Results for 'negation'

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  1. Negation on the Australian Plan.Francesco Berto & Greg Restall - 2019 - Journal of Philosophical Logic 48 (6):1119-1144.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities (...)
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  2. Cancellation, Negation, and Rejection.Niels Skovgaard-Olsen, Peter Collins, Karolina Krzyżanowska, Ulrike Hahn & Karl Christoph Klauer - 2019 - Cognitive Psychology 108:42-71.
    In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, and Klauer, 2016a) can be classified as being produced by a) a conversational implicature, b) a (probabilistic) presupposition failure, or c) a conventional implicature. After considering several alternative hypotheses and the accumulating evidence from other studies as (...)
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  3.  48
    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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  4. Negation, Denial, and Rejection.David Ripley - 2011 - Philosophy Compass 6 (9):622-629.
    At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather (...)
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  5.  17
    Weak Negation in Inquisitive Semantics.Vít Punčochář - 2015 - Journal of Logic, Language and Information 24 (3):323-355.
    This paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The main (...)
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  6.  55
    Constructive Negation, Implication, and Co-Implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
    In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.
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  7.  16
    Boolean Negation and Non-Conservativity I: Relevant Modal Logics.Tore Fjetland Øgaard - forthcoming - Logic Journal of the IGPL.
    Many relevant logics can be conservatively extended by Boolean negation. Mares showed, however, that E is a notable exception. Mares’ proof is by and large a rather involved model-theoretic one. This paper presents a much easier proof-theoretic proof which not only covers E but also generalizes so as to also cover relevant logics with a primitive modal operator added. It is shown that from even very weak relevant logics augmented by a weak K-ish modal operator, and up to the (...)
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  8.  8
    Boolean Negation and Non-Conservativity III: The Ackermann Constant.Tore Fjetland Øgaard - forthcoming - Logic Journal of the IGPL.
    It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.
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  9.  35
    Negation And Contradiction.Richard Routley Val Routley, Richard Sylvan & Richard Routley - 1985 - Revista Columbiana de Mathematicas:201 - 231.
    The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a (...)
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  10.  6
    Boolean Negation and Non-Conservativity II: The Variable-Sharing Property.Tore Fjetland Øgaard - forthcoming - Logic Journal of the IGPL.
    Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the Boolean (...)
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  11. A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
     
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  12. 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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  13. Metalinguistic Negation and Echoic Use.Robyn Carston - unknown
    What I hope to achieve in this paper is some rather deeper understanding of the semantic and pragmatic properties of utterances which are said to involve the phenomenon of metalinguistic negation[FN1]. According to Laurence Horn, who has been primarily responsible for drawing our attention to it, this is a special non-truthfunctional use of the negation operator, which can be glossed as 'I object to U' where U is a linguistic utterance. This is to be distinguished from descriptive truthfunctional (...)
     
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  14.  23
    Negation in Weak Positional Calculi.Marcin Tkaczyk - 2013 - Logic and Logical Philosophy 22 (1):3-19.
    Four weak positional calculi are constructed and examined. They refer to the use of the connective of negation within the scope of the positional connective “R” of realization. The connective of negation may be fully classical, partially analogical or independent from the classical, truth-functional negation. It has been also proved that the strongest system, containing fully classical connective of negation, is deductively equivalent to the system MR from Jarmużek and Pietruszczak.
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  15. Negation, Anti-Realism, and the Denial Defence.Imogen Dickie - 2010 - Philosophical Studies 150 (2):161 - 185.
    Here is one argument against realism. (1) Realists are committed to the classical rules for negation. But (2) legitimate rules of inference must conserve evidence. And (3) the classical rules for negation do not conserve evidence. So (4) realism is wrong. Most realists reject 2. But it has recently been argued that if we allow denied sentences as premisses and conclusions in inferences we will be able to reject 3. And this new argument against 3 generates a new (...)
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  16.  49
    Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star).Greg Restall - 1999 - In Dov M. Gabbay & Heinrich Wansing (eds.), What is Negation? Kluwer Academic Publishers. pp. 53-76.
  17. Metalinguistic Negation and Metaphysical Affirmation.Mahrad Almotahari - 2014 - Philosophical Studies 167 (3):497-517.
    In a series of articles, Kit Fine presents some highly compelling objections to monism, the doctrine that spatially coincident objects are identical. His objections rely on Leibniz’s Law and linguistic environments that appear to be immune to the standard charge of non-transparency and substitution failure. In this paper, I respond to Fine’s objections on behalf of the monist. Following Benjamin Schnieder, I observe that arguments from Leibniz’s Law are valid only if they involve descriptive, rather than metalinguistic, negation. Then (...)
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  18.  99
    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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  19.  9
    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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  20.  24
    Negation, Structure, Transformation: Alain Badiou and the New Metaphysics.Becky Vartabedian - 2018 - Open Philosophy 1 (1):213-222.
    In this article, I discuss Alain Badiou’s 2008 address titled “The Three Negations.” Though the text was originally presented in a symposium concerning the relationship of law to Badiou’s theory of the event, I discuss the way this brief address offers an introduction to the broad sweep of Badiou’s metaphysics, outlining his accounts of being, appearing, and transformation. To do so, Badiou calls on the resources of three paradigms of negation: from classical Aristotelian logic, from Brouwer’s intuitionist logic, and (...)
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  21. Quasi-Realism, Negation and the Frege-Geach Problem.Nicholas Unwin - 1999 - Philosophical Quarterly 49 (196):337-352.
    Expressivists, such as Blackburn, analyse sentences such as 'S thinks that it ought to be the case that p' as S hoorays that p'. A problem is that the former sentence can be negated in three different ways, but the latter in only two. The distinction between refusing to accept a moral judgement and accepting its negation therefore cannot be accounted for. This is shown to undermine Blackburn's solution to the Frege-Geach problem.
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  22. 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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  23. Negation and Non-Being.Richard M. Gale - 1976 - Blackwell.
     
