Search results for 'Negation (Logic' (try it on Scholar)

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  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.
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  2.  36
    John Cantwell (2008). The Logic of Conditional Negation. 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. Barbara Klunder & B. Klunder (1992). Topos Based Semantic for Constructive Logic with Strong Negation. 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.  7
    Takuro Onishi (forthcoming). Understanding Negation Implicationally in the Relevant Logic R. Studia Logica:1-19.
    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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  5.  15
    Michael De & Hitoshi Omori (2015). Classical Negation and Expansions of Belnap–Dunn Logic. 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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  6.  2
    François Lepage (2016). A Square of Oppositions in Intuitionistic Logic with Strong Negation. 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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  7.  19
    M. Spinks & R. Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. II. 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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  8.  15
    Gemma Robles (2008). The Basic Constructive Logic for Negation-Consistency. 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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  9.  4
    Eric Toms (1962). Being, Negation, and Logic. Oxford, Blackwell.
  10. Pramod Kumar (1998). Negation, Logic, and Semantics. K. P. Jayaswal Research Institute.
     
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  11.  28
    Matthew Spinks & Robert Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. I. 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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  12.  14
    Norihiro Kamide (2004). Quantized Linear Logic, Involutive Quantales and Strong Negation. 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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  13.  14
    Tero Tulenheimo (2014). IF Modal Logic and Classical Negation. 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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  14.  11
    Petr Cintula & George Metcalfe (2010). Admissible Rules in the Implication–Negation Fragment of Intuitionistic Logic. 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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  15.  9
    Chrysida Galanaki, Panos Rondogiannis & William W. Wadge (2008). An Infinite-Game Semantics for Well-Founded Negation in Logic Programming. 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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  16. Norihiro Kamide (2002). Sequent Calculi for Intuitionistic Linear Logic with Strong Negation. 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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  17.  6
    Jacek Hawranek & Jan Zygmunt (1983). Notes on the Semantics for the Logic with Semi-Negation. 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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  18.  17
    Juha Kontinen & Jouko Väänänen (2010). A Remark on Negation in Dependence Logic. 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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  19.  65
    Graham Priest (1999). Negation as Cancellation, and Connexive Logic. 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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  20.  68
    Jaakko Hintikka (2002). Negation in Logic and in Natural Language. 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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  21.  16
    Andrzej Sendlewski (1995). Axiomatic Extensions of the Constructive Logic with Strong Negation and the Disjunction Property. 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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  22.  10
    José M. Méndez, Francisco Salto & Gemma Robles (2007). El Sistema Bp+ : Una Lógica Positiva Mínima Para la Negación Mínima (the System Bp+: A Minimal Positive Logic for Minimal Negation). 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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  23.  14
    Jacek Hawranek & Jan Zygmunt (1984). On the Degree of Complexity of Sentential Logics.II. An Example of the Logic with Semi-Negation. 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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  24. Nicholas Unwin (2001). Norms and Negation: A Problem for Gibbard's Logic. 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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  25.  8
    Antonino Drago (2001). Vasiliev's Paraconsistent Logic Interpreted by Means of the Dual Role Played by the Double Negation Law. 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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  26.  15
    Félix Bou, Àngel García-Cerdaña & Ventura Verdú (2006). On Two Fragments with Negation and Without Implication of the Logic of Residuated Lattices. 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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  27.  2
    M. Spinks & R. Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. II. Studia Logica 89 (3):401-425.
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  28. Matthew Spinks & Robert Veroff (2008). Constructive Logic with Strong Negation is a Substructural Logic. I. Studia Logica 88 (3):325-348.
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  29.  18
    José M. Méndez, Gemma Robles & Francisco Salto (2007). The Basic Constructive Logic for Negation-Consistency Defined with a Propositional Falsity Constant. Bulletin of the Section of Logic 36 (1-2):45-58.
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  30.  27
    Yuri Gurevich (1977). Intuitionistic Logic with Strong Negation. 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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  31.  13
    Jacek Geisler & Marek Nowak (forthcoming). Conditional Negation on the Positive Logic. Bulletin of the Section of Logic.
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  32.  68
    Jamie Tappenden, Negation, Denial and Language Change in Philosophical Logic.
    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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  33.  10
    George Metcalfe (2009). A Sequent Calculus for Constructive Logic with Strong Negation as a Substructural Logic. Bulletin of the Section of Logic 38 (1):1-7.
  34.  32
    Kosta Došen (1981). A Reduction of Classical Propositional Logic to the Conjunction-Negation Fragment of an Intuitionistic Relevant Logic. Journal of Philosophical Logic 10 (4):399 - 408.
  35.  13
    Roberto Arpaia (2004). On a Substructural Logic with Minimal Negation. Bulletin of the Section of Logic 33 (3):143-156.
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  36. J. Mendez, F. Salto & G. Robles (2002). Anderson And Belnap's Minimal Positive Logic With Minimal Negation. Reports on Mathematical Logic:117-130.
     
