Applied Logic Series

What is Negation?

Editors: Gabbay, Dov M., Wansing, Heinrich (Eds.)

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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.

Table of contents (14 chapters)

  • Negation: Two Points of View

    Avron, Arnon

    Pages 3-22

  • A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation

    Dunn, J. Michael

    Pages 23-51

  • Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star)

    Restall, Greg

    Pages 53-76

  • Negation in the Light of Modal Logic

    Došen, Kosta

    Pages 77-86

  • Negation and Contradiction

    Gabbay, Dov (et al.)

    Pages 89-100

Buy this book

eBook $229.00
price for USA (gross)
  • ISBN 978-94-015-9309-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $299.00
price for USA
  • ISBN 978-0-7923-5569-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $299.00
price for USA
  • ISBN 978-90-481-5169-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
What is Negation?
Editors
  • Dov M. Gabbay
  • Heinrich Wansing
Series Title
Applied Logic Series
Series Volume
13
Copyright
1999
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-9309-0
DOI
10.1007/978-94-015-9309-0
Hardcover ISBN
978-0-7923-5569-4
Softcover ISBN
978-90-481-5169-1
Series ISSN
1386-2790
Edition Number
1
Number of Pages
XI, 335
Topics