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  1. Non-Deterministic Matrices: Theory and Applications to Algebraic Semantics.Ana Claudia de Jesus Golzio - 2022 - Bulletin of Symbolic Logic 28 (2):260-261.
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  • Towards an hyperalgebraic theory of non-algebraizable logics.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana C. Golzio - 2016 - CLE E-Prints 16 (4):1-27.
    Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics (...)
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  • Non-deterministic algebras and algebraization of logics.Ana Claudia Golzio & Marcelo E. Coniglio - 2015 - Filosofia da Linguagem E da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese).
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  • Formal inconsistency and evolutionary databases.Walter A. Carnielli, João Marcos & Sandra De Amo - 2000 - Logic and Logical Philosophy 8 (2):115-152.
    This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) (...)
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  • Pragmatic truth and approximation to truth.Irene Mikenberg, Newton C. A. Costa & Rolando Chuaqui - 1986 - Journal of Symbolic Logic 51 (1):201-221.
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  • Semantics of Non-deterministic Character for LFIs.Marcelo Coniglio & Walter Carnielli - 2016 - In Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation. Basel, Switzerland: Springer International Publishing.
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  • Modal logics with Belnapian truth values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.
    Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with respect to (...)
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  • Notes on N-lattices and constructive logic with strong negation.D. Vakarelov - 1977 - Studia Logica 36 (1-2):109-125.
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  • An alternative approach for Quasi-Truth.Marcelo E. Coniglio & Luiz H. Da Cruz Silvestrini - 2014 - Logic Journal of the IGPL 22 (2):387-410.
    In 1986, Mikenberg et al. introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present article, the notion of predicates as triples is recursively extended, in a natural way, to (...)
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  • (1 other version)Pragmatic Truth and Approximation to Truth.Mikenberg Irene, C. A. Da Costa Newton & Chuaqui Rolando - 1986 - Journal of Symbolic Logic 51 (1):201 - 221.
    There are several conceptions of truth, such as the classical correspondence conception, the coherence conception and the pragmatic conception. The classical correspondence conception, or Aristotelian conception, received a mathematical treatment in the hands of Tarski (cf. Tarski [1935] and [1944]), which was the starting point of a great progress in logic and in mathematics. In effect, Tarski's semantic ideas, especially his semantic characterization of truth, have exerted a major influence on various disciplines, besides logic and mathematics; for instance, linguistics, the (...)
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  • Non-deterministic Matrices and Modular Semantics of Rules.Arnon Avron - unknown
    We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straightforward way. Our main tool for this task is the use of finite Nmatrices, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set (...)
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  • Modal twist-structures over residuated lattices.H. Ono & U. Rivieccio - 2014 - Logic Journal of the IGPL 22 (3):440-457.
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  • (1 other version)On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov - 2009 - Studia Logica 91 (3):407-428.
    This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ t and ⊨ f, determined via truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN 3 as a twist-structure over the two-element Boolean algebra.
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  • Twist-structures semantics for the logics of the hierarchy InPk.Fernando M. Ramos & Víctor L. Fernández - 2009 - Journal of Applied Non-Classical Logics 19 (2):183-209.
    In this work we define, in a general way, an algebraic semantics for the logics of the hierarchy InPk. This semantics is defined by means of an alternative construction, with respect to the usual algebraic semantics, and it is known in the literature as Twist-structures semantics. Besides that, we modify such construction, defining the so-called ω-Twist-structures here. This adaptation allows us to prove adequacy theorems for every logic of the hierarchy InPk.
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  • (1 other version)On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov - 2009 - Studia Logica 91 (3):407 - 428.
    This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.
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  • (1 other version)Pragmatic truth and approximation to truth.Irene Mikenberg, Newton C. A. da Costa & Rolando Chuaqui - 1986 - Journal of Symbolic Logic 51 (1):201-221.
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  • (1 other version)Foundations of Mathematical Logic.William Craig - 1963 - Journal of Symbolic Logic 45 (2):377-378.
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