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
  •  12
    Paraconsistency: The Logical Way to the Inconsistent
    with Walter Alexandr Carnielli and Itala Maria Lof D'ottaviano
    Marcel Dekker. 2002.
    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.
  •  434
    Paraconsistent Belief Revision based on a formal consistency operator
    with Rafael R. Testa and Márcio M. Ribeiro
    CLE E-Prints 15 (8): 01-11. 2015.
    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 necessa…Read more
  •  57
    An alternative approach for Quasi-Truth
    Logic 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
  •  211
    On graph-theoretic fibring of logics
    with A. Sernadas, C. Sernadas, and J. Rasga
    Journal of Logic and Computation 19 (6): 1321-1357. 2009.
    A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive syste…Read more
  •  51
    Hilbert-style Presentations of Two Logics Associated to Tetravalent Modal Algebras
    with Martín Figallo
    Studia Logica 102 (3): 525-539. 2014.
    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
  •  55
    Combining logics
    Stanford Encyclopedia of Philosophy. 2008.
    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) a…Read more
  •  31
    On the ordered Dedekind real numbers in toposes
    with Luís A. Sbardellini
    In Edward H. Haeusler, Wagner Sanz & Bruno Lopes (eds.), Why is this a Proof? Festschrift for Luiz Carlos Pereira, College Publications. pp. 87-105. 2015.
    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…Read more
  •  36
    Towards a stronger notion of translation between logics
    Manuscrito 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
  •  115
    A Paraconsistentist Approach to Chisholm's Paradox
    with Newton Marques Peron
    Principia: 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
  •  1
    Two's Company: The humbug of many logical values
    with Carlos Caleiro, Walter Carnielli, and João Marcos
    In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic, Birkhäuser Verlog. pp. 169-189. 2005.
    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 than…Read more
  •  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