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Applied Logic Series

Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

Authors: Carnielli, W., Coniglio, M., Gabbay, D.M., Gouveia, P., Sernadas, C.

  • First book addressing both composition and decomposition of logics
  • Tool box for combining and decomposing logics in different guises
  • Mathematical approach
  • Several examples in such diverse areas as software specification, knowledge representation, argumentation theory, networks, security protocols and quantum computing
  • Written by internationally leading researchers in the field of pure and applied logic and philosophy
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eBook $179.00
price for USA (gross)
  • ISBN 978-1-4020-6782-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-1-4020-6781-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $229.00
price for USA
  • ISBN 978-90-481-7725-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete.

The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning.

This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics).

Reviews

From the reviews:

“This is an advanced book on the combination of logics, which is a recent hot topic in logical research. The merit of the book is that it provides an overview of the scene, besides proving original theorems, in the scope of a general methodology for combination called fibring. … This book will be of interest to a large audience given that it also deals with applications of fibring in different areas.” (Alexandre Costa-Leite, Mathematical Reviews, Issue 2010 a)


Table of contents (11 chapters)

  • Introductory overview

    Carnielli, Walter (et al.)

    Pages 1-36

  • Splicing logics: Syntactic fibring

    Carnielli, Walter (et al.)

    Pages 37-89

  • