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

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  1. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. Springer.score: 8.0
    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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  2. Pablo Cobreros (2010). Paraconsistent Vagueness: A Positive Argument. Synthese 183 (2):211-227.score: 8.0
    Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least (...)
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  3. Otavio Bueno & Newton da Costa (2007). Quasi-Truth, Paraconsistency, and the Foundations of Science. Synthese 154 (3):383 - 399.score: 8.0
    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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  4. Bryson Brown (1999). Yes, Virginia, There Really Are Paraconsistent Logics. Journal of Philosophical Logic 28 (5):489-500.score: 8.0
    B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever "negation" symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics - the preservationist logics - (...)
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  5. Greg Restall (2002). Paraconsistency Everywhere. Notre Dame Journal of Formal Logic 43 (3):147-156.score: 8.0
    “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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  6. Newton C. A. Costa & Walter A. Carnielli (1986). On Paraconsistent Deontic Logic. Philosophia 16 (3-4):293-305.score: 8.0
    This paper develops the first deontic logic in the context of paraconsistent logics.
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  7. Maarten McKubre-Jordens & Zach Weber (2012). Real Analysis in Paraconsistent Logic. Journal of Philosophical Logic 41 (5):901-922.score: 8.0
    This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.
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  8. Francesco Paoli (2003). Quine and Slater on Paraconsistency and Deviance. Journal of Philosophical Logic 32 (5):531-548.score: 8.0
    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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  9. Gemma Robles & José M. Méndez (2010). Paraconsistent Logics Included in Lewis’ S4. Review of Symbolic Logic 3 (03):442-466.score: 8.0
    As is known, a logic S is paraconsistent if the rule ECQ (E contradictione quodlibet) is not a rule of S. Not less well known is the fact that Lewis’ modal logics are not paraconsistent. Actually, Lewis vindicates the validity of ECQ in a famous proof currently known as the “Lewis’ proof” or “Lewis’ argument.” This proof essentially leans on the Disjunctive Syllogism as a rule of inference. The aim of this paper is to define a series of paraconsistent logics (...)
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  10. Juliana Bueno-Soler (2010). Two Semantical Approaches to Paraconsistent Modalities. Logica Universalis 4 (1):137-160.score: 8.0
    In this paper we extend the anodic systems introduced in Bueno-Soler (J Appl Non Class Logics 19(3):291–310, 2009) by adding certain paraconsistent axioms based on the so called logics of formal inconsistency , introduced in Carnielli et al. (Handbook of philosophical logic, Springer, Amsterdam, 2007), and define the classes of systems that we call cathodic . These classes consist of modal paraconsistent systems, an approach which permits us to treat with certain kinds of conflicting situations. Our interest in this paper (...)
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  11. Nicholas D. McGinnis (2013). The Unexpected Applicability of Paraconsistent Logic: A Chomskyan Route to Dialetheism. [REVIEW] Foundations of Science 18 (4):625-640.score: 8.0
    Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived. Strikingly these logics have found a wide range of application, despite the misgivings of philosophers as prominent as Lewis and Putnam. Such applications, I will argue, are of significant philosophical interest. They suggest ways to employ these logics in philosophical and scientific theories. To this end I will sketch out a ‘naturalized semantic dialetheism’ following Priest’s early (...)
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  12. Diderik Batens (1998). Paraconsistency and its Relation to Worldviews. Foundations of Science 3 (2):259-283.score: 8.0
    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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  13. Torben Braüner (2006). Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic. Journal of Logic, Language and Information 15 (3):179-194.score: 8.0
    In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.
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  14. Walter A. Carnielli & João Marcos (1999). Limits for Paraconsistent Calculi. Notre Dame Journal of Formal Logic 40 (3):375-390.score: 8.0
    This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...)
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  15. O. Arieli, A. Avron & A. Zamansky (2011). Ideal Paraconsistent Logics. Studia Logica 99 (1-3):31-60.score: 8.0
    We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n -valued logics, each one of which is not (...)
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  16. 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.score: 8.0
    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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  17. Norihiro Kamide (2009). Proof Systems Combining Classical and Paraconsistent Negations. Studia Logica 91 (2):217 - 238.score: 8.0
    New propositional and first-order paraconsistent logics (called L ω and FL ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L ω and FL ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L ω and FL ω are proved. The cut-elimination theorems for L ω and FL ω are shown using both syntactical ways via the embedding theorems and semantical ways (...)
