Results for 'Negation (Logic'

859 found
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  1. Table Des Matieres Editorial Preface 3.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 - Logique Et Analyse 41:1.
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  2.  50
    The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.
    It is argued that the "inner" negation $\mathord{\sim}$ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: $\mathord{\sim}$ is read '$A$ is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g., "If Jim went to the party he (...)
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  3.  4
    Topos Based Semantic for Constructive Logic with Strong Negation.Barbara Klunder & B. Klunder - 1992 - Mathematical Logic Quarterly 38 (1):509-519.
    The aim of the paper is to show that topoi are useful in the categorial analysis of the constructive logic with strong negation. In any topos ϵ we can distinguish an object Λ and its truth-arrows such that sets ϵ have a Nelson algebra structure. The object Λ is defined by the categorial counterpart of the algebraic FIDEL-VAKARELOV construction. Then it is possible to define the universal quantifier morphism which permits us to make the first order predicate calculus. The (...)
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  4.  3
    Contradictoriness, Paraconsistent Negation and Non-Intended Models of Classical Logic.Carlos A. Oller - 2016 - In Holger Andreas & Peter Verdee (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Trends In Logic. Dordrecht: Springer. pp. 103-110.
    It is usually accepted in the literature that negation is a contradictory-forming operator and that two statements are contradictories if and only if it is logically impossible for both to be true and logically impossible for both to be false. These two premises have been used by Hartley Slater [Slater, 1995] to argue that paraconsistent negation is not a “real” negation because a sentence and its paraconsistent negation can be true together. In this paper we claim (...)
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  5.  7
    Classical and Empirical Negation in Subintuitionistic Logic.Michael De & Hitoshi Omori - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 217-235.
    Subintuitionistic (propositional) logics are those in a standard intuitionistic language that result by weakening the frame conditions of the Kripke semantics for intuitionistic logic. In this paper we consider two negation expansions of subintuitionistic logic, one by classical negation and the other by what has been dubbed “empirical” negation. We provide an axiomatization of each expansion and show them sound and strongly complete. We conclude with some final remarks, including avenues for future research.
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  6.  36
    Classical Negation and Expansions of Belnap–Dunn Logic.Michael De & Hitoshi Omori - 2015 - Studia Logica 103 (4):825-851.
    We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal (...)
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  7.  26
    Understanding Negation Implicationally in the Relevant Logic R.Takuro Onishi - 2016 - Studia Logica 104 (6):1267-1285.
    A star-free relational semantics for relevant logic is presented together with a sound and complete sequent proof theory. It is an extension of the dualist approach to negation regarded as modality, according to which de Morgan negation in relevant logic is better understood as the confusion of two negative modalities. The present work shows a way to define them in terms of implication and a new connective, co-implication, which is modeled by respective ternary relations. The defined negations are (...)
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  8.  14
    A Square of Oppositions in Intuitionistic Logic with Strong Negation.François Lepage - 2016 - Logica Universalis 10 (2-3):327-338.
    In this paper, we introduce a Hilbert style axiomatic calculus for intutionistic logic with strong negation. This calculus is a preservative extension of intuitionistic logic, but it can express that some falsity are constructive. We show that the introduction of strong negation allows us to define a square of opposition based on quantification on possible worlds.
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  9.  19
    Book Review: Carnielli, W., Coniglio, M. Paraconsistent Logic: Consistency, Contradiction and Negation. Logic, Epistemology, and the Unity of Science Series. [REVIEW]Henrique Antunes & Vincenzo Ciccarelli - 2018 - Manuscrito 41 (2):111-122.
    Review of the book "Paraconsistent Logic: Consistency, Contradiction, and Negation by Water Carnielli and Marcelo Coniglio.
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  10.  25
    The Basic Constructive Logic for Negation-Consistency.Gemma Robles - 2008 - Journal of Logic, Language and Information 17 (2):161-181.
    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.
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  11.  11
    Being, Negation, and Logic.Eric Toms - 1962 - Blackwell.
  12.  4
    Proof Theory for Positive Logic with Weak Negation.Marta Bílková & Almudena Colacito - forthcoming - Studia Logica:1-38.
    Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and (...)
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  13.  12
    Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo E. Coniglio - 2016 - Basel, Switzerland: Springer International Publishing.
  14.  46
    Constructive Logic with Strong Negation is a Substructural Logic. I.Matthew Spinks & Robert Veroff - 2008 - Studia Logica 88 (3):325-348.
