11 found
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  1.  17
    Cut-free Sequent Calculus and Natural Deduction for the Tetravalent Modal Logic.Martín Figallo - 2021 - Studia Logica 109 (6):1347-1373.
    The tetravalent modal logic is one of the two logics defined by Font and Rius :481–518, 2000) in connection with Monteiro’s tetravalent modal algebras. These logics are expansions of the well-known Belnap–Dunn’s four-valued logic that combine a many-valued character with a modal character. In fact, $${\mathcal {TML}}$$ TML is the logic that preserves degrees of truth with respect to tetravalent modal algebras. As Font and Rius observed, the connection between the logic $${\mathcal {TML}}$$ TML and the algebras is not so (...)
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  2.  59
    Hilbert-style Presentations of Two Logics Associated to Tetravalent Modal Algebras.Marcelo E. Coniglio & Martín Figallo - 2014 - Studia Logica 102 (3):525-539.
    We analyze the variety of A. Monteiro’s tetravalent modal algebras under the perspective of two logic systems naturally associated to it. Taking profit of the contrapositive implication introduced by A. Figallo and P. Landini, sound and complete Hilbert-style calculi for these logics are presented.
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  3.  32
    On the logic that preserves degrees of truth associated to involutive Stone algebras.Liliana M. Cantú & Martín Figallo - 2020 - Logic Journal of the IGPL 28 (5):1000-1020.
    Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, and (...)
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  4.  28
    Some model-theoretic results on the 3-valued paraconsistent first-order logic qciore.Marcelo E. Coniglio, Tadeo G. Gomez & Martín Figallo - forthcoming - Review of Symbolic Logic:1-41.
    The 3-valued paraconsistent logic Ciore was developed by Carnielli, Marcos and de Amo under the name LFI2, in the study of inconsistent databases from the point of view of logics of formal inconsistency (LFIs). They also considered a first-order version of Ciore called LFI2*. The logic Ciore enjoys extreme features concerning propagation and retropropagation of the consistency operator: a formula is consistent if and only if some of its subformulas is consistent. In addition, Ciore is algebraizable in the sense of (...)
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  5.  28
    Normal Proofs and Tableaux for the Font-Rius Tetravalent Modal Logic.Marcelo E. Coniglio & Martin Figallo - forthcoming - Logic and Logical Philosophy:1-33.
    Tetravalent modal logic (TML) was introduced by Font and Rius in 2000. It is an expansion of the Belnap-Dunn four-valued logic FOUR, a logical system that is well-known for the many applications found in several fields. Besides, TML is the logic that preserves degrees of truth with respect to Monteiro’s tetravalent modal algebras. Among other things, Font and Rius showed that TML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in a (...)
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  6.  23
    Proof-Theoretic Aspects of Paraconsistency with Strong Consistency Operator.Victoria Arce Pistone & Martín Figallo - forthcoming - Studia Logica:1-38.
    In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (_LFI_) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such _LFI_s. Here, we intend to make a first step in this direction. On the other hand, the logic _Ciore_ was developed to provide new logical systems in the study of inconsistent databases from the point of view of _LFI_s. (...)
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  7.  12
    On a Four-Valued Logic of Formal Inconsistency and Formal Undeterminedness.Marcelo E. Coniglio, G. T. Gomez–Pereira & Martín Figallo - forthcoming - Studia Logica:1-42.
    Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce a four-valued expansion (...)
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  8.  31
    Symmetric operators on modal pseudocomplemented De Morgan algebras.Aldo Figallo-Orellano, Alicia Ziliani & Martín Figallo - 2017 - Logic Journal of the IGPL 25 (4):496-511.
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  9.  21
    A Formal Framework for Hypersequent Calculi and Their Fibring.Marcelo E. Coniglio & Martín Figallo - 2014 - In Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, Volume I. New York: Springer. pp. 73-93.
    Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between logics (...)
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  10.  26
    On a four-valued modal logic with deductive implication.Marcelo E. Coniglio & Martín Figallo - 2014 - Bulletin of the Section of Logic 43 (1/2):1-18.
    In this paper we propose to enrich the four-valued modal logic associated to Monteiro's Tetravalent modal algebras (TMAs) with a deductive implication, that is, such that the Deduction Meta-theorem holds in the resulting logic. All this lead us to establish some new connections between TMAs, symmetric (or involutive) Boolean algebras, and modal algebras for extensions of S5, as well as their logical counterparts.
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  11.  23
    Correction to: Cut-free Sequent Calculus and Natural Deduction for the Tetravalent Modal Logic.Martín Figallo - 2022 - Studia Logica 110 (3):879-879.