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  18. Olivier Esser (2003). A Strong Model of Paraconsistent Logic. Notre Dame Journal of Formal Logic 44 (3):149-156.score: 8.0
    The purpose of this paper is mainly to give a model of paraconsistent logic satisfying the "Frege comprehension scheme" in which we can develop standard set theory (and even much more as we shall see). This is the continuation of the work of Hinnion and Libert.
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  19. Frode Bjørdal (2011). The Inadequacy of a Proposed Paraconsistent Set Theory. Review of Symbolic Logic 4 (1):106-108.score: 8.0
    We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a quite classical nonprimitive notion of identity, so that the relation is an equivalence relation and also obeys full substitutivity: a = b -> F(b)). With this as background it is shown that the proposed theory also proves the negation of x=x. While not by itself showing that the proposed system is trivial in the sense of proving all statements, it is argued that this (...)
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  20. Gemma Robles (2013). A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Logica Universalis 7 (4):507-532.score: 8.0
    Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one differing only from G3 in the interpretation of negation is to be remarked. The logics are defined in the Hilbert-style way and also by means of proof-theoretical and semantical consequence relations. The RM-semantics is defined upon the models for Routley and Meyer’s basic positive logic B+, the weakest positive RM-semantics. In this way, it is to be expected that the (...)
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  21. Walter Carnielli & Abilio Rodrigues, On Philosophical Motivations for Paraconsistency: An Ontology-Free Interpretation of the Logics of Formal Inconsistency.score: 8.0
    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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  22. 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.score: 8.0
    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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  23. Norihiro Kamide (2007). Extended Full Computation-Tree Logics for Paraconsistent Model Checking. Logic and Logical Philosophy 15 (3):251-276.score: 8.0
    It is known that the full computation-tree logic CTL * is an important base logic for model checking. The bisimulation theorem for CTL* is known to be useful for abstraction in model checking. In this paper, the bisimulation theorems for two paraconsistent four-valued extensions 4CTL* and 4LCTL* of CTL* are shown, and a translation from 4CTL* into CTL* is presented. By using 4CTL* and 4LCTL*, inconsistency-tolerant and spatiotemporal reasoning can be expressed as a model checking framework.
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  24. Joao Marcos (2008). Possible-Translations Semantics for Some Weak Classically-Based Paraconsistent Logics. Journal of Applied Non-Classical Logics 18 (1):7-28.score: 8.0
    In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...)
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  25. Joke Meheus* (2006). An Adaptive Logic Based on Jaśkowskiˈs Approach to Paraconsistency. Journal of Philosophical Logic 35 (6):539 - 567.score: 8.0
    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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  26. Can Başkent (2013). Some Topological Properties of Paraconsistent Models. Synthese 190 (18):4023-4040.score: 8.0
    In this work, we investigate the relationship between paraconsistent semantics and some well-known topological spaces such as connected and continuous spaces. We also discuss homotopies as truth preserving operations in paraconsistent topological models.
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  27. Soma Dutta & Mihir K. Chakraborty (2011). Negation and Paraconsistent Logics. Logica Universalis 5 (1):165-176.score: 8.0
    Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation ( ${\neg}$ ) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out to (...)
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  28. Zoran Majkić (2008). Weakening of Intuitionistic Negation for Many-Valued Paraconsistent da Costa System. Notre Dame Journal of Formal Logic 49 (4):401-424.score: 8.0
    In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. After that, (...)
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  29. 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.score: 8.0
    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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  30. Sergei P. Odintsov (2010). Priestley Duality for Paraconsistent Nelson's Logic. Studia Logica 96 (1):65 - 93.score: 8.0
    The variety of N4┴ -lattices provides an algebraic semantics for the logic N4┴, a version of Nelson's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of N4┴-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
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  31. Ofer Arieli, Arnon Avron & Anna Zamansky (2011). Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics. Studia Logica 97 (1):31 - 60.score: 8.0
    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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  32. Norihiro Kamide & Heinrich Wansing (2010). Symmetric and Dual Paraconsistent Logics. Logic and Logical Philosophy 19 (1-2):7-30.score: 8.0
    Two new first-order paraconsistent logics with De Morgan-type negations and co-implication, called symmetric paraconsistent logic (SPL) and dual paraconsistent logic (DPL), are introduced as Gentzen-type sequent calculi. The logic SPL is symmetric in the sense that the rule of contraposition is admissible in cut-free SPL. By using this symmetry property, a simpler cut-free sequent calculus for SPL is obtained. The logic DPL is not symmetric, but it has the duality principle. Simple semantics for SPL and DPL are introduced, and the (...)