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  37.  24
    José M. Mendez & Francisco Salto (1998). A Natural Negation Completion of Urquhart's Many-Valued Logic C. Journal of Philosophical Logic 27 (1):75-84.
  38.  8
    M. Spinks & R. Veroff (2010). Slaney's Logic F is Constructive Logic with Strong Negation. Bulletin of the Section of Logic 39 (3/4):161-173.
  39.  8
    S. C. Kleene (1949). Review: K. R. Popper, On the Theory of Deduction, Part I. Derivation and its Generalizations; K. R. Popper, On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation; K. R. Popper, The Trivialization of Mathematical Logic. [REVIEW] Journal of Symbolic Logic 14 (1):62-63.
  40.  25
    Marie la Palme Reyes, John Macnamara, Gonzalo E. Reyes & And Houman Zolfaghari (1994). The Non-Boolean Logic of Natural Language Negation. Philosophia Mathematica 2 (1):45-68.
    Since antiquity two different negations in natural languages have been noted: predicate negation (not honest) and predicate term negation (dishonest). The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two (not dishonest) and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.
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  41.  8
    Storrs McCall (1962). A Simple Decision Procedure for One-Variable Implicational/Negation Formulae in Intuitionist Logic. Notre Dame Journal of Formal Logic 3 (2):120-122.
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  42.  10
    Seiki Akama (1987). Constructive Predicate Logic with Strong Negation and Model Theory. Notre Dame Journal of Formal Logic 29 (1):18-27.
  43.  4
    David Nelson (1970). Review: A. Bialynicki-Birula, H. Rasiowa, On Constructible Falsity in the Constructive Logic with Strong Negation. [REVIEW] Journal of Symbolic Logic 35 (1):138-138.
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  44.  11
    Frederic B. Fitch (1954). A Definition of Negation in Extended Basic Logic. Journal of Symbolic Logic 19 (1):29-36.
  45.  3
    Marie La Palme Reyes, John Macnamara, Gonzalo E. Reyes & Houman Zolfaghari (1994). The Non-Boolean Logic of Natural Language Negation. Philosophia Mathematica 2 (1):45-68.
    Since antiquity two different negations in natural languages have been noted: predicate negation and predicate term negation . The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.
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  46. Melvin Fitting (1992). Review: Michael Gelfond, Vladimir Lifschitz, Robert A. Kowalski, Kenneth A. Bowen, The Stable Model Semantics for Logic Programming; Kit Fine, Jens Erik Fenstad, Ivan T. Frolov, Risto Hilpinen, The Justification of Negation as Failure. [REVIEW] Journal of Symbolic Logic 57 (1):274-277.
     
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  47. Gene F. Rose (1964). Review: Storrs McCall, A Simple Decision Procedure for One-Variable Implication/Negation Formulae in Intuitionist Logic. [REVIEW] Journal of Symbolic Logic 29 (4):212-212.
     
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  48.  1
    Alan Rose (1952). Review: Takeo Sugihara, Negation in Many-Valued Logic. [REVIEW] Journal of Symbolic Logic 17 (4):278-279.
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  49.  1
    Burton Dreben (1955). Review: Frederic B. Fitch, A Simplification of Basic Logic; Frederic B. Fitch, A Definition of Negation in Extended Basic Logic. [REVIEW] Journal of Symbolic Logic 20 (1):81-81.
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  50.  1
    David Nelson (1969). Review: H. Rasiowa, $Mathcal{N}$-Lattices and Constructive Logic with Strong Negation. [REVIEW] Journal of Symbolic Logic 34 (1):118-118.
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