9 found
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  1.  46
    On a Definition of a Variety of Monadic ℓ-Groups.José Luis Castiglioni, Renato A. Lewin & Marta Sagastume - 2014 - Studia Logica 102 (1):67-92.
    In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor ${{\mathsf{K}^\bullet}}$ , motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case (...)
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  2.  52
    On the algebraizability of annotated logics.Renato A. Lewin, Irene F. Mikenberg & María G. Schwarze - 1997 - Studia Logica 59 (3):359-386.
    Annotated logics were introduced by V.S. Subrahmanian as logical foundations for computer programming. One of the difficulties of these systems from the logical point of view is that they are not structural, i.e., their consequence relations are not closed under substitutions. In this paper we give systems of annotated logics that are equivalent to those of Subrahmanian in the sense that everything provable in one type of system has a translation that is provable in the other. Moreover these new systems (...)
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  3.  23
    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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  4.  26
    The logic of equilibrium and abelian lattice ordered groups.Adriana Galli, Renato A. Lewin & Marta Sagastume - 2004 - Archive for Mathematical Logic 43 (2):141-158.
    We introduce a deductive system Bal which models the logic of balance of opposing forces or of balance between conflicting evidence or influences. ‘‘Truth values’’ are interpreted as deviations from a state of equilibrium, so in this sense, the theorems of Bal are to be interpreted as balanced statements, for which reason there is only one distinguished truth value, namely the one that represents equilibrium. The main results are that the system Bal is algebraizable in the sense of [5] and (...)
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  5.  39
    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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  6.  26
    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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  7.  30
    Involutions defined by monadic terms.Renato A. Lewin - 1988 - Studia Logica 47 (4):387 - 389.
    We prove that there are two involutions defined by monadic terms that characterize Monadic Algebras. We further prove that the variety of Monadic Algebras is the smallest variety of Interior Algebras where these involutions give rise to an interpretation from the variety of Bounded Distributive Lattices into it.
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  8.  28
    Interpretations into monadic algebras.Renato A. Lewin - 1987 - Studia Logica 46 (4):329 - 342.
    In [3], O. C. García and W. Taylor make an in depth study of the lattice of interpretability types of varieties first introduced by W. Neumann [5]. In this lattice several varieties are identified so in order to distinguish them and understand the fine structure of the lattice, we propose the study of the interpretations between them, in particular, how many there are and what these are. We prove, among other things, that there are eight interpretations from the variety of (...)
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  9.  71
    P1 algebras.Renato A. Lewin, Irene F. Mikenberg & Maria G. Schwarze - 1994 - Studia Logica 53 (1):21 - 28.
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