-
Some Extensions of mbCIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
-
Semantics of Non-deterministic Character for LFIsIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
-
Paraconsistent Set TheoryIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
-
9Fibring in the Leibniz HierarchyLogic Journal of the IGPL 15 (5-6): 475-501. 2007.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
-
86A graph-theoretic account of logicsJournal 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
-
108Non-deterministic algebraization of logics by swap structures1Logic 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
-
142AGM-Like Paraconsistent Belief ChangeLogic 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
-
6Errata and Addenda to ‘Finite non-deterministic semantics for some modal systems’Journal of Applied Non-Classical Logics 26 (4): 336-345. 2016.In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally point…Read more
-
Paraconsistency: The Logical Way to the InconsistentBulletin of Symbolic Logic 9 (3): 410-412. 2003.
-
11Xlth Latin American Symposium on Mathematical Logic Merida, Venezuela, 6-1 0 July, 1998Annals of Pure and Applied Logic 108 (1-3): 79-101. 2001.
-
13Modules 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
-
18Transfers between logics and their applicationsStudia Logica 72 (3): 367-400. 2002.In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attribute…Read more
-
12Fibring 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
-
159Recovery operators, paraconsistency and dualityLogic 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
-
97A model-theoretic analysis of Fidel-structures for mbCIn 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
-
91Maximality in finite-valued Lukasiewicz logics defined by order filtersJournal of Logic and Computation 29 (1): 125-156. 2019.In this paper we consider the logics
-
7Paraconsistent Logic: Consistency, Contradiction and NegationSpringer International Publishing. 2016.This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Para…Read more
-
112Modal logic S4 as a paraconsistent logic with a topological semanticsIn Caleiro Carlos, Dionisio Francisco, Gouveia Paula, Mateus Paulo & Rasga João (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
-
26Non-commutative topology and quantalesStudia 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
-
4New dimensions on translations between logicsLogica 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.
-
8Towards an hyperalgebraic theory of non-algebraizable logicsCLE 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
-
12Combining Valuations with Society SemanticsJournal 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
-
80A categorial approach to the combination of logicsManuscrito 22 (2): 69-94. 1999.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
-
11Logics of formal inconsistency arising from systems of fuzzy logicLogic 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
-
16On the set of intermediate logics between the truth- and degree-preserving Łukasiewicz logicsLogic Journal of the IGPL 24 (3): 288-320. 2016.
-
13On the way to a Wider model theory: Completeness theorems for first-order logics of formal inconsistencyReview 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
-
59Non-deterministic algebras and algebraization of logicsFilosofia da Linguagem E da Lógica (Philosophy of Language and Philosophy of Logic, in Portuguese). 2015.
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 |