    The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. This answers a longstanding question of Nelson (...)
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  15.  18
    Quantized Linear Logic, Involutive Quantales and Strong Negation.Norihiro Kamide - 2004 - Studia Logica 77 (3):355-384.
    A new logic, quantized intuitionistic linear logic, is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's involutive quantales. Some cut-free sequent calculi with a new property quantization principle and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks.
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  16.  40
    Constructive Logic with Strong Negation is a Substructural Logic. II.M. Spinks & R. Veroff - 2008 - Studia Logica 89 (3):401-425.
    The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew. The main result of Part I of this series [41] shows that the equivalent variety semantics of N and the equivalent variety semantics of NFL ew are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of (...)
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  17.  23
    IF Modal Logic and Classical Negation.Tero Tulenheimo - 2014 - Studia Logica 102 (1):41-66.
    The present paper provides novel results on the model theory of Independence friendly modal logic. We concentrate on its particularly well-behaved fragment that was introduced in Tulenheimo and Sevenster (Advances in Modal Logic, 2006). Here we refer to this fragment as ‘Simple IF modal logic’ (IFML s ). A model-theoretic criterion is presented which serves to tell when a formula of IFML s is not equivalent to any formula of basic modal logic (ML). We generalize the notion of bisimulation familiar (...)
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  18.  14
    Admissible Rules in the Implication–Negation Fragment of Intuitionistic Logic.Petr Cintula & George Metcalfe - 2010 - Annals of Pure and Applied Logic 162 (2):162-171.
    Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.
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  19.  6
    Sequent Calculi for Intuitionistic Linear Logic with Strong Negation.Norihiro Kamide - 2002 - Logic Journal of the IGPL 10 (6):653-678.
    We introduce an extended intuitionistic linear logic with strong negation and modality. The logic presented is a modal extension of Wansing's extended linear logic with strong negation. First, we propose three types of cut-free sequent calculi for this new logic. The first one is named a subformula calculus, which yields the subformula property. The second one is termed a dual calculus, which has positive and negative sequents. The third one is called a triple-context calculus, which is regarded as (...)
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  20.  16
    An Infinite-Game Semantics for Well-Founded Negation in Logic Programming.Chrysida Galanaki, Panos Rondogiannis & William W. Wadge - 2008 - Annals of Pure and Applied Logic 151 (2-3):70-88.
    We present an infinite-game characterization of the well-founded semantics for function-free logic programs with negation. Our game is a simple generalization of the standard game for negation-less logic programs introduced by van Emden [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 37–53] in which two players, the Believer and the Doubter, compete by trying to prove a query. The standard game is equivalent to the minimum Herbrand model semantics of logic programming in (...)
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  21.  12
    Something, Nothing and Leibniz’s Question. Negation in Logic and Metaphysics.Jan Woleński - 2018 - Studies in Logic, Grammar and Rhetoric 54 (1):175-190.
    This paper discusses the concept of nothing from the point of logic and ontology. It is argued that the category of nothing as a denial of being is subjected to various interpretations. In particular, this thesis concerns the concept of negation as used in metaphysics. Since the Leibniz question ‘Why is there something rather than nothing?’ and the principle of sufficient reason is frequently connected with the status of nothing, their analysis is important for the problem in question. Appendix (...)
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  22.  7
    Negation as Cancellation, Connexive Logic, and qLPm.Heinrich Wansing - 2018 - Australasian Journal of Logic 15 (2):476-488.
    In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination (...)
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  23.  9
    Paraconsistent Logic and Weakening of Intuitionistic Negation.Zoran Majkić - 2012 - Journal of Intelligent Systems 21 (3):255-270.
    . A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. In an earlier paper [Notre Dame J. Form. Log. 49, 401–424], we developed the systems of weakening of intuitionistic negation logic, called and, in the spirit of da Costa's approach by preserving, differently from da Costa, the fundamental properties of negation: antitonicity, inversion and additivity for distributive lattices. Taking into account these results, we make some observations on the modified systems (...)
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  24.  15
    Notes on the Semantics for the Logic with Semi-Negation.Jacek Hawranek & Jan Zygmunt - 1983 - Bulletin of the Section of Logic 12 (4):152-155.
    . In our paper, presented here in abstract form, we consider the sentential logic with semi-negation. It should be stressed, however, that our main interest is not that logic itself but rather more general matters concerning the theory of matrix semantics for sentential logics. The logic with semi-negation provides a relevant example for elucidating such basic notions of matrix semantics as degree of complexity, degree of uniformity, and self-referentiality. Thus our paper being a contribution to the theory of (...)
