Search results for 'Paraconsistency' (try it on Scholar)

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  1.  9
    Jonas R. Becker Arenhart (2015). Liberating Paraconsistency From Contradiction. 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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  2.  39
    Walter Carnielli & Abilio Rodrigues, On Philosophical Motivations for Paraconsistency: An Ontology-Free Interpretation of the Logics of Formal Inconsistency.
    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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  3. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. 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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  4.  79
    Achille C. Varzi (2000). Supervaluationism and Paraconsistency. In Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.), Frontiers in Paraconsistent Logic. Research Studies Press 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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  5.  14
    András Kertész & Csilla Rákosi (2013). Paraconsistency and Plausible Argumentation in Generative Grammar: A Case Study. [REVIEW] 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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  6.  17
    Diderik Batens (1998). Paraconsistency and its Relation to Worldviews. 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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  7.  5
    Evandro L. Gomes & Ítala M. L. D.?Ottaviano (2011). Aristotle's Theory of Deduction and Paraconsistency. Principia 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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  8.  4
    William H. F. Altman (2011). A Brief Prehistory of Philosophical Paraconsistency. Principia 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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  9.  8
    Joke Meheus* (2006). An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency. 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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  10.  5
    Ofer Arieli, Arnon Avron & Anna Zamansky (2011). Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics. 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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  11.  6
    Edwin D. Mares (2013). Information, Negation, and Paraconsistency. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer 43--55.
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  12.  6
    Koji Tanaka (2003). Three Schools of Paraconsistency. 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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  13.  21
    Newton C. A. da Costa (2001). Paraconsistency. Theoria 16 (1):119-145.
    In this expository paper, we examine some philosophical and technical issues brought by paraconsistency (such as, motivations for developing a paraconsistent logic, the nature of this logic, and its application to set theory). 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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  14.  9
    Newton C. A. Da Costa & Otávio Bueno (2001). Paraconsistency: Towards a Tentative Interpretation. 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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  15.  13
    Gemma Robles & José M. Méndez (2009). Strong Paraconsistency and the Basic Constructive Logic for an Even Weaker Sense of Consistency. 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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  16.  39
    JC Beall & David Ripley (2003). Review of Paradox and Paraconsistency. [REVIEW] 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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  17.  21
    Sahid Rahman & Walter A. Carnielli (2000). The Dialogical Approach to Paraconsistency. 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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  18.  15
    John Grant & V. S. Subrahmanian (2000). Applications of Paraconsistency in Data and Knowledge Bases. 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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  19.  2
    Alessio Moretti (2010). The Critics of Paraconsistency and of Many-Valuedness and the Geometry of Oppositions. 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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  20.  4
    Jean Paul Van Bendegem (2001). Paraconsistency and Dialogue Logic Critical Examination and Further Explorations. Synthese 127 (1/2):35 - 55.
    The first part of this paper presents a sympathetic and critical examination of the approach of Shahid Rahman and Walter Carnielli, as presented in their paper "The Dialogical Approach to Paraconsistency". In the second part, possible extensions are presented and evaluated: (a) top-down analysis of a dialogue situation versus bottom-up, (b) the specific role of ambiguities and how to deal with them, and (c) the problem of common knowledge and background knowledge in dialogues. In the third part, I claim (...)
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  21. Valentin Bazhanov (2011). The Dawn of Paraconsistency:Russia's Logical Thoughtin the Turn of Xx Century. 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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  22. Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'ottaviano (2002). Paraconsistency the Logical Way to the Inconsistent : Proceedings of the World Congress Held in São Paulo. 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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  23. Conrad Amus (2012). Paraconsistency on the Rocks of Dialetheism. Logique Et Analyse 55 (217):3-21.
  24. Jørgen Villadsen (2005). Supra-Logic: Using Transfinite Type Theory with Type Variables for Paraconsistency. Journal of Applied Non-Classical Logics 15 (1):45-58.
  25. Otavio Bueno & Newton da Costa (2007). Quasi-Truth, Paraconsistency, and the Foundations of Science. 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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  26.  4
    John Woods (2003). Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences. 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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  27.  16
    Andrzej Wiśniewski, Guido Vanackere & Dorota Leszczyńska (2005). Socratic Proofs and Paraconsistency: A Case Study. Studia Logica 80 (2-3):431 - 466.
    This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.