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  24. Why the Negation Problem Is Not a Problem for Expressivism.Jeremy Schwartz & Christopher Hom - 2014 - Noûs 48 (2):824-845.
    The Negation Problem states that expressivism has insufficient structure to account for the various ways in which a moral sentence can be negated. We argue that the Negation Problem does not arise for expressivist accounts of all normative language but arises only for the specific examples on which expressivists usually focus. In support of this claim, we argue for the following three theses: 1) a problem that is structurally identical to the Negation Problem arises in non-normative cases, (...)
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  25.  78
    Negation and Negative Concord in Romance.Ivan A. Sag & Henriëtte De Swart - 2002 - Linguistics and Philosophy 25 (4):373-417.
    This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. (...)
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  26. Moral Expressivism and Sentential Negation.Neil Sinclair - 2011 - Philosophical Studies 152 (3):385-411.
    This paper advances three necessary conditions on a successful account of sentential negation. First, the ability to explain the constancy of sentential meaning across negated and unnegated contexts (the Fregean Condition). Second, the ability to explain why sentences and their negations are inconsistent, and inconsistent in virtue of the meaning of negation (the Semantic Condition). Third, the ability of the account to generalize regardless of the topic of the negated sentence (the Generality Condition). The paper discusses three accounts (...)
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  27.  63
    Negation in the Context of Gaggle Theory.J. Michael Dunn & Chunlai Zhou - 2005 - Studia Logica 80 (2-3):235-264.
    We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that (...)
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  28. A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
    I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture (...)
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  29.  16
    Classical Negation and Game-Theoretical Semantics.Tero Tulenheimo - 2014 - Notre Dame Journal of Formal Logic 55 (4):469-498.
    Typical applications of Hintikka’s game-theoretical semantics give rise to semantic attributes—truth, falsity—expressible in the $\Sigma^{1}_{1}$-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, $L_{1}$ and $L_{2}$, in both of which two negation signs are available: $\rightharpoondown $ and $\sim$. The latter is the usual GTS negation which transposes the players’ roles, (...)
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  30.  85
    Empirical Negation.Michael De - 2013 - Acta Analytica 28 (1):49-69.
    An extension of intuitionism to empirical discourse, a project most seriously taken up by Dummett and Tennant, requires an empirical negation whose strength lies somewhere between classical negation (‘It is unwarranted that. . . ’) and intuitionistic negation (‘It is refutable that. . . ’). I put forward one plausible candidate that compares favorably to some others that have been propounded in the literature. A tableau calculus is presented and shown to be strongly complete.
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  31.  51
    Negation for Expressivists: A Collection of Problems with a Suggestion for Their Solution.James Dreier - 2006 - Oxford Studies in Metaethics 1:217-233.
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  32.  38
    Boolean Negation and All That.Graham Priest - 1990 - Journal of Philosophical Logic 19 (2):201 - 215.
    We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...)
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  33.  15
    Negation and Partial Axiomatizations of Dependence and Independence Logic Revisited.Fan Yang - 2019 - Annals of Pure and Applied Logic 170 (9):1128-1149.
    In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations (...)
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  34.  87
    Negation and Quantification in Aristotle.Michael V. Wedin - 1990 - History and Philosophy of Logic 11 (2):131-150.
    Two main claims are defended. The first is that negative categorical statements are not to be accorded existential import insofar as they figure in the square of opposition. Against Kneale and others, it is argued that Aristotle formulates his o statements, for example, precisely to avoid existential commitment. This frees Aristotle's square from a recent charge of inconsistency. The second claim is that the logic proper provides much thinner evidence than has been supposed for what appears to be the received (...)
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  35.  5
    Negation in the Language of Theology – Some Issues.Adam Olszewski - 2018 - Philosophical Problems in Science 65:87-107.
    The paper consists of two parts. In the first one I present some general remarks regarding the history of negation and attempt to answer the philosophical question concerning the essence of negation. In the second part I resume the theological teaching on the degrees of certainty and point to five forms of negation – known from other areas of research -- as applied in the framework of theological investigations.
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  36.  59