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  25. Negation as Cancellation, and Connexive Logic.Graham Priest - 1999 - Topoi 18 (2):141-148.
    Of the various accounts of negation that have been offered by logicians in the history of Western logic, that of negation as cancellation is a very distinctive one, quite different from the explosive accounts of modern "classical" and intuitionist logics, and from the accounts offered in standard relevant and paraconsistent logics. Despite its ancient origin, however, a precise understanding of the notion is still wanting. The first half of this paper offers one. Both conceptually and historically, the account (...)
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  26.  22
    A Remark on Negation in Dependence Logic.Juha Kontinen & Jouko Väänänen - 2011 - Notre Dame Journal of Formal Logic 52 (1):55-65.
    We show that for any pair $\phi$ and $\psi$ of contradictory formulas of dependence logic there is a formula $\theta$ of the same logic such that $\phi\equiv\theta$ and $\psi\equiv\neg\theta$. This generalizes a result of Burgess.
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  27.  13
    Semi-Intuitionistic Logic with Strong Negation.Juan Manuel Cornejo & Ignacio Viglizzo - 2018 - Studia Logica 106 (2):281-293.
    Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.
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  28.  21
    Axiomatic Extensions of the Constructive Logic with Strong Negation and the Disjunction Property.Andrzej Sendlewski - 1995 - Studia Logica 55 (3):377 - 388.
    We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B V, thenA×B is a homomorphic image of some well-connected algebra ofV.We prove:• each varietyV of Nelson algebras with PQWC lies in the fibre –1(W) for some varietyW of Heyting algebras having PQWC, • for any varietyW of Heyting algebras with PQWC the least and (...)
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  29.  89
    Negation in Logic and in Natural Language.Jaakko Hintikka - 2002 - Linguistics and Philosophy 25 (5-6):585-600.
    In game-theoretical semantics, perfectlyclassical rules yield a strong negation thatviolates tertium non datur when informationalindependence is allowed. Contradictorynegation can be introduced only by a metalogicalstipulation, not by game rules. Accordingly, it mayoccur (without further stipulations) onlysentence-initially. The resulting logic (extendedindependence-friendly logic) explains several regularitiesin natural languages, e.g., why contradictory negation is abarrier to anaphase. In natural language, contradictory negationsometimes occurs nevertheless witin the scope of aquantifier. Such sentences require a secondary interpretationresembling the so-called substitutionalinterpretation of quantifiers.This interpretation is (...)
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  30.  28
    El Sistema Bp+ : Una Lógica Positiva Mínima Para la Negación Mínima (the System Bp+: A Minimal Positive Logic for Minimal Negation).José M. Méndez, Francisco Salto & Gemma Robles - 2007 - Theoria 22 (1):81-91.
    Entendemos el concepto de “negación mínima” en el sentido clásico definido por Johansson. El propósito de este artículo es definir la lógica positiva mínima Bp+, y probar que la negación mínima puede introducirse en ella. Además, comentaremos algunas de las múltiples extensiones negativas de Bp+.“Minimal negation” is classically understood in a Johansson sense. The aim of this paper is to define the minimal positive logic Bp+ and prove that a minimal negation can be inroduced in it. In addition, (...)
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  31.  23
    On the Degree of Complexity of Sentential Logics.II. An Example of the Logic with Semi-Negation.Jacek Hawranek & Jan Zygmunt - 1984 - Studia Logica 43 (4):405 - 413.
    In this paper being a sequel to our [1] the logic with semi-negation is chosen as an example to elucidate some basic notions of the semantics for sentential calculi. E.g., there are shown some links between the Post number and the degree of complexity of a sentential logic, and it is proved that the degree of complexity of the sentential logic with semi-negation is 20. This is the first known example of a logic with such a degree of (...)
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  32. Norms and Negation: A Problem for Gibbard’s Logic.Nicholas Unwin - 2001 - Philosophical Quarterly 51 (202):60-75.
    A difficulty is exposed in Allan Gibbard's solution to the embedding/Frege-Geach problem, namely that the difference between refusing to accept a normative judgement and accepting its negation is ignored. This is shown to undermine the whole solution.
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  33.  14
    Vasiliev's Paraconsistent Logic Interpreted by Means of the Dual Role Played by the Double Negation Law.Antonino Drago - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):281-294.
