Cognitive Technologies

Conditionals and Modularity in General Logics

Authors: Gabbay, Dov M., Schlechta, Karl

  • The authors present results on modularity and interpolation for monotonic and nonmonotonic logic, using a semantic approach and revealing new insights.
  • The first monograph on this topic.
  • This book is useful for researchers and advanced students.
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eBook $109.00
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  • ISBN 978-3-642-19068-1
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Hardcover $149.00
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  • ISBN 978-3-642-19067-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
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  • ISBN 978-3-642-27065-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation.

The book will be of value to researchers and graduate students in logic and theoretical computer science.

About the authors

The first author is one of the foremost authorities on nonclassical logics and their applications in computing, the second author has written three related research monographs.

Reviews

From the book reviews:

“The book contains many of the authors’ recently published or unpublished results, which should provide motivation for new research. In their presentation, the authors adhere to the rule that relevant examples must accompany each new notion, making this book easier and more interesting to read. Undoubtedly, this fine and clearly written book will be an appropriate reference for researchers and students in mathematics, logic and theoretical computer science.” (Branislav Boričić, Mathematical Reviews, February, 2015)

“The authors’ work focuses mainly on propositional logic. It consists of seven chapters, where the first chapter is an introduction that presents a useful summary of the topics dealt with in the other chapters, and main results for each of the topics. … this work is suitable for a research seminar in logic which would focus on some of those subjects or related topics.” (Max A. Freund, Zentralblatt MATH, Vol. 1234, 2012)

"This book is a tour de force achieved by perhaps the only people who could pull this off. It provides one fresh unified view of conditionals, non-monotonic reasoning, interpolation, and modularity of information, based on fine-grained neighbourhood models. The new ideas in this book will reverberate in the community for quite a while to come." Johan van Benthem (University of Amsterdam and Stanford University)

Table of contents (7 chapters)

  • Introduction

    Gabbay, Dov M. (et al.)

    Pages 1-30

  • Basic Definitions

    Gabbay, Dov M. (et al.)

    Pages 31-83

  • Towards a Uniform Picture of Conditionals

    Gabbay, Dov M. (et al.)

    Pages 85-112

  • Monotone and Antitone Semantic and Syntactic Interpolation

    Gabbay, Dov M. (et al.)

    Pages 113-151

  • Laws About Size and Interpolation in Non-monotonic Logics

    Gabbay, Dov M. (et al.)

    Pages 153-195

Buy this book

eBook $109.00
price for USA
  • ISBN 978-3-642-19068-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-642-19067-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-642-27065-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Conditionals and Modularity in General Logics
Authors
Series Title
Cognitive Technologies
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-19068-1
DOI
10.1007/978-3-642-19068-1
Hardcover ISBN
978-3-642-19067-4
Softcover ISBN
978-3-642-27065-9
Series ISSN
1611-2482
Edition Number
1
Number of Pages
IX, 233
Topics