Search results for 'Paraconsistent logic' (try it on Scholar)

1000+ found
Sort by:
  1. Jair Minoro Abe, Curry Algebras Pt, Paraconsistent Logic, Newton Ca da Costa, Otavio Bueno, Jacek Pasniczek, Beyond Consistent, Complete Possible Worlds, Vm Popov & Inverse Negation (1998). Table Des Matieres Editorial Preface 3. Logique Et Analyse 41:1.score: 240.0
     
    My bibliography  
     
    Export citation  
  2. Maarten McKubre-Jordens & Zach Weber (2012). Real Analysis in Paraconsistent Logic. Journal of Philosophical Logic 41 (5):901-922.score: 186.0
    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.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  3. Olivier Esser (2003). A Strong Model of Paraconsistent Logic. Notre Dame Journal of Formal Logic 44 (3):149-156.score: 186.0
    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.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  4. Torben Braüner (2006). Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic. Journal of Logic, Language and Information 15 (3):179-194.score: 168.0
    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.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  5. Newton C. A. Costa & Walter A. Carnielli (1986). On Paraconsistent Deontic Logic. Philosophia 16 (3-4):293-305.score: 158.0
    This paper develops the first deontic logic in the context of paraconsistent logics.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  6. Sergei P. Odintsov (2010). Priestley Duality for Paraconsistent Nelson's Logic. Studia Logica 96 (1):65 - 93.score: 156.0
    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.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  7. Bryson Brown (1999). Yes, Virginia, There Really Are Paraconsistent Logics. Journal of Philosophical Logic 28 (5):489-500.score: 138.0
    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 (...)
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  8. 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: 138.0
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  9. Norihiro Kamide & Heinrich Wansing (2010). Symmetric and Dual Paraconsistent Logics. Logic and Logical Philosophy 19 (1-2):7-30.score: 138.0
    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 (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  10. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. Springer.score: 132.0
    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 (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  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: 128.0
    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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  12. Soma Dutta & Mihir K. Chakraborty (2011). Negation and Paraconsistent Logics. Logica Universalis 5 (1):165-176.score: 128.0
    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 (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  13. Jean-Yves Béziau (2006). The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem. Logic and Logical Philosophy 15 (2):99-111.score: 126.0
    We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  14. Alexej P. Pynko (2002). Extensions of Hałkowska–Zajac's Three-Valued Paraconsistent Logic. Archive for Mathematical Logic 41 (3):299-307.score: 126.0
    As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we (...)
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  15. Gemma Robles (2013). A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Logica Universalis 7 (4):507-532.score: 124.0
    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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  16. Joachim Bromand (2002). Why Paraconsistent Logic Can Only Tell Half the Truth. Mind 111 (444):741-749.score: 120.0
    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 (...) logic in order to avoid strengthened liar paradoxes. (shrink)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  17. Elias H. Alves (1984). Paraconsistent Logic and Model Theory. Studia Logica 43 (1-2):17 - 32.score: 120.0
    The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  18. Newton C. A. da Costa & Décio Krause, Remarks on the Applications of Paraconsistent Logic to Physics.score: 120.0
    In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.
    Direct download  
     
