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4In a previous article we introduced the concept of restricted Nmatrices (in short, RNmatrices), which generalize non-deterministic (in short, Nmatrices) in the following sense: a RNmatrix is a Nmatrix together with a subset of valuations over it, from which the consequence relation is defined. Within this semantical framework we have characterized each paraconsistent logic Cn in the hierarchy of da Costa by means of a (n+2)-valued RNmatrix, which also provides a relatively simple decision proced…Read more
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36Towards a stronger notion of translation between logicsManuscrito 28 (2): 231-262. 2005.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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58An alternative approach for Quasi-TruthLogic Journal of the IGPL 22 (2): 387-410. 2014.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 natur…Read more
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231Some investigations on mbC and mCiIn Cezar A. Mortari (ed.), Tópicos de lógicas não clássicas, Nel/ufsc. pp. 11-70. 2014.
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73Modal Extensions of Sub-classical Logics for Recovering Classical LogicLogica Universalis 7 (1): 71-86. 2013.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 allo…Read more
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90A Paraconsistentist Approach to Chisholm's ParadoxPrincipia: An International Journal of Epistemology 13 (3): 299-326. 2009.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 …Read more
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25Dugundji’s Theorem RevisitedLogica Universalis 8 (3-4): 407-422. 2014.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 sho…Read more
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31Modal logic with non-deterministic semantics: Part I—Propositional caseLogic Journal of the IGPL 28 (3): 281-315. 2020.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 eve…Read more
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36On discourses addressed by infidel logiciansIn Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications, Springer. pp. 27--41. 2013.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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23To distribute or not to distribute?Logic Journal of the IGPL 19 (4): 466-583. 2011.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. A de…Read more
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113Fibring non-truth-functional logics: Completeness preservationJournal of Logic, Language and Information 12 (2): 183-211. 2003.Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that th…Read more
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27Modules in the category of sheaves over quantalesAnnals of Pure and Applied Logic 108 (1-3): 103-136. 2001.In this paper we develop the elementary theory of modules in the category Sh of sheaves over right-sided idempotent quantales. The main ingredient is the construction of a logic sound for Sh . As an application we prove that in Sh , a finitely generated projective module is free , a result that is relevant to the study of representation of non-commutative C ∗ -algebras
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Aristóteles, paraconsistentismo e a tradição budistaO Que Nos Faz Pensar 23 163-175. 2008.This paper 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 reasonin…Read more
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |