Results for 'paraconsistency'

261 found
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  1.  60
    On Formal Aspects of the Epistemic Approach to Paraconsistency.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2018 - In Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain. London: College Publications. pp. 48-74.
    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 are given (...)
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  2.  22
    Liberating Paraconsistency From Contradiction.Jonas R. Becker Arenhart - 2015 - Logica Universalis 9 (4):523-544.
    In this paper we propose to take seriously the claim that at least some kinds of paraconsistent negations are subcontrariety forming operators. We shall argue that from an intuitive point of view, by considering paraconsistent negations as formalizing that particular kind of opposition, one needs not worry with issues about the meaning of true contradictions and the like, given that “true contradictions” are not involved in these paraconsistent logics. Our strategy will consist in showing that, on the one hand, the (...)
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  3. On Philosophical Motivations for Paraconsistency: An Ontology-Free Interpretation of the Logics of Formal Inconsistency.Walter Carnielli & Abilio Rodrigues - manuscript
    In this paper 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 in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically (...)
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  4. Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2013 - Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  5. Supervaluationism and Paraconsistency.Achille C. Varzi - 2000 - In Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.), Frontiers in Paraconsistent Logic. Research Studies Press. pp. 279–297.
    Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...)
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  6.  37
    An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency.Joke Meheus* - 2006 - Journal of Philosophical Logic 35 (6):539-567.
    In this paper, I present the modal adaptive logic $AJ^{r}$ (based on S5) as well as the discussive logic $D_{2}^{r}$ that is defined from it. $D_{2}^{r}$ is a (nonmonotonic) alternative for Jaśkowski's paraconsistent system D₂. Like D₂, $D_{2}^{r}$ validates all single-premise rules of Classical Logic. However, for formulas that behave consistently, $D_{2}^{r}$ moreover validates all multiple-premise rules of Classical Logic. Importantly, and unlike in the case of D₂, this does not require the introduction of discussive connectives. It is argued that (...)
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  7.  37
    Paraconsistency and its Relation to Worldviews.Diderik Batens - 1998 - Foundations of Science 3 (2):259-283.
    The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some stands with respect to para-consistency. It then discusses some sources of inconsistency that are specific for worldviews, and the import of the paraconsistent turn for the worldviews enterprise.
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  8.  28
    Paraconsistency, Pluralistic Models and Reasoning in Climate Science.Bryson Brown - 2017 - Humana Mente 10 (32):179-194.
    Scientific inquiry is typically focused on particular questions about particular objects and properties. This leads to a multiplicity of models which, even when they draw on a single, consistent body of concepts and principles, often employ different methods and assumptions to model different systems. Pluralists have remarked on how scientists draw on different assumptions to model different systems, different aspects of systems and systems under different conditions and defended the value of distinct, incompatible models within science at any given time. (...)
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  9.  25
    Aristotle's Theory of Deduction and Paraconsistency.Evandro L. Gomes & Ítala M. L. D.?Ottaviano - 2010 - Principia: An International Journal of Epistemology 14 (1):71-97.
    No Órganon Aristóteles descreve alguns esquemas dedutivos nos quais a presença de inconsistências não acarreta a trivialização da teoria lógica envolvida. Esta tese é corroborada por três diferentes situações teóricas estudadas por ele, as quais são apresentadas neste trabalho. Analizamos o esquema de inferência utilizado por Aristóteles no Protrepticus e o método de demonstração indireta para os silogismos categóricos. Ambos os métodos exemplificam como Aristóteles emprega estratégias de redução ao absurdo logicamente clássicas. Na sequência, discutimos os silogismos válidos a partir (...)
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  10.  39
    Paraconsistency and Plausible Argumentation in Generative Grammar: A Case Study. [REVIEW]András Kertész & Csilla Rákosi - 2013 - Journal of Logic, Language and Information 22 (2):195-230.
    While the analytical philosophy of science regards inconsistent theories as disastrous, Chomsky allows for the temporary tolerance of inconsistency between the hypotheses and the data. However, in linguistics there seem to be several types of inconsistency. The present paper aims at the development of a novel metatheoretical framework which provides tools for the representation and evaluation of inconsistencies in linguistic theories. The metatheoretical model relies on a system of paraconsistent logic and distinguishes between strong and weak inconsistency. Strong inconsistency is (...)
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  11.  26
    A Brief Prehistory of Philosophical Paraconsistency.William H. F. Altman - 2010 - Principia: An International Journal of Epistemology 14 (1):1-14.
    Celebrando o papel de Newton da Costa na história da paraconsistência, este trabalho examina o uso e abuso da deliberada auto-contradição. Iniciado por Parmênides, desenvolvido por Platão, e continuado por Cícero, uma antiga tradição filosófica usava deliberadamente discursos paraconsistentes para revelar a verdade. Nos tempos modernos, o decisionismo tem usado uma deliberada auto-contradição contra a revelação Judaico-Cristã. DOI:10.5007/1808-1711.2010v14n1p1.
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  12. Priest’s Anti-Exceptionalism, Candrakīrti and Paraconsistency.Koji Tanaka - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Dordrecht: Springer Verlag. pp. 127-138.
    Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Crucial to Priest’s anti-exceptionalism is the existence of ‘data’ that can force the revision of logical theory. He claims that classical logic is inadequate to the available data and, thus, needs to be revised. But what kind of data can overturn classical logic? Priest claims that the data is our intuitions about the (...)
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  13.  19
    Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics.Ofer Arieli, Arnon Avron & Anna Zamansky - 2011 - Studia Logica 97 (1):31 - 60.
    Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all (...)
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  14.  20
    Paraconsistency and its Philosophical Interpretations.Eduardo Barrio & Bruno Da Re - 2018 - Australasian Journal of Logic 15 (2):151-170.
    Many authors have considered that the notions of paraconsistency and dialetheism are intrinsically connected, in many cases, to the extent of confusing both phenomena. However, paraconsistency is a formal feature of some logics that consists in invalidating the rule of explosion, whereas dialetheism is a semantical/ontological position consisting in accepting true contradictions. In this paper, we argue against this connection and show that it is perfectly possible to adopt a paraconsistent logic and reject dialetheism, and, moreover, that there (...)
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  15.  6
    The evidence approach to paraconsistency versus the paraconsistent approach to evidence.Jonas Rafael Becker Arenhart - forthcoming - Synthese:1-23.
    In this paper, we analyze the epistemic approach to paraconsistency. This approach is advanced as an alternative to dialetheism on what concerns interpreting paraconsistency and contradictions; instead of having to accept that there are true contradictions, it is suggested that we may understand such situations as involving only conflicting evidence, which restricts contradictions to a notion of evidence weaker than truth. In this paper, we first distinguish two conflicting programs entangled in the proposal: interpreting paraconsistency in general (...)
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  16.  63
    The Dialogical Approach to Paraconsistency.Sahid Rahman & Walter A. Carnielli - 2000 - Synthese 125 (1-2):201-232.
    Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, say A and ¬A have been asserted.The dialogical approach suggests a way of studying thedynamic process of contradictions through which thetwo (...)
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  17. Recovery Operators, Paraconsistency and Duality.Walter A. Carnielli, Marcelo E. Coniglio & Abilio Rodrigues Filho - forthcoming - Logic Journal of the IGPL.
    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 (...)
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  18.  29
    Three Schools of Paraconsistency.Koji Tanaka - 2003 - Australasian Journal of Logic 1:28-42.
    A logic is said to be paraconsistent if it does not allow everything to follow from contradictory premises. There are several approaches to paraconsistency. This paper is concerned with several philosophical positions on paraconsistency. In particular, it concerns three ‘schools’ of paraconsistency: Australian, Belgian and Brazilian. The Belgian and Brazilian schools have raised some objections to the dialetheism of the Australian school. I argue that the Australian school of paraconsistency need not be closed down on the (...)
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  19.  5
    Inferential Semantics, Paraconsistency, and Preservation of Evidence.Walter Carnielli & Abilio Rodrigues - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 165-187.
    Proof-theoretic semantics provides meanings to the connectives of intuitionistic logic without the need for a semantics in the standard sense of an attribution of semantic values to formulas. Meanings are given by the inference rules that, in this case, do not express preservation of truth but rather preservation of availability of a constructive proof. Elsewhere we presented two paraconsistent systems of natural deduction: the Basic Logic of Evidence and the Logic of Evidence and Truth. The rules of BLE have been (...)
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  20.  61
    Paraconsistency.Newton C. A. Da Costa - 2001 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 16 (1):119-145.
    In this expository paper, we examine some philosophical and technical issues brought by paraconsistency. We also suggest a way of accommodating these issues by considering some problems in the philosophy of logic from a new perspective.
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  21.  29
    Paraconsistency: Towards a Tentative Interpretation.Newton C. A. Da Costa & Otávio Bueno - 2001 - Theoria 16 (40):119-145.
    In this expository paper, we examine some philosophical and technical issues brought by paraconsistency . We also suggest a way of accommodating these issues by considering some problems in the philosophy of logic from a new perspective.
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  22.  2
    Introduction to Graham Priest on Dialetheism and Paraconsistency.Thomas Macaulay Ferguson & Can Başkent - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 1-2.
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  23.  17
    Information, Negation, and Paraconsistency.Edwin D. Mares - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 43--55.
  24.  15
    The Dawn of Paraconsistency: Russia's Logical Thought in the Turn of XX Century.Valentin A. Bazhanov - 2011 - Manuscrito 34 (1):89-98.
    The paper deals with the factors which enabled N. A. Vasiliev to put forward in 1910 - 12 the idea of logics free of the laws of contradiction and excluded middle, the idea of metalogic and to construct his imaginary logic as novel non-classical system. It is shown that background of Vasiliev’s ideas lies deeply in Russia’s culture and particular approach to logical discourse. Several Russian scholars expressed ideas similar to Vasiliev’s though not in such explicit form. This period might (...)
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  25.  44
    Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency.Gemma Robles & José M. Méndez - 2009 - Journal of Logic, Language and Information 18 (3):357-402.
    In a standard sense, consistency and paraconsistency are understood as the absence of any contradiction and as the absence of the ECQ (‘E contradictione quodlibet’) rule, respectively. The concepts of weak consistency (in two different senses) as well as that of F -consistency have been defined by the authors. The aim of this paper is (a) to define alternative (to the standard one) concepts of paraconsistency in respect of the aforementioned notions of weak consistency and F -consistency; (b) (...)
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  26.  37
    Paraconsistency in Classical Logic.Gabriele Pulcini & Achille C. Varzi - 2018 - Synthese 195 (12):5485-5496.
    Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit “in the negative”. More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of (...)
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  27.  48
    Review of Paradox and Paraconsistency[REVIEW]JC Beall & David Ripley - 2003 - Notre Dame Philosophical Reviews.
    When physicists disagree as to whose theory is right, they can (if we radically idealize) form an experiment whose results will settle the difference. When logicians disagree, there seems to be no possibility of resolution in this manner. In Paradox and Paraconsistency John Woods presents a picture of disagreement among logicians, mathematicians, and other “abstract scientists” and points to some methods for resolving such disagreement. Our review begins with (very) short sketches of the chapters. Following the sketches, we respond (...)
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  28.  75
    Applications of Paraconsistency in Data and Knowledge Bases.John Grant & V. S. Subrahmanian - 2000 - Synthese 125 (1-2):121-132.
    The study of paraconsistent logic as a branch of mathematics and logic has been pioneered by Newton da Costa. With the growing advent of distributed and often inconsistent databases over the last ten years, there has been growing interest in paraconsistency amongst researchers in databases and knowledge bases. In this paper, we provide a brief survey of work in paraconsistent databases and knowledge bases affected by Newton da Costa's important and lasting contributions to the field.
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  29.  4
    Total Paraconsistency.Bruno Da Ré - 2019 - Humanities Journal of Valparaiso 13:90-101.
    In the context of non-classical logics, many philosophers have been particularly interested in the paraconsistent logics. In addition to traditional definitions, in recent years, new ways of characterizing the notion of paraconsistency have been proposed. In all of these definitions the rule or the meta-rule of explosion is abandoned. In this article, I present those definitions and evaluate the role that the negation and the transitivity play in each of them. Finally, I propose a new definition of paraconsistency (...)
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  30.  22
    The Critics of Paraconsistency and of Many-Valuedness and the Geometry of Oppositions.Alessio Moretti - 2010 - Logic and Logical Philosophy 19 (1-2):63-94.
    In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By (...)
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  31.  5
    A Brief Prehistory of Philosophical Paraconsistency DOI:10.5007/1808-1711.2010v14n1p1.William H. F. Altman - 2010 - Principia: An International Journal of Epistemology 14 (1):1-14.
    In celebration of Newton da Costa’s place in the history of paraconsistency, this paper considers the use and abuse of deliberate self-contradiction. Beginning with Parmenides, developed by Plato, and continued by Cicero, an ancient philosophical tradition used deliberately paraconsistent discourses to reveal the truth. In modern times, decisionism has used deliberate self-contradiction against Judeo-Christian revelation. • DOI:10.5007/1808-1711.2010v14n1p1.
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  32.  5
    Paraconsistency the Logical Way to the Inconsistent : Proceedings of the World Congress Held in São Paulo.Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'ottaviano - 2002 - Marcel Dekker.
    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.
