44 found
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Marcelo E. Coniglio [35]Marcelo Coniglio [8]Marcelo Esteban Coniglio [3]
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Marcelo E. Coniglio
University of Campinas
Marcelo Coniglio
University of Campinas
  1.  40
    Non-Deterministic Algebraization of Logics by Swap Structures.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - forthcoming - Logic Journal of the IGPL.
    Multialgebras (or hyperalgebras or non-deterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of (...)
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  2.  13
    Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo E. Coniglio - 2016 - Basel, Switzerland: Springer International Publishing.
  3.  71
    Swap Structures Semantics for Ivlev-Like Modal Logics.Marcelo E. Coniglio & Ana Claudia Golzio - forthcoming - Soft Computing.
    In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...)
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  4.  22
    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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  5.  32
    On Formal Aspects of the Epistemic Approach to Paraconsistency.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2018 - In Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain. London: College Publications. pp. 48-74.
    This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...)
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  6.  75
    A Graph-Theoretic Account of Logics.A. Sernadas, C. Sernadas, J. Rasga & Marcelo E. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1281-1320.
    A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...)
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  7. Two's Company: The Humbug of Many Logical Values.Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos - 2005 - In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlag. pp. 169-189.
    The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more (...)
     
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  8.  25
    Finite Non-Deterministic Semantics for Some Modal Systems.Marcelo E. Coniglio, Luis Fariñas del Cerro & Newton M. Peron - 2015 - Journal of Applied Non-Classical Logics 25 (1):20-45.
    Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of the paper (...)
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  9.  86
    New Dimensions on Translations Between Logics.Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D’Ottaviano - 2009 - Logica Universalis 3 (1):1-18.
    After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
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  10. 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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  11.  29
    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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  12.  19
    On the Way to a Wider Model Theory: Completeness Theorems for First-Order Logics of Formal Inconsistency.Walter Carnielli, Marcelo E. Coniglio, Rodrigo Podiacki & Tarcísio Rodrigues - 2014 - Review of Symbolic Logic 7 (3):548-578.
    This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logics, and can be easily extended to a large family of quantified paraconsistent (...)
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  13. Paraconsistent Belief Revision Based on a Formal Consistency Operator.Rafael R. Testa, Marcelo E. Coniglio & Márcio M. Ribeiro - 2015 - CLE E-Prints 15 (8):01-11.
    In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion of formal (...)
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  14.  15
    Logics of Formal Inconsistency Arising From Systems of Fuzzy Logic.Marcelo E. Coniglio, Francesc Esteva & Lluís Godo - 2014 - Logic Journal of the IGPL 22 (6):880-904.
    This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of (...)
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  15. 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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  16.  69
    Recovery Operators, Paraconsistency and Duality.Walter A. Carnielli, Marcelo E. Coniglio & Abilio Rodrigues Filho - forthcoming - Logic Journal of the IGPL.
    There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...)
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  17. A Categorial Approach to the Combination of Logics.Walter A. Carnielli & Marcelo E. Coniglio - 1999 - Manuscrito 22 (2):69-94.
    In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...)
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  18.  7
    Dugundji’s Theorem Revisited.Marcelo E. Coniglio & Newton M. Peron - 2014 - Logica Universalis 8 (3-4):407-422.
    In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal logic (...)
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  19.  3
    Recovery Operators, Paraconsistency and Duality.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - forthcoming - Logic Journal of the IGPL.
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  20.  3
    Modal Logic with Non-Deterministic Semantics: Part I—Propositional Case.Marcelo E. Coniglio, Fariñas Del Cerro Luis & Marques Peron Newton - forthcoming - Logic Journal of the IGPL.
    Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices, in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the axiom was replaced by the deontic axiom. In this paper, we propose even weaker systems, by eliminating (...)
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  21.  16
    On Discourses Addressed by Infidel Logicians.Walter Carnielli & Marcelo E. Coniglio - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 27--41.
    We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.
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  22.  7
    On the Set of Intermediate Logics Between the Truth- and Degree-Preserving Łukasiewicz Logics.Marcelo E. Coniglio, Francesc Esteva & Lluís Godo - 2016 - Logic Journal of the IGPL 24 (3):288-320.
  23.  10
    Combining Valuations with Society Semantics.Víctor L. Fernández & Marcelo E. Coniglio - 2003 - Journal of Applied Non-Classical Logics 13 (1):21-46.
    Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to many-valued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called Pn and a hierarchy (...)
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  24.  42
    Recovering a Logic From its Fragments by Meta-Fibring.Marcelo Esteban Coniglio - 2007 - Logica Universalis 1 (2):377-416.
    . In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multiple-conclusion consequence relations and sequent calculi, respectively, are introduced. The main feature (...)
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  25.  55
    AGM-Like Paraconsistent Belief Change.Rafael R. Testa, Marcelo E. Coniglio & Marcio M. Ribeiro - 2017 - Logic Journal of the IGPL 25 (4):632-672.
    Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...)
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  26.  92
    Some Investigations on mbC and mCi.Marcelo E. Coniglio & Tarcísio G. Rodrígues - 2014 - In Cezar A. Mortari (ed.), Tópicos de lógicas não clássicas. NEL/UFSC. pp. 11-70.
  27.  29
    Combining Logics.Walter Carnielli & Marcelo E. Coniglio - 2008 - Stanford Encyclopedia of Philosophy.
    Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...)
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  28.  70
    Some Results on Ordered Structures in Toposes.Luís Sbardellini & Marcelo Coniglio - 2006 - Reports on Mathematical Logic:181-198.