    There is More to Negation Than Modality.Michael De & Hitoshi Omori - 2018 - Journal of Philosophical Logic 47 (2):281-299.
    There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto, 761–793, 2015) defends at length in a recent paper. According to one such modal account, (...)
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  37. The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
    Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival (...)
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  38.  19
    Minimal Negation in the Ternary Relational Semantics.G. Robles, J. Mendez & F. Salto - 2005 - Reports on Mathematical Logic:47-65.
    Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.
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  39.  38
    Negation As Refutation.Melvin Fitting - unknown
    A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilattice notion. An efficient implementation based on semantic tableaux is sketched; it reduces to SLD resolution when negations are not involved. The resulting (...)
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  40.  13
    The Negation of the Singular Cardinal Hypothesis From o=K++.Moti Gitik - 1989 - Annals of Pure and Applied Logic 43 (3):209-234.
  41.  68
    Classical Negation Can Be Expressed by One of its Halves.Jean-Yves Beziau - 1999 - Logic Journal of the IGPL 7 (2):145-151.
    We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an (...)
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  42.  28
    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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  43. Characterizing Negation to Face Dialetheism.Francesco Berto - 2006 - Logique Et Analyse 49 (195):241-263.
  44.  4
    Classical Negation Can Be Expressed by One of its Halves.J.-Y. Beziau - 1999 - Logic Journal of the IGPL 7 (2):145-151.
    We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an (...)
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  45.  59
    Dualising Intuitionictic Negation.Graham Priest - 2009 - Principia: An International Journal of Epistemology 13 (2):165-184.
    One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. (...)
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  46.  11
    Thinking Negation in Early Hinduism and Classical Indian Philosophy.Purushottama Bilimoria - 2017 - Logica Universalis 11 (1):13-33.
    A number of different kinds of negation and negation of negation are developed in Indian thought, from ancient religious texts to classical philosophy. The paper explores the Mīmāṃsā, Nyāya, Jaina and Buddhist theorizing on the various forms and permutations of negation, denial, nullity, nothing and nothingness, or emptiness. The main thesis argued for is that in the broad Indic tradition, negation cannot be viewed as a mere classical operator turning the true into the false, nor (...)
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  47.  10
    Negation And Negative Concord In Romance.Henriëtte De Swart & Ivan Sag - 2002 - Linguistics and Philosophy 25 (4):373-417.
    This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. (...)
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  48. Negation, `Presupposition' and the Semantics/ Pragmatics Distinction.Robyn Carston - 1998 - Journal of Linguistics 34:309-350.
    A cognitive pragmatic approach is taken to some long-standing problem cases of negation, the so-called presupposition denial cases. It is argued that a full account of the processes and levels of representation involved in their interpretation typically requires the sequential pragmatic derivation of two different propositions expressed. The first is one in which the presupposition is preserved and, following the rejection of this, the second involves the echoic (metalinguistic) use of material falling in the scope of the negation. (...)
     
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  49. Dynamic Negation and Negative Information.Sebastian Sequoiah-grayson - 2009 - Review of Symbolic Logic 2 (1):233-248.
    This essay proposes a procedural interpretation of negative information in terms of split negation as procedural prohibition. Information frames and models are introduced, with negation defined as the implication of bottom, 0. A method for extracting the procedures prohibited by complex formulas is outlined, and the relationship between types of prohibited procedures is identified. Definitions of negation types in terms of the implication of 0 on an informational interpretation have been criticized. This criticism turns on the definitions (...)
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  50. Non-Descriptive Negation for Normative Sentences.Andrew Alwood - 2016 - Philosophical Quarterly 66 (262):1-25.
    Frege-Geach worries about embedding and composition have plagued metaethical theories like emotivism, prescriptivism and expressivism. The sharpened point of such criticism has come to focus on whether negation and inconsistency have to be understood in descriptivist terms. Because they reject descriptivism, these theories must offer a non-standard account of the meanings of ethical and normative sentences as well as related semantic facts, such as why certain sentences are inconsistent with each other. This paper fills out such a solution to (...)
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