University of São Paulo
Department of Philosophy, Languages and Literature, and Human Sciences
PhD, 1997
Campinas, São Paulo, Brazil
Areas of Specialization
Logic and Philosophy of Logic
Areas of Interest
Logic and Philosophy of Logic
  •  14
    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 intro…Read more
  •  51
    Non-commutative topology and quantales
    with Francisco Miraglia
    Studia Logica 65 (2): 223-236. 2000.
    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, which permits us to ex…Read more
  •  71
    New dimensions on translations between logics
    with Walter A. Carnielli and Itala M. L. D’Ottaviano
    Logica Universalis 3 (1): 1-18. 2009.
    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.
  •  8
    Towards an hyperalgebraic theory of non-algebraizable logics
    with Aldo Figallo-Orellano and Ana C. Golzio
    CLE E-Prints 16 (4): 1-27. 2016.
    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. …Read more
  •  28
    Combining Valuations with Society Semantics
    with Víctor L. Fernández
    Journal of Applied Non-Classical Logics 13 (1): 21-46. 2003.
    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 hierarch…Read more
  •  46
    Equality in linear logic
    with Francisco Miraglia
    Logique Et Analyse 39 (153-154): 113-151. 1996.
  •  401
    In this paper we propose a very general denition 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, sin…Read more
  •  45
    Logics of formal inconsistency arising from systems of fuzzy logic
    with Francesc Esteva and Lluís Godo
    Logic Journal of the IGPL 22 (6): 880-904. 2014.
    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…Read more
  •  30
  •  39
    On the way to a Wider model theory: Completeness theorems for first-order logics of formal inconsistency
    with Walter Carnielli, Rodrigo Podiacki, and Tarcísio Rodrigues
    Review of Symbolic Logic 7 (3): 548-578. 2014.
    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 logi…Read more
  •  300
    Non-deterministic algebras and algebraization of logics
    Filosofia da Linguagem E da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese). 2015.
  •  227
    Some results on ordered structures in toposes
    with Luís Sbardellini
    Reports on Mathematical Logic 181-198. 2006.
    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,
  •  47
    Finite non-deterministic semantics for some modal systems
    with Luis Fariñas del Cerro and Newton M. Peron
    Journal of Applied Non-Classical Logics 25 (1): 20-45. 2015.
    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 anothe…Read more
  •  45
    An Event on Brazilian Logic: Proceedings of the XIII Brazilian Logic Conference
    with Walter Carnielli and Itala D'ottaviano
    Logic Journal of the IGPL 13 (1): 1-3. 2005.
    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.
  •  21
    On a four-valued modal logic with deductive implication
    with Martín Figallo
    Bulletin of the Section of Logic 43 (1/2): 1-18. 2014.
    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.
  •  55
    Recovering a logic from its fragments by meta-fibring
    Logica Universalis 1 (2): 377-416. 2007.
    .  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 fea…Read more