What is Negation?

1. Front Matter

   Pages i-xi

   PDF

2. Models, Relevance and Impossibility

   1. Front Matter

      Pages 1-1

      PDF

   2. Negation: Two Points of View

      • Arnon Avron

      Pages 3-22

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

      • J. Michael Dunn

      Pages 23-51

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

      • Greg Restall

      Pages 53-76

   5. Negation in the Light of Modal Logic

      • Kosta Došen

      Pages 77-86

3. Paraconsistency, Partiality and Logic Programming

   1. Front Matter

      Pages 87-87

      PDF

   2. Negation and Contradiction

      • Dov Gabbay, Anthony Hunter

      Pages 89-100

   3. What Not? A Defence of Dialetheic Theory of Negation

      • Graham Priest

      Pages 101-120

   4. Partial Logics with Two Kinds of Negation as a Foundation for Knowledge-Based Reasoning

      • Heinrich Herre, Jan Jaspars, Gerd Wagner

      Pages 121-159

   5. From Here to There: Stable Negation in Logic Programming

      • David Pearce

      Pages 161-181

4. Absurdity, Falsity and Refutability

   1. Front Matter

      Pages 183-183

      PDF

   2. Antirealism and Falsity

      • Michael Hand

      Pages 185-198

   3. Negation, Absurdity and Contrariety

      • Neil Tennant

      Pages 199-222

   4. Negation As Falsity: A Reply to Tennant

      • Heinrich Wansing

      Pages 223-238

5. Negations, Natural Language and the Liar

   1. Front Matter

      Pages 239-239

      PDF

   2. Models for Non-Boolean Negations in Natural Languages Based on Aspect Analysis

      • M. La Palme Reyes, J. Macnamara, G. E. Reyes, H. Zolfaghari

      Pages 241-260

   3. Negation, Denial and Language Change in Philosophical Logic

      • Jamie Tappenden

      Pages 261-298

   4. What is That Item Designated Negation?

      • Richard Sylvan

      Pages 299-324

6. Back Matter

   Pages 325-335

   PDF

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

• King’s College, London, UK

  Dov M. Gabbay

• University of Leipzig, Leipzig, Germany

  Heinrich Wansing

Policies and ethics