    I prove that the three basic propositions of Vasiliev's paraconsistent logic have a semantic interpretation by means of the intuitionist logic. The interpèretation is confirmed by amens of the da Costa's model of Vasiliev's paraconsistent logic.
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  34.  28
    On Two Fragments with Negation and Without Implication of the Logic of Residuated Lattices.Félix Bou, Àngel García-Cerdaña & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (5):615-647.
    The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this (...)
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  35.  6
    Negation and Partial Axiomatizations of Dependence and Independence Logic Revisited.Fan Yang - 2019 - Annals of Pure and Applied Logic 170 (9):1128-1149.
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  36.  26
    Robert K. Meyer. Intuitionism, Entailment, Negation. Truth, Syntax and Modality, Proceedings of the Temple University Conference on Alternative Semantics, Edited by Hugues Leblanc, Studies in Logic and the Foundations of Mathematics, Vol. 68, North-Holland Publishing Company, Amsterdam and London1973, Pp. 168–198. [REVIEW]Melvin Fitting - 1977 - Journal of Symbolic Logic 42 (2):315.
  37.  19
    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.
  38.  16
    Michael Gelfond and Vladimir Lifschitz. The Stable Model Semantics for Logic Programming. Logic Programming, Proceedings of the Fifth International Conference and Symposium, Volume 2, Edited by Robert A. Kowalski and Kenneth A. Bowen, Series in Logic Programming, The MIT Press, Cambridge, Mass., and London, 1988, Pp. 1070–1080. - Kit Fine. The Justification of Negation as Failure. Logic, Methodology and Philosophy of Science VIII, Proceedings of the Eighth International Congress of Logic, Methodology and Philosophy of Science, Moscow, 1987, Edited by Jens Erik Fenstad, Ivan T. Frolov, and Risto Hilpinen, Studies in Logic and the Foundations of Mathematics, Vol. 126, North-Holland, Amsterdam Etc. 1989, Pp. 263–301. [REVIEW]Melvin Fitting - 1992 - Journal of Symbolic Logic 57 (1):274-277.
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  39.  83
    Negation, Denial and Language Change in Philosophical Logic.Jamie Tappenden - unknown
    This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form the (...)
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  40.  33
    Intuitionistic Logic with Strong Negation.Yuri Gurevich - 1977 - Studia Logica 36 (1-2):49 - 59.
    This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension of (...)
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  41. Anderson And Belnap's Minimal Positive Logic With Minimal Negation.J. Mendez, F. Salto & G. Robles - 2002 - Reports on Mathematical Logic:117-130.
     
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  42.  19
    Constructive Predicate Logic with Strong Negation and Model Theory.Seiki Akama - 1987 - Notre Dame Journal of Formal Logic 29 (1):18-27.
  43.  23
    A Sequent Calculus for Constructive Logic with Strong Negation as a Substructural Logic.George Metcalfe - 2009 - Bulletin of the Section of Logic 38 (1/2):1-7.
  44.  24
    The Basic Constructive Logic for Negation-Consistency Defined with a Propositional Falsity Constant.José M. Méndez, Gemma Robles & Francisco Salto - 2007 - Bulletin of the Section of Logic 36 (1-2):45-58.
  45.  45
    A Reduction of Classical Propositional Logic to the Conjunction-Negation Fragment of an Intuitionistic Relevant Logic.Kosta Došen - 1981 - Journal of Philosophical Logic 10 (4):399 - 408.
  46.  6
    Logics with Impossibility as the Negation and Regular Extensions of the Deontic Logic D2.Krystyna Mruczek-Nasieniewska & Marek Nasieniewski - 2018 - Bulletin of the Section of Logic 46 (3/4).
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  47.  11
    A Simple Decision Procedure for One-Variable Implicational/Negation Formulae in Intuitionist Logic.Storrs McCall - 1962 - Notre Dame Journal of Formal Logic 3 (2):120-122.
  48.  27
    On a Substructural Logic with Minimal Negation.Roberto Arpaia - 2004 - Bulletin of the Section of Logic 33 (3):143-156.
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  49.  20
    Conditional Negation on the Positive Logic.Jacek Geisler & Marek Nowak - forthcoming - Bulletin of the Section of Logic.
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  50.  35
    A Natural Negation Completion of Urquhart's Many-Valued Logic C.José M. Mendez & Francisco Salto - 1998 - Journal of Philosophical Logic 27 (1):75-84.
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