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  33. Manuel Bremer (2008). The Logic of Truth in Paraconsistent Internal Realism. Studia Philosophica Estonica 1 (1):76-83.score: 7.0
    The paper discusses which modal principles should hold for a truth operator answering to the truth theory of internal realism. It turns out that the logic of truth in internal realism is isomorphic to the modal system S4.
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  34. Evandro L. Gomes & Ítala M. L. D.?Ottaviano (2011). Aristotle's Theory of Deduction and Paraconsistency. Principia 14 (1):71-97.score: 7.0
    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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  35. Tomasz Skura (2009). The RM Paraconsistent Refutation System. Logic and Logical Philosophy 18 (1):65-70.score: 7.0
    The aim of this paper is to study the refutation system consisting of the refutation axiom p ∧ ¬p → q and the refutation rules: reverse substitution and reverse modus ponens (B/A, if A → B ∈ RM). It is shown that the refutation system is characteristic for the logic of the 3-element RM algebra.
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  36. William H. F. Altman (2011). A Brief Prehistory of Philosophical Paraconsistency. Principia 14 (1):1-14.score: 7.0
    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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  37. Peter Apostoli (1996). Modal Aggregation and the Theory of Paraconsistent Filters. Mathematical Logic Quarterly 42 (1):175-190.score: 7.0
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  38. Newton C. A. Da Costa & Roque Da C. Caiero (2014). K-Transforms in Classical and Paraconsistent Logics. Logic and Logical Philosophy 7:63.score: 7.0
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  39. Arief Daynes (2006). A New Technique for Proving Realisability and Consistency Theorems Using Finite Paraconsistent Models of Cut‐Free Logic. Mathematical Logic Quarterly 52 (6):540-554.score: 7.0
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  40. Renato A. Lewin & Irene F. Mikenberg (2010). First Order Theory for Literal‐Paraconsistent and Literal‐Paracomplete Matrices. Mathematical Logic Quarterly 56 (4):425-433.score: 7.0
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  41. Eduardo Hirsh & Renato A. Lewin (2008). Algebraization of Logics Defined by Literal-Paraconsistent or Literal-Paracomplete Matrices. Mathematical Logic Quarterly 54 (2):153-166.score: 7.0
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  42. Renato A. Lewin & Irene F. Mikenberg (2006). Literal‐Paraconsistent and Literal‐Paracomplete Matrices. Mathematical Logic Quarterly 52 (5):478-493.score: 7.0
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  43. Jason L. Megill (2004). Are We Paraconsistent? On the Lucas-Penrose Argument and the Computational Theory of Mind. Auslegung 27 (1):23-30.score: 7.0
     
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  44. Otavio Bueno, Outline of a Paraconsistent Category Theory.score: 6.0
    The aim of this paper is two-fold: (1) To contribute to a better knowledge of the method of the Argentinean mathematicians Lia Oubifia and Jorge Bosch to formulate category theory independently of set theory. This method suggests a new ontology of mathematical objects, and has a profound philosophical significance (the underlying logic of the resulting category theory is classical iirst—order predicate calculus with equality). (2) To show in outline how the Oubina-Bosch theory can be modified to give rise to a (...)
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  45. Zach Weber (2010). Transfinite Numbers in Paraconsistent Set Theory. Review of Symbolic Logic 3 (1):71-92.score: 6.0
    This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...)
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  46. Bryson Brown & Graham Priest (2004). Chunk and Permeate, a Paraconsistent Inference Strategy. Part I: The Infinitesimal Calculus. Journal of Philosophical Logic 33 (4):379-388.score: 6.0
    In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind - specifically concerning the preservation of the consistency of each chunk (...)
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  47. Joachim Bromand (2002). Why Paraconsistent Logic Can Only Tell Half the Truth. Mind 111 (444):741-749.score: 6.0
    The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought into paraconsistent logic (...)
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  48. Srećko Kovač (2009). First-Order Belief and Paraconsistency. Logic and Logical Philosophy 18 (2):127-143.score: 6.0
    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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  49. JC Beall & David Ripley (2003). Review of Paradox and Paraconsistency. [REVIEW] Notre Dame Philosophical Reviews.score: 6.0
    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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