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What is Negation? (Paperback, Softcover reprint of hardcover 1st ed. 1999)
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What is Negation? (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Series: Applied Logic Series, 13
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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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