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Applied Logic Series

The Semantics and Proof Theory of the Logic of Bunched Implications

Authors: Pym, David J.

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eBook $209.00
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  • ISBN 978-94-017-0091-7
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Hardcover $269.00
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  • ISBN 978-1-4020-0745-3
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  • Usually dispatched within 3 to 5 business days.
Softcover $269.00
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  • ISBN 978-90-481-6072-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This is a monograph about logic. Specifically, it presents the mathe­ matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono­ graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel­ opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu­ tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.

Reviews

From the reviews:

"This monograph presents a mathematical theory of the logic of BI … . Due to the author’s clear and approachable style this book may be interesting to a large circle of logicians, mathematicians and computer scientists. In particular, it could be useful to graduate students, specialists and researchers in the field of applications of logic in programming. In addition to its other qualities, this book also presents a significant contribution to a new area of mathematical logic—fibring logic … .” (Branislav Boricic, Mathematical Reviews, Issue 2008 i)


Table of contents (16 chapters)

Buy this book

eBook $209.00
price for USA
  • ISBN 978-94-017-0091-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $269.00
price for USA
  • ISBN 978-1-4020-0745-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $269.00
price for USA
  • ISBN 978-90-481-6072-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Semantics and Proof Theory of the Logic of Bunched Implications
Authors
Series Title
Applied Logic Series
Series Volume
26
Copyright
2002
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-017-0091-7
DOI
10.1007/978-94-017-0091-7
Hardcover ISBN
978-1-4020-0745-3
Softcover ISBN
978-90-481-6072-3
Series ISSN
1386-2790
Edition Number
1
Number of Pages
XLIX, 290
Topics