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
  •  501
    Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account
    with Walter Carnielli and David Fuenmayor
    Review of Symbolic Logic 15 (3): 771-806. 2022.
    One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative resu…Read more
  •  439
    AGM-Like Paraconsistent Belief Change
    with Rafael R. Testa and Marcio M. Ribeiro
    Logic Journal of the IGPL 25 (4): 632-672. 2017.
    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 …Read more
  •  387
    Recovery operators, paraconsistency and duality
    Logic Journal of the IGPL 28 (5): 624-656. 2020.
    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 parac…Read more
  •  375
    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
  •  371
    A model-theoretic analysis of Fidel-structures for mbC
    In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 189-216. 2019.
    In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theo…Read more
  •  363
    Swap structures semantics for Ivlev-like modal logics
    with Ana Claudia Golzio
    Soft Computing 23 (7): 2243-2254. 2019.
    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 tec…Read more
  •  362
    Modal logic S4 as a paraconsistent logic with a topological semantics
    with Leonardo Prieto-Sanabria
    In Carlos Caleiro, Francisco Dionisio, Paula Gouveia, Paulo Mateus & João Rasga (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas, College Publications. pp. 171-196. 2017.
    In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This c…Read more
  •  356
    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
  •  346
    Twist-Valued Models for Three-valued Paraconsistent Set Theory
    Logic and Logical Philosophy 30 (2): 187-226. 2021.
    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…Read more
  •  325
    A graph-theoretic account of logics
    with A. Sernadas, C. Sernadas, and J. Rasga
    Journal of Logic and Computation 19 (6): 1281-1320. 2009.
    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 conseq…Read more
  •  317
    Genuine paracomplete logics
    with Verónica Borja Macías and Alejandro Hernández-Tello
    Logic Journal of the IGPL 31 (5): 961-987. 2023.
    In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws $\varphi,\neg \varphi \vdash \psi$ and $\vdash \neg (\varphi \wedge \neg \varphi)$. In that paper, the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above-mentioned are $\vdash \varphi, \neg \varphi$ and $\neg …Read more
  •  313
    First-order swap structures semantics for some Logics of Formal Inconsistency
    with Aldo Figallo-Orellano and Ana Claudia Golzio
    Journal of Logic and Computation 30 (6): 1257-1290. 2020.
    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproac…Read more
  •  307
    Non-deterministic algebraization of logics by swap structures1
    with Aldo Figallo-Orellano and Ana Claudia Golzio
    Logic Journal of the IGPL 28 (5): 1021-1059. 2020.
    Multialgebras 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 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 …Read more
  •  291
    Maximality in finite-valued Lukasiewicz logics defined by order filters
    with Francesc Esteva, Joan Gispert, and Lluis Godo
    Journal of Logic and Computation 29 (1): 125-156. 2019.
    In this paper we consider the logics
  •  288
    Modal logic with non-deterministic semantics: Part I—Propositional case
    with Luis Fariñas del Cerro and Newton Peron
    Logic 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 (which he called quasi-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 (T) axiom was replaced by the deontic…Read more
  •  283
    On formal aspects of the epistemic approach to paraconsistency
    In Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain, College Publications. pp. 48-74. 2018.
    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 a…Read more
  •  261
    Non-deterministic algebras and algebraization of logics
    with Ana Claudia Golzio
    Filosofia da Linguagem E da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese). 2015.
  •  250
    Paracomplete logics which are dual to the paraconsistent logics L3A and L3B
    with Alejandro Hernández-Tello and Verónica Borja-Macı́as
    LANMR 2019: Proceedings of the 12th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning. 2020.
    In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting t…Read more
  •  211
    Some investigations on mbC and mCi
    with Tarcísio G. Rodrígues
    In Cezar A. Mortari (ed.), Tópicos de lógicas não clássicas, Nel/ufsc. pp. 11-70. 2014.
  •  193
    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,
  •  180
    On the expressive power of Łukasiewicz square operator
    with Francesc Esteva, Tommaso Flaminio, and Lluis Godo
    Journal of Logic and Computation. forthcoming.
    The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the Ł…Read more
  •  177
    G'3 as the logic of modal 3-valued Heyting algebras
    with Aldo Figallo-Orellano, Alejandro Hernández-Tello, and Miguel Perez-Gaspar
    IfCoLog Journal of Logics and Their Applications 9 (1): 175-197. 2022.
    In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel 3-valued logic G3. From this, the three logics coincide up-to language, taking into acc…Read more
  •  170
    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
  •  165
    Weakly Free Multialgebras
    with Guilherme V. Toledo
    Bulletin of the Section of Logic 51 (1): 109-141. 2022.
    In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a…Read more
  •  103
    Fibring non-truth-functional logics: Completeness preservation
    with C. Caleiro, W. A. Carnielli, A. Sernadas, and C. Sernadas
    Journal 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
  •  99
    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.
  •  81
    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
  •  48
    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
  •  48
    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