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Summary

In classical logic, every sentence is entailed by a contradiction: A and ¬A together entail B, for any sentences A and B whatsoever. This principle is often known as ex contradictione sequitur quodlibet (from a contradiction, everything follows), or the explosion principle. In paraconsistent logic, by contrast, this principle does not hold: arbitrary contradictions do not paraconsistently entail every sentence. Accordingly, paraconsistent logics are said to be contradiction tolerant. Semantics for paraconsistent logics can be given in a number of ways, but a common theme is that a sentence is allowed to be both true and false simultaneously. This can be achieved by introducing a third truth-value, thought of as both true and false; alternatively, it can be achieved (in the propositional case) be replacing the usual valuation function with a relation between sentences and the usual truth-values, true and false, so that a sentence may be related to either or both of these. Those who think there really are true contradictions are dialethists. Not all paraconsistent logicians are dialethists: some present paraconsistent logic as a better notion of what follows from what, or as a way to reason about inconsistent data.

Key works Asenjo 1966 and da Costa 1974 develop the Logic of Paradox (based on theor earlier work on paraconsistency in the 1950s)Priest et al 1989 is a classic early collection of papers. Priest 1987 is the classic philosophical defense of paraconsistent logic (and of dialethism). 
Introductions da Costa & Bueno 2010 and Priest 2008 are good encyclopaedia entries on paraconsistent logic. The introduction to Priest 2005 is a clear statement of the case for paraconsistent logics; chapter 7 of Priest 2001 gives basic logical details of a few paraconsistent logics.
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  1. Paradoxes of Logical Equivalence and Identity.Andrew Bacon - 2013 - Topoi (1):1-10.
    In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.
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  2. Inconsistency in Empirical Science.Luis Felipe Bartolo Alegre - manuscript
    This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.
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  3. A logically neutral(ish) framework for empirical testing.Luis Felipe Bartolo Alegre - manuscript
    In this paper, I propose a formal framework for modelling the process of testing empirical statements, hypotheses, theories, and research programmes. Unlike the diverse forms of falsificationism, this framework does not require any commitment to classical logic or to any specific system of logic, as it aims to be useful regardless of the logic we presuppose. On this regard, the paper will focus on how this framework applies to two logical contexts: the classical and the paraconsistent contexts. I will show (...)
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  4. Can we test inconsistent empirical theories?Luis Felipe Bartolo Alegre - manuscript
    This paper discusses the logical possibility of testing inconsistent empirical theories. The main challenge for answering this affirmatively is to avoid that the inconsistent consequences of a theory both corroborate it and falsify it. I answer affirmatively by showing that we can define a class of empirical sentences whose truth would force us to abandon such inconsistent theory: the class of its potential rejecters. Despite this, I show that the observational contradictions implied by a theory could only be verified (provided (...)
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  5. On the philosophical motivations for the logics of formal consistency and inconsistency.Walter Carnielli & Rodrigues Abilio - manuscript
    We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.
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  6. Reinterpreting the universe-multiverse debate in light of inter-model inconsistency in set theory.Daniel Kuby - manuscript
    In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these positions on the (...)
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  7. Inconsistency in empirical sciences.Luis Felipe Bartolo Alegre -
    This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.
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  8. Bohr's atomic model and paraconsistent logic.Pandora Hadzidaki -
    Bohr’s atomic model is one of the better known examples of empirically successful, albeit inconsistent, theoretical schemes in the history of physics. For this reason, many philosophers use this model to illustrate their position for the occurrence and the function of inconsistency in science. In this paper, I proceed to a critical comparison of the structure and the aims of Bohr’s research program – the starting point of which was the formulation of his model – with some of its contemporary (...)
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  9. Vita impossibile del signor Clark Costa.Michelangelo Antonioni - forthcoming - Cinema.
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  10. Cruz Costa e Herdeiros nos Idos de Sessenta.Paulo Arantes - forthcoming - Filosofia.
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  11. Logical argumentation by dynamic proof systems.Ofer Arieli & Christian Straßer - forthcoming - Theoretical Computer Science.
    In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according (...)
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  12. Inference to the Best Contradiction?Sam Baron - forthcoming - British Journal for the Philosophy of Science.
    I argue that there is nothing about the structure of inference to the best explanation (IBE) that prevents it from establishing a contradiction in general, though there are some potential limitations on when it can be used for this purpose. Studying the relationship between IBE and contradictions is worthwhile for three reasons. First, it enhances our understanding of IBE. We see that, in many cases, IBE does not require explanations to be consistent, though there are some cases where consistency may (...)
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  13. Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - forthcoming - Review of Symbolic Logic 15 (3):771-806.
    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 results hold (...)
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  14. What is Logical Monism?Justin Clarke-Doane - forthcoming - In Christopher Peacocke & Paul Boghossian (eds.), Normative Realism.
    Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...)
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  15. Two-sided Sequent Calculi for FDE-like Four-valued Logics.Barteld Kooi & Allard Tamminga - forthcoming - Journal of Philosophical Logic:1-24.
    We present a method that generates two-sided sequent calculi for four-valued logics like "first degree entailment" (FDE). (We say that a logic is FDE-like if it has finitely many operators of finite arity, including negation, and if all of its operators are truth-functional over the four truth-values 'none', 'false', 'true', and 'both', where 'true' and 'both' are designated.) First, we show that for every n-ary operator * every truth table entry f*(x1,...,xn) = y can be characterized in terms of a (...)
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  16. The Logic of Exemplarity.Jakub Mácha - forthcoming - Law and Literature (online first):1-15.
    The topic of exemplarity has attracted considerable interest in philosophy, legal theory, literary studies and art recently. There is broad consensus that exemplary cases mediate between singular instances and general concepts or norms. The aim of this article is to provide an additional perspective on the logic of exemplarity. First, inspired by Jacques Derrida’s discussion of exemplarity, I shall argue that there is a kind of différance between (singular) examples and (general) exemplars. What an example exemplifies, the exemplarity of the (...)
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  17. Against Classical Paraconsistent Metatheory.Koji Tanaka & Patrick Girard - forthcoming - Analysis.
    There was a time when 'logic' just meant classical logic. The climate is slowly changing and non-classical logic cannot be dismissed off-hand. However, a metatheory used to study the properties of non-classical logic is often classical. In this paper, we will argue that this practice of relying on classical metatheories is problematic. In particular, we will show that it is a bad practice because the metatheory that is used to study a non-classical logic often rules out the very logic it (...)
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  18. Epimorphism between Fine and Ferguson’s Matrices for Angell’s AC.Richard Zach - forthcoming - Logic and Logical Philosophy:1-19.
    Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.
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  19. The Philosophy of Exemplarity: Singularity, Particularity, and Self-Reference.Mácha Jakub - 2023 - New York: Routledge.
    This book offers an original philosophical perspective on exemplarity. Inspired by Wittgenstein’s later work and Derrida’s theory of deconstruction, it argues that examples are not static entities but rather oscillate between singular and universal moments. There is a broad consensus that exemplary cases mediate between singular instances and universal concepts or norms. In the first part of the book, Mácha contends that there is a kind of différance between singular examples and general exemplars or paradigms. Every example is, in part, (...)
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  20. The Universal Theory Tool Building Toolkit Is Substructural.Shay Allen Logan - 2022 - In Ivo Duntsch & Edwin D. Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 261-285.
    Consider the set of inferences that are acceptable to use in all our theory building endeavors. Call this set of inferences the universal theory building toolkit, or just ’the toolkit’ for short. It is clear that the toolkit is tightly connected to logic in a variety of ways. Beall, for example, has argued that logic just is the toolkit. This paper avoids making a stand on that issue and instead investigates reasons for thinking that, logic or not, the toolkit is (...)
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  21. The Exoteric Square of Opposition.Jean-Yves Beziau & Ioannis Vandoulakis (eds.) - 2022 - Birkhauser.
    The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...)
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  22. Two Decision Procedures for da Costa’s $$C_n$$ C n Logics Based on Restricted Nmatrix Semantics.Marcelo E. Coniglio & Guilherme V. Toledo - 2022 - Studia Logica 110 (3):601-642.
    Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da Costa's calculi (...)
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  23. O raciocínio abdutivo no contexto da explicação científica.Ulisses Eliano - 2022 - Dissertation, Unicamp - Universidade Estadual de Campinas
    Este trabalho tem como principal objetivo apresentar uma abordagem lógico-formal capaz de apreender alguns aspectos do raciocínio abdutivo – o raciocínio responsável pela criação de hipóteses explicativas para fatos surpreendentes -, mediante tanto as noções filosófico-conceituais da canônica abdução peirceana quanto as de explicação científica. No caso desta última, procurarei evidenciar, inicialmente, pontos de contraste entre as concepções de explicação científica de Aristóteles e de Carl Hempel, a fim de elucidar, de modo mais satisfatório, em que medida, de fato, teorias (...)
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  24. Minimally Nonstandard K3 and FDE.Rea Golan & Ulf Hlobil - 2022 - Australasian Journal of Logic 19 (5):182-213.
    Graham Priest has formulated the minimally inconsistent logic of paradox (MiLP), which is paraconsistent like Priest’s logic of paradox (LP), while staying closer to classical logic. We present logics that stand to (the propositional fragments of) strong Kleene logic (K3) and the logic of first-degree entailment (FDE) as MiLP stands to LP. That is, our logics share the paracomplete and the paraconsistent-cum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to (...)
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  25. Depth Relevance and Hyperformalism.Shay Allen Logan - 2022 - Journal of Philosophical Logic 51 (4):721-737.
    Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result (...)
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  26. Further Reflections on Quasi-factivism: A Reply to Baumann.Michael J. Shaffer - 2022 - Logos and Episteme 13 (2):207-215.
    This paper is a response to Baumann's comments on "Can Knowledge Really be Non-fative?" In this paper Baumann's suggestions for how those who deny the factivty of knowledge might deal with the argument from inconsistency and explosion are addressed.
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  27. Towards Tractable Approximations to Many-Valued Logics: the Case of First Degree Entailment.Alejandro Solares-Rojas & Marcello D’Agostino - 2022 - In Igor Sedlár (ed.), The Logica Yearbook, 2021. London, UK: pp. 57-76.
    FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...)
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  28. Semantics for Pure Theories of Connexive Implication.Yale Weiss - 2022 - Review of Symbolic Logic 15 (3):591-606.
    In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of (...)
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  29. Non-classical Comparative Logic I: Standard Categorical Logic–from SLe to IFLe.Amer Amikhteh & Seyed Ahmad Mirsanei - 2021 - Logical Studies 12 (1):1-24.
    n this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other rules of (...)
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  30. The Contradictory Christ, Oxford: Oxford University Press.Jc Beall - 2021 - Oxford: Oxford University Press.
    This book argues that the standard (orthodox) doctrine of incarnation (of "God enfleshed") is best understood along glut-theoretic lines: the incarnate God is a contradictory being. Example: because God, the Christ figure is all-knowing; but because human, ignorant. And so on. Standard theological theory in the tradition recognizes the apparent contradiction in its core doctrines; Beall argues that the appearance should be accepted as veridical.
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  31. Dialetheism and Modus Tollens.Ben Blumson & Theresa Helke - 2021 - The Reasoner 15 (4):30.
    Suppose that some contradictions are true – for example, that as I walk through the door, I’m inside and I’m not inside. Then we argue 'if I'm walking through the door, I'm inside; I'm not inside; therefore, I'm not walking through the door' is an invalid instance of modus tollens.
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  32. Twist-Valued Models for Three-valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - 2021 - Logic and Logical Philosophy 30 (2):187-226.
    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 axioms of (...)
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  33. Degree-Preserving Gödel Logics with an Involution: Intermediate Logics and Paraconsistency.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - 2021 - In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Springer Verlag. pp. 107-139.
    In this paper we study intermediate logics between the logic G≤∼, the degree preserving companion of Gödel fuzzy logic with involution G∼ and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts G≤n∼. Although G≤∼ and G≤ are explosive w.r.t. Gödel negation ¬, they are paraconsistent w.r.t. the involutive negation ∼. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between (...)
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  34. A Family of Strict/Tolerant Logics.Melvin Fitting - 2021 - Journal of Philosophical Logic 50 (2):363-394.
    Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while consequences are treated more tolerantly. More specifically, ST is a three-valued logic with left sides of sequents understood as if in Kleene’s Strong Three Valued Logic, and right sides as if in Priest’s Logic of Paradox. Surprisingly, this hybrid validates the same sequents that classical logic does. A version of this result has been extended to meta, metameta, … (...)
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  35. Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $$mathbf {L3AG}$$ L 3 A G and $$mathbf {L3BG}$$ L 3 B G.Alejandro Hernández-Tello, Miguel Pérez-Gaspar & Verónica Borja Macías - 2021 - Logica Universalis 15 (1):87-121.
    Genuine Paraconsistent logics \ and \ were defined in 2016 by Béziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernández-Tello et al, provide implications for both logics and define the logics \ and \. In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that \ and \ satisfy a restricted version of the Substitution Theorem, and that (...)
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  36. Hyperdoctrines and the Ontology of Stratified Semantics.Shay Logan - 2021 - In Davide Fazio, Antonio Ledda & Francesco Paoli (eds.), Algebraic Perspectives on Substructural Logics. Springer International Publishing. pp. 169-193.