    My bibliography  
     
    Export citation  
  19. Arthur Buchsbaum & Tarcisio Pequeno (1993). A Reasoning Method for a Paraconsistent Logic. Studia Logica 52 (2):281 - 289.score: 120.0
    A proof method for automation of reasoning in a paraconsistent logic, the calculus C1* of da Costa, is presented. The method is analytical, using a specially designed tableau system. Actually two tableau systems were created. A first one, with a small number of rules in order to be mathematically convenient, is used to prove the soundness and the completeness of the method. The other one, which is equivalent to the former, is a system of derived rules designed to (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  20. Blaise Pascal, Paraconsistent Logic! (A Reply to Slater) Jean-Yves BéziauFoot Note 1_.score: 120.0
    Paraconsistent logic is the study of logics in which there are some theories embodying contradictions but which are not trivial, in particular in a paraconsistent logic, the ex contradictione sequitur quod libet, which can be formalized as Cn(T, a,¬a)=F is not valid. Since nearly half a century various systems of paraconsistent logic have been proposed and studied. This field of research is classified under a special section (B53) in the Mathematical Reviews and watching this (...)
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  21. Pandora Hadzidaki, Bohr's Atomic Model and Paraconsistent Logic.score: 120.0
    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 (...)
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  22. Andrés Bobenrieth (2007). Hilbert, Trivialization and Paraconsistent Logic. The Proceedings of the Twenty-First World Congress of Philosophy 5:37-43.score: 120.0
    The origin of Paraconsistent Logic is closely related with the argument that from the assertion of two mutually contradictory statements any other statement can be deduced, which can be referred to as ex contradict!one sequitur quodlibet (ECSQ). Despite its medieval origin, only in the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this paper is to study what happened before: from Principia Mathematica to that time, when (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  23. Valentin A. Bazhanov (2008). Heuristic Ground of Paraconsistent Logic. Proceedings of the Xxii World Congress of Philosophy 13:5-8.score: 120.0
    The paper deals with the heuristic prerequisites of paraconsistent logic in the case of imaginary logic of N.A. Vasiliev proposed in 1910.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  24. Ayda I. Arruda (1989). Aspects of the Historical Development of Paraconsistent Logic. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 99--130.score: 120.0
    No categories
     
    My bibliography  
     
    Export citation  
  25. Joke Meheus (2000). An Extremely Rich Paraconsistent Logic and the Adaptive Logic Based on It. In Frontiers of Paraconsistent Logic. Research Studies Press. 189-201.score: 120.0
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  26. Graham Priest & Richard Routley (1989). Systems of Paraconsistent Logic. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 142--155.score: 120.0
    No categories
     
    My bibliography  
     
    Export citation  
  27. Arnon Avron, 5-Valued Non-Deterministic Semantics for The Basic Paraconsistent Logic mCi.score: 116.0
    One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.
     
    My bibliography  
     
    Export citation  
  28. Sergei P. Odintsov (2005). The Class of Extensions of Nelson's Paraconsistent Logic. Studia Logica 80 (2-3):291 - 320.score: 114.0
    The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  29. Norihiro Kamide (2007). Extended Full Computation-Tree Logics for Paraconsistent Model Checking. Logic and Logical Philosophy 15 (3):251-276.score: 114.0
    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.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  30. Alexej P. Pynko (1995). Algebraic Study of Sette's Maximal Paraconsistent Logic. Studia Logica 54 (1):89 - 128.score: 114.0
    The aim of this paper is to study the paraconsistent deductive systemP 1 within the context of Algebraic Logic. It is well known due to Lewin, Mikenberg and Schwarse thatP 1 is algebraizable in the sense of Blok and Pigozzi, the quasivariety generated by Sette's three-element algebraS being the unique quasivariety semantics forP 1. In the present paper we prove that the mentioned quasivariety is not a variety by showing that the variety generated byS is not equivalent to (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  31. 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: 114.0
    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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  32. Hitoshi Omori & Toshiharu Waragai (2009). On Béziau's Logic Z. Logic and Logical Philosophy 17 (4):305-320.score: 114.0
    In [1] Béziau developed the paraconsistent logic Z, which is definitionally equivalent to the modal logic S5 (cf. Remark 2.3), and gave an axiomatization of the logic Z: the system HZ. In the present paper, we prove that some axioms of HZ are not independent and then propose another axiomatization of Z. We also discuss a new perspective on the relation between S5 and classical propositional logic (CPL) with the help of the new axiomatization of (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  33. Gemma Robles & José M. Méndez (2008). The Basic Constructive Logic for a Weak Sense of Consistency. Journal of Logic, Language and Information 17 (1):89-107.score: 110.0
    In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  34. José M. Méndez & Gemma Robles (2009). The Basic Constructive Logic for Absolute Consistency. Journal of Logic, Language and Information 18 (2):199-216.score: 110.0
    In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic BKc6, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc6 up to contractionless intuitionistic logic. All logics defined in this paper are paraconsistent logics.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  35. Gemma Robles (2008). The Basic Constructive Logic for Negation-Consistency. Journal of Logic, Language and Information 17 (2):161-181.score: 110.0
    In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BKc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  36. Jean-Yves Béziau (2003). Logic May Be Simple. Logic, Congruence and Algebra. Logic and Logical Philosophy 5:129-147.score: 110.0
    This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these concepts are related (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  37. Newton C. A. Da Costa, Otávio Bueno & Steven French (1998). The Logic of Pragmatic Truth. Journal of Philosophical Logic 27 (6):603-620.score: 108.0
    The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity (...)
    Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  38. N. Da Costa & C. De Ronde (2013). The Paraconsistent Logic of Quantum Superpositions. Foundations of Physics 43 (7):845-858.score: 108.0
    Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  39. Newton Carneiro Affonso da Costa (2010). Logic and Ontology. Principia 6 (2):279-298.score: 108.0
    In view of the presertt state of development of non cktssicallogic, especially of paraconsistent logic, a new stand regardmg the relatzons between logtc and ontology is deferded In a parody of a dicturn of Quine, my stand may be summarized as follows To be is to be the value of a vanable a specific language with a given underlymg logic Yet my stand differs from Qutne's, because, among other reasons, I accept some first order heterodox logIcs as (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  40. R. Silvestre (2013). Paranormal Modal Logic – Part II: K?, K and Classical Logic and Other Paranormal Modal Systems. Logic and Logical Philosophy 22 (1):89-130.score: 108.0
    In this two-part paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics – including normal modal logics, paranormal modal logics and classical logic – can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that (...)
    Direct download (12 more)  
     
