Constructive Negations and Paraconsistency (Trends in Logic)
Language: English
Published by Springer Netherlands, 2008
Series: Book 9 of 53 - Trends in Logic
- Softcover
- New

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248 pages. 8.90x5.98x0.63 inches. In Stock.
Seller Inventory # x-9048177448
- Title
- Constructive Negations and Paraconsistency (Trends in Logic)
- Author
- Sergei Odintsov
- Publisher
- Springer Netherlands
- Publication year
- 2008
- Condition
- Brand New
- Binding
- Paperback
- Language
- English
- ISBN 10
- 9048177448
- ISBN 13
- 9789048177448
- Item weight
- 0.4 kilograms
- Series
- Book 9 of 53: Trends in Logic
Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.
"Synopsis" may belong to another edition of this title.
From the Back Cover
This book presents the author’s recent investigations of the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity (L.E.J. Brouwer) and the strong negation (D. Nelson) are studied in the setting of paraconsistent logic.
The paraconsistent logics are those, which admit inconsistent but non-trivial theories, i.e., the logics which allow making inferences in non-trivial fashion from an inconsistent set of hypotheses. Logics in which all inconsistent theories are trivial are called explosive. In the intuitionistic logic Li, the negation is defined as reduction to absurdity. The concept of strong negation is realized in the Nelson logic N3. Both logics are explosive and have paraconsistent analogs: Johansson’s logic Lj and paraconsistent Nelson’s logic N4. It will be shown that refusing the explosion axiom "contradiction implies everything" does not lead to decrease of the expressive power of a logic. To understand, which new expressive possibilities have the logics Lj and N4 as compared to the explosive logics Li and N3, we study the lattices of extensions of the logics Lj and N4. This is the first case when lattices of paraconsistent logics are systematically investigated. The study is based on algebraic methods, demonstrates the remarkable regularity and the similarity of structures of both lattices of logics, and gives essential information on the paraconsistent nature of logics Lj and N4.
The methods developed in this book can be applied for investigation of other classes of paraconsistent logics.
"About the title" may belong to another edition of this title.
Revaluation Books
Exeter, United Kingdom
AbeBooks seller since January 6, 2003
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