© 1999

What is Negation?

  • Dov M. Gabbay
  • Heinrich Wansing

Part of the Applied Logic Series book series (APLS, volume 13)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Models, Relevance and Impossibility

  3. Paraconsistency, Partiality and Logic Programming

    1. Front Matter
      Pages 87-87
    2. Dov Gabbay, Anthony Hunter
      Pages 89-100
  4. Absurdity, Falsity and Refutability

    1. Front Matter
      Pages 183-183
    2. Michael Hand
      Pages 185-198
    3. Neil Tennant
      Pages 199-222
    4. Heinrich Wansing
      Pages 223-238
  5. Negations, Natural Language and the Liar

    1. Front Matter
      Pages 239-239
    2. M. La Palme Reyes, J. Macnamara, G. E. Reyes, H. Zolfaghari
      Pages 241-260
    3. Richard Sylvan
      Pages 299-324
  6. Back Matter
    Pages 325-335

About this book


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.


artificial intelligence classification intelligence language linguistics logic modal logic programming

Editors and affiliations

  • Dov M. Gabbay
    • 1
  • Heinrich Wansing
    • 2
  1. 1.King’s CollegeLondonUK
  2. 2.University of LeipzigLeipzigGermany

Bibliographic information

  • Book Title What is Negation?
  • Editors Dov M. Gabbay
    Heinrich Wansing
  • Series Title Applied Logic Series
  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-5569-4
  • Softcover ISBN 978-90-481-5169-1
  • eBook ISBN 978-94-015-9309-0
  • Series ISSN 1386-2790
  • Edition Number 1
  • Number of Pages XI, 335
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Logic
    Artificial Intelligence
    Philosophy of Language
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