    My bibliography  
     
    Export citation  
  41. Ricardo S. Silvestre (2012). Paranormal Modal Logic–Part I: The System K? And the Foundations of the Logic of Skeptical and Credulous Plausibility. Logic and Logical Philosophy 21 (1):65-96.score: 108.0
    In this two-parts paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics  including normal modal logics, paranormal modal logics and classical logic can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that paranormal (...)
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  42. Newton C. A. Da Costa & Roque Da C. Caiero (2014). K-Transforms in Classical and Paraconsistent Logics. Logic and Logical Philosophy 7:63.score: 108.0
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  43. Graham Priest (2011). First-Order da Costa Logic. Studia Logica 97 (1):183 - 198.score: 108.0
    Priest (2009) formulates a propositional logic which, by employing the worldsemantics for intuitionist logic, has the same positive part but dualises the negation, to produce a paraconsistent logic which it calls 'Da Costa Logic'. This paper extends matters to the first-order case. The paper establishes various connections between first order da Costa logic, da Costa's own Cω, and classical logic. Tableau and natural deductions systems are provided and proved sound and complete.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  44. Koji Tanaka (2013). Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic. In. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. 15--25.score: 104.0
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  45. Gerson Zaverucha (1992). Relevant Logic as a Basis for Paraconsistent Epistemic Logics. Journal of Applied Non-Classical Logics 2 (2):225-241.score: 104.0
    ABSTRACT In this work we argue for relevant logics as a basis for paraconsistent epistemic logics. In order to do so, a paraconsistent nonmonotonic multi-agent epistemic logic, MDR (for Modal Defeasible Relevant), is briefly introduced. In MDR each agent has two kinds of belief: an absolute belief that P, represented by AiP, and a defeasible belief that P, represented by DiP. Therefore, an agent can reason with his own absolute and defeasible beliefs about the world and also (...)
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  46. Joao Marcos (2005). Nearly Every Normal Modal Logic is Paranormal. Logique Et Analyse 48 (189-192):279-300.score: 104.0
    An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  47. Greg Restall (2002). Paraconsistency Everywhere. Notre Dame Journal of Formal Logic 43 (3):147-156.score: 102.0
    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 (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  48. Manuel Bremer (2008). The Logic of Truth in Paraconsistent Internal Realism. Studia Philosophica Estonica 1 (1):76-83.score: 102.0
    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.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  49. Gemma Robles & José M. Méndez (2010). Paraconsistent Logics Included in Lewis’ S4. Review of Symbolic Logic 3 (03):442-466.score: 102.0
    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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
1 — 50 / 1000