What is Negation?

What is Negation?

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The notion of negation is one of the central logical notions. It has been studied since antiquity and has been subjected to thorough investigations in the development of philosophical logic, linguistics, artificial intelligence and logic programming. The properties of negation-in combination with those of other logical operations and structural features of the deducibility relation-serve as gateways among logical systems. Therefore negation plays an important role in selecting logical systems for particular applications. At the moment negation is a 'hot topic', and there is an urgent need for a comprehensive account of this logical key concept. We therefore have asked leading scholars in various branches of logic to contribute to a volume on "What is Negation?". The result is the present neatly focused collection of re- search papers bringing together different approaches toward a general characteri- zation of kinds of negation and classifications thereof. The volume is structured into four interrelated thematic parts. Part I is centered around the themes of Models, Relevance and Impossibility. In Chapter 1 (Negation: Two Points of View), Arnon Avron develops two characteri- zations of negation, one semantic the other proof-theoretic. Interestingly and maybe provokingly, under neither of these accounts intuitionistic negation emerges as a genuine negation. J. Michael Dunn in Chapter 2 (A Comparative Study of Various Model-theoretic Treatments of Negation: A History of Formal Negation) surveys a detailed correspondence-theoretic classifcation of various notions of negation in terms of properties of a binary relation interpreted as incompatibility.
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Product details

  • Paperback | 335 pages
  • 154.94 x 228.6 x 22.86mm | 498.95g
  • Springer
  • Dordrecht, Netherlands
  • English
  • Softcover reprint of hardcover 1st ed. 1999
  • XI, 335 p.
  • 9048151694
  • 9789048151691

Table of contents

Preface. Part I: Models, Relevance and Impossibility. Negation: Two Points of View; A. Avron. A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation; J.M. Dunn.. Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star); G. Restall. Negation in the Light of Modal Logic; K. Dosen. Part II: Paraconsistency, Partiality and Logic Programming. Negation and Contradiction; D. Gabbay, A. Hunter. What not? A Defence of Dialetheic Theory of Negation; G. Priest. Partial Logics with Two Kinds of Negation as a Foundation for Knowledge-Based Reasoning; H. Herre, et al. From Here to There: Stable Negation in Logic Programming; D. Pearce. Part III: Absurdity, Falsity and Refutability. Antirealism and Falsity; M. Hand. Negation, Absurdity and Contrariety; N. Tennant. Negation as Falsity: A Reply to Tennant; H. Wansing. Part IV: Negations, Natural Language and The Liar. Models for Non-Boolean Negations in Natural Languages Based on Aspect Analysis; M. La Palme Reyes, et al. Negation, Denial and Language Change in Philosophical Logic; J. Tappenden. What is That Item Designated Negation? R. Sylvan. Index.
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