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  33.  54
    An Epistemic Approach to Paraconsistency: A Logic of Evidence and Truth.Walter Carnielli & Abilio Rodrigues - 2017 - Synthese 196 (9):3789-3813.
    The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and Truth. The latter is a logic of (...)
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  34. Paraconsistency on the Rocks of Dialetheism.Conrad Amus - 2012 - Logique Et Analyse 55 (217):3-21.
  35. Quasi-Truth, Paraconsistency, and the Foundations of Science.Otávio Bueno & Newton C. A. da Costa - 2007 - Synthese 154 (3):383-399.
    In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, (...)
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  36. Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences.John Woods - 2002 - Cambridge University Press.
    In a world plagued by disagreement and conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible, systems. Do these disagreements admit of resolution? Can such resolution be achieved without disturbing assumptions that the theorems of logic and mathematics state objective truths about the real world? In this original and historically rich book John Woods explores apparently intractable disagreements in logic (...)
     
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  37.  63
    Quine and Slater on Paraconsistency and Deviance.Francesco Paoli - 2003 - Journal of Philosophical Logic 32 (5):531-548.
    In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...)
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  38.  20
    Strict Paraconsistency of Truth-Degree Preserving Intuitionistic Logic with Dual Negation.J. L. Castiglioni & R. C. Ertola Biraben - 2014 - Logic Journal of the IGPL 22 (2):268-273.
  39.  18
    Paraconsistency and Sette’s Calculus P1.Janusz Ciuciura - 2015 - Logic and Logical Philosophy 24 (2).
  40.  7
    Anti-Intuitionism and Paraconsistency.Andreas B. M. Brunner & Walter A. Carnielli - 2005 - Journal of Applied Logic 3 (1):161-184.
  41.  3
    Recovery Operators, Paraconsistency and Duality.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - forthcoming - Logic Journal of the IGPL.
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  42. Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences.John Woods - 2004 - Bulletin of Symbolic Logic 10 (1):116-118.
     
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  43.  10
    Combining Linear-Time Temporal Logic with Constructiveness and Paraconsistency.Norihiro Kamide & Heinrich Wansing - 2010 - Journal of Applied Logic 8 (1):33-61.
  44.  18
    How Do Madhyamikas Think? Notes on Jay Garfield, Graham Priest, and Paraconsistency.Tom J. F. Tillemans - 2009 - In Mario D'Amato, Jay L. Garfield & Tom J. F. Tillemans (eds.), Pointing at the Moon: Buddhism, Logic, Analytic Philosophy. Oxford University Press.
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  45.  37
    Perfect Validity, Entailment and Paraconsistency.Neil Tennant - 1984 - Studia Logica 43 (1-2):181 - 200.
    This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every unsatisfiable set is (...)
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  46.  10
    Paraconsistency:The Logical Way to the Inconsistent.Walter Carnielli (ed.) - 2002 - CRC Press.
    The Logical Way to the Inconsistent Walter Alexandr Carnielli, Marcelo Coniglio, Itala Maria Lof D'ottaviano. Beyond Truth(-Preservation) R.E. JENNINGS Laboratory for Logic and Experimental Philosophy, Simon Fraser University, Burnaby, ...
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  47.  26
    Paraconsistency, Paracompleteness, Gentzen Systems, and Trivalent Semantics.Arnon Avron - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):12-34.
    A quasi-canonical Gentzen-type system is a Gentzen-type system in which each logical rule introduces either a formula of the form , or of the form , and all the active formulas of its premises belong to the set . In this paper we investigate quasi-canonical systems in which exactly one of the two classical rules for negation is included, turning the induced logic into either a paraconsistent logic or a paracomplete logic, but not both. We provide a constructive coherence criterion (...)
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  48.  54
    Against Global Paraconsistency.Diderik Batens - 1990 - Studies in East European Thought 39 (3-4):209-229.
  49.  27
    Paraconsistency and Analyticity.Carlos A. OLLER - 1999 - Logic and Logical Philosophy 7 (1):91-99.
    William Parry conceived in the early thirties a theory of entail-
    ment, the theory of analytic implication, intended to give a formal expression to the idea that the content of the conclusion of a valid argument must be included in the content of its premises. This paper introduces a system of analytic, paraconsistent and quasi-classical propositional logic that does not validate the paradoxes of Parry’s analytic implication. The interpretation of the expressions of this logic will be given in terms of a (...)
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  50. The Philosophical Significance and Inevitability of Paraconsistency.Graham Priest & Richard Routley - 1989 - In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 483--537.
     
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