    I present a version of Kit Fine's stratified semantics for the logic RWQ and define a natural family of related structures called RW hyperdoctrines. After proving that RWQ is sound with respect to RW hyperdoctrines, we show how to construct, for each stratified model, a hyperdoctrine that verifies precisely the same sentences. Completeness of RWQ for hyperdoctrinal semantics then follows from completeness for stratified semantics, which is proved in an appendix. By examining the base category of RW hyperdoctrines, we find (...)
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  37. Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.
    Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...)
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  38. On Not Saying What We Shouldn't Have to Say.Shay Logan & Leach-Krouse Graham - 2021 - Australasian Journal of Logic 18 (5):524-568.
    In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.
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  39. A family of genuine and non-algebraisable C-systems.Mauricio Osorio, Aldo Figallo-Orellano & Miguel Pérez-Gaspar - 2021 - Journal of Applied Non-Classical Logics 31 (1):56-84.
    In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsist...
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  40. L'ontologia della logica immaginaria. Aristotele e Vasil'ev a confronto.Niccolò Rossi - 2021 - Verifiche: Rivista Trimestrale di Scienze Umane 50 (1):147-176.
    The aim of this paper is to show how the invention of imaginary logic by Nikolaj A. Vasil’ev, forerunner of various logical and metaphysical theories appeared in the 20th century, is grounded on a revaluation of Aristotelian ontology. I shall introduce the reason why Aristotle believes that the study of the principle of contradiction is part of ontology (§ 2); I shall explain why Vasil’ev considers the law of contradiction an empirical law, and not a logical one (§ 3.1). I (...)
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  41. A Hierarchy of Classical and Paraconsistent Logics.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Journal of Philosophical Logic 49 (1):93-120.
    In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to (...)
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  42. A recovery operator for nontransitive approaches.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Review of Symbolic Logic 13 (1):80-104.
    In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...)
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  43. La contrastación de teorías inconsistentes no triviales.Luis Felipe Bartolo Alegre - 2020 - Dissertation, Universidad Nacional Mayor de San Marcos
    This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. (...)
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  44. On classical set-compatibility.Luis Felipe Bartolo Alegre - 2020 - El Jardín de Senderos Que Se Bifurcan y Confluyen: Filosofía, Lógica y Matemáticas.
    In this paper, I generalise the logical concept of compatibility into a broader set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite objects under some operation. I formalise opposition as an operation ′ ∶ E → E, where E is the set of opposable elements of our universe U, and I propose some models. From this, I define a relation ℘U × ℘U × ℘U^℘U, which has (mutual) logical compatibility (...)
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  45. Recovery operators, paraconsistency and duality.Walter A. Carnielli, Marcelo E. Coniglio & Abilio Rodrigues Filho - 2020 - Logic Journal of the IGPL 28 (5):624-656.
    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 paraconsistent scenario, while LFUs recover the (...)
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  46. Paraconsistent Logics for Knowledge Representation and Reasoning: advances and perspectives.Walter A. Carnielli & Rafael Testa - 2020 - 18th International Workshop on Nonmonotonic Reasoning.
    This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the importance of (...)
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  47. Non-deterministic algebraization of logics by swap structures1.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Logic Journal of the IGPL 28 (5):1021-1059.
    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 of logics by swap structures are given. Specifically, (...)
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  48. First-order swap structures semantics for some Logics of Formal Inconsistency.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Journal of Logic and Computation 30 (6):1257-1290.
    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 aproaches to quantified LFIs presented in the literature. The case of QmbC, (...)
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  49. The Philosophy of Logic of Francisco Miró Quesada Cantuarias.Newton da Costa, José Carlos Cifuentes & Luis Felipe Bartolo Alegre - 2020 - South American Journal of Logic 6 (2):189-208.
    In this historical article, Newton da Costa discusses Francisco Miró Quesada’s philosophical ideas about logic. He discusses the topics of reason, logic, and action in Miró Quesada’s work, and in the final section he offers his critical view. In particular, he disagrees with Miró Quesada’s stance on the historicity of reason, for whom “reason is essentially absolute”, whereas for da Costa it “is being constructed in the course of history”. Da Costa concludes by emphasizing the importance of Miró Quesada’s theory (...)
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  50. A model-theoretic analysis of Fidel-structures for mbC.Marcelo E. Coniglio - 2020 - In Can Baskent and Thomas Ferguson (ed.), Graham Priest on Dialetheism and Paraconsistency. Springer. pp. 189-216.
    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 Theory in order to (...)
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