    A topos version of Cantor’s back and forth theorem is established and used to prove that the ordered structure of the rational numbers (Q, <) is homogeneous in any topos with natural numbers object. The notion of effective homogeneity is introduced, and it is shown that (Q, <) is a minimal effectively homogeneous structure, that is, it can be embedded in every other effectively homogeneous ordered structure.
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  29.  3
    Fibring in the Leibniz Hierarchy.Victor Fernández & Marcelo Coniglio - 2007 - Logic Journal of the IGPL 15 (5-6):475-501.
    This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.
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  30.  24
    An Event on Brazilian Logic: Proceedings of the XIII Brazilian Logic Conference.Walter Carnielli, Marcelo Coniglio & Itala D'ottaviano - 2005 - Logic Journal of the IGPL 13 (1):1-3.
    This volume corresponds to the Proceedings of the XIII Brazilian Logic Conference held at the CLE - Centre for Logic, Epistemology and the History of Science in Campinas, SP, Brazil from May 26-30, 2003 under the auspices of the SBL - Brazilian Logic Society and the ASL - Association for Symbolic Logic.
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  31.  44
    Equality in Linear Logic.Marcelo E. Coniglio & Francisco Miraglia - 1996 - Logique Et Analyse 39 (153-154):113-151.
  32.  1
    Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - manuscript
    Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...)
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  33.  55
    Modal Extensions of Sub-Classical Logics for Recovering Classical Logic.Marcelo E. Coniglio & Newton M. Peron - 2013 - Logica Universalis 7 (1):71-86.
    In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to (...)
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  34.  33
    Towards a Stronger Notion of Translation Between Logics.Marcelo Coniglio - 2005 - Manuscrito 28 (2):231-262.
    The concept of translation between logics was originally introduced in order to prove the consistency of a logic system in terms of the consistency of another logic system. The idea behind this is to interpret a logic into another one. In this survey we address the following question: Which logical properties a logic translation should preserve? Several approaches to the concept of translation between logics are discussed and analyzed.
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  35. Ouro Preto (Minas Gerais), Brazil July 29–August 1, 2003.France Xii, Marcelo Coniglio, Gilles Dowek, Jouko Väänanen, Renata Wassermann, Eric Allender, Jean-Baptiste Joinet & Dale Miller - 2004 - Bulletin of Symbolic Logic 10 (2).
  36.  14
    On the Ordered Dedekind Real Numbers in Toposes.Marcelo E. Coniglio & Luís A. Sbardellini - 2015 - In Edward H. Haeusler, Wagner Sanz & Bruno Lopes (eds.), Why is this a Proof? Festschrift for Luiz Carlos Pereira. College Publications. pp. 87-105.
    In 1996, W. Veldman and F. Waaldijk present a constructive (intuitionistic) proof for the homogeneity of the ordered structure of the Cauchy real numbers, and so this result holds in any topos with natural number object. However, it is well known that the real numbers objects obtained by the traditional constructions of Cauchy sequences and Dedekind cuts are not necessarily isomorphic in an arbitrary topos with natural numbers object. Consequently, Veldman and Waaldijk's result does not apply to the ordered structure (...)
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  37.  12
    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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  38.  11
    To Distribute or Not to Distribute?Jean-Yves Béziau & Marcelo E. Coniglio - 2011 - Logic Journal of the IGPL 19 (4):466-583.
    In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. (...)
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  39.  22
    Non-Commutative Topology and Quantales.Marcelo E. Coniglio & Francisco Miraglia - 2000 - Studia Logica 65 (2):223-236.
    The relationship between q-spaces (c.f. [9]) and quantum spaces (c.f. [5]) is studied, proving that both models coincide in the case of Spec A, the spectrum of a non-commutative C*-algebra A. It is shown that a sober T 1 quantum space is a classical topological space. This difficulty is circumvented through a new definition of point in a quantale. With this new definition, it is proved that Lid A has enough points. A notion of orthogonality in quantum spaces is introduced, (...)
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  40.  6
    A Formal Framework for Hypersequent Calculi and Their Fibring.Marcelo E. Coniglio & Martín Figallo - 2015 - In Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, Volume I. 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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  41. Aristóteles, paraconsistentismo e a tradição budista.Walter Carnielli & Marcelo Coniglio - 2008 - O Que Nos Faz Pensar 23:163-175.
    This paper (in Portuguese) defends that the both the Buddhist tradition and the Aristotelian allow us to think of the distinction between to reason with contradictions and to accept them, understanding ' accept a contradiction ' by taking it as consistent. From this viewpoint, none of two would disagree with most contemporary paraconsistent views. -/- The conclusions are, thus, that, firstly, there is no compelling reason to endorse any kind of metaphysical dialetheism, and, second, that a coherent form of reasoning (...)
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  42. Filosofia da Linguagem e da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese).Marcelo Carvalho, Celso Braida, João Carlos Salles & Marcelo E. Coniglio (eds.) - 2015 - ANPOF.
  43.  4
    Paraconsistency the Logical Way to the Inconsistent : Proceedings of the World Congress Held in São Paulo.Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'ottaviano - 2002 - Marcel Dekker.
    This impressive compilation of the material presented at the Second World Congress on Paraconsistency held in Juquehy-Sao Sebastião, São Paulo, Brazil, represents an integrated discussion of all major topics in the area of paraconsistent logic---highlighting philosophical and historical aspects, major developments and real-world applications.
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  44.  70
    A Paraconsistentist Approach to Chisholm's Paradox.Marcelo Esteban Coniglio & Newton Marques Peron - 2009 - Principia: An International Journal of Epistemology 13 (3):299-326.
    The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do (...)
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