework. This means that literal formulas, i.e. atomic formulas and their iterated negations, may behave poorly specially regarding their negations, but more complex formulas, i.e. formulas that include a binary connective are well behaved. This situation may and does (...)
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  • Algebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices.Eduardo Hirsh & Renato A. Lewin - 2008 - Mathematical Logic Quarterly 54 (2):153-166.
    We study the algebraizability of the logics constructed using literal-paraconsistent and literal-paracomplete matrices described by Lewin and Mikenberg in [11], proving that they are all algebraizable in the sense of Blok and Pigozzi in [3] but not finitely algebraizable. A characterization of the finitely algebraizable logics defined by LPP-matrices is given.We also make an algebraic study of the equivalent algebraic semantics of the logics associated to the matrices ℳ32,2, ℳ32,1, ℳ31,1, ℳ31,3, and ℳ4 appearing in [11] proving that they are (...)
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