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  28.  3
    Walter Carnielli (ed.) (2002). Paraconsistency:The Logical Way to the Inconsistent. 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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  29.  33
    Francesco Paoli (2003). Quine and Slater on Paraconsistency and Deviance. 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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  30.  1
    Grzegorz Malinowski (2004). Inferential Paraconsistency. Logic and Logical Philosophy 8:83.
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  31.  24
    Diderik Batens (1990). Against Global Paraconsistency. Studies in East European Thought 39 (3-4):209-229.
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  32.  19
    Neil Tennant (1984). Perfect Validity, Entailment and Paraconsistency. 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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  33.  9
    Jan A. Bergstra & Inge Bethke (2015). Note on Paraconsistency and Reasoning About Fractions. Journal of Applied Non-Classical Logics 25 (2):120-124.
    We apply a paraconsistent strategy to reasoning about fractions.
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  34. Graham Priest & Richard Routley (1989). The Philosophical Significance and Inevitability of Paraconsistency. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag 483--537.
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  35.  24
    Igor Urbas (1990). Paraconsistency. Studies in East European Thought 39 (3-4):343-354.
  36.  5
    Carlos A. OLLER (1999). Paraconsistency and Analyticity. 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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  37.  9
    A. D. Irvine (2007). John Woods, Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences. Studia Logica 85 (3):425-428.
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  38.  10
    Diderik Batens, Chris Mortenson, Graham Priest, Jean Paul Van Bendegem, Joke Meheus, Joachim Van Meirvenne & Erik Weber (1996). First World Congress on Paraconsistency. Studia Logica 56 (291).
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  39.  6
    Arnon Avron (1990). Relevance and Paraconsistency---A New Approach. II. The Formal Systems. Notre Dame Journal of Formal Logic 31 (2):169-202.
  40.  8
    Erik C. W. Krabbe (2004). Book Review: John Woods, Paradox and Paraconsistency: Conflict Resolution in the Abstract Sciences (2003). Cambridge:CambridgeUniversity Press. Pp. Xviii+362, ISBN 0-521-81094-9 (Cloth), 0-521-00934-0 (Paper). [REVIEW] Argumentation 18 (4):495-499.
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  41.  24
    Arnon Avron (1990). Relevance and Paraconsistency--A New Approach. Journal of Symbolic Logic 55 (2):707-732.
  42.  3
    Newton [Y.] Otávio Bueno Da Costa (1996). Consistency, Paraconsistency and Truth: Logic, the Whole Logic and Nothing but the Logic. Ideas Y Valores 100:48-60.
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  43.  52
    Greg Restall (2002). Paraconsistency Everywhere. Notre Dame Journal of Formal Logic 43 (3):147-156.
    “Paraconsistent” means “beyond the consistent” [3, 15]. Paraconsistent logics tolerate inconsistencies in a way that traditional logics do not. In a paraconsistent logic, the inference of explosion A, ∼AB is rejected. This may be for any of a number of reasons [16]. For proponents of relevance [1, 2] the argument has gone awry when we infer an irrelevant B from the inconsistent premises. Those who argue that inconsistent theories may have some logical content but do not commit us to everything, (...)
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  44.  13
    Francesco Berto, Strong Paraconsistency and Exclusion Negation.
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  45.  12
    Francesco Berto (2012). How to Rule Out Things with Words: Strong Paraconsistency and the Algebra of Exclusion1. In Greg Restall & Gillian Kay Russell (eds.), New Waves in Philosophical Logic. Palgrave Macmillan 169.
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  46.  43
    Srećko Kovač (2009). First-Order Belief and Paraconsistency. Logic and Logical Philosophy 18 (2):127-143.
    A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...)
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  47.  7
    Hristo Smolenov (1983). Paraconsistency, Paracompleteness and Intentional Contradictions. Bulletin of the Section of Logic 12 (1):8-12.
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  48.  5
    Igor Urbas (1989). Paraconsistency and the $\Rm C$-Systems of da Costa. Notre Dame Journal of Formal Logic 30 (4):583-597.
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  49. Alan Weir (1998). Naive Set Theory, Paraconsistency and Indeterminacy I. Logique Et Analyse 41:219-66.
     
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  50.  27
    Vladimir L. Vasyukov (2011). Paraconsistency in Categories: Case of Relevance Logic. Studia Logica 98 (3):429-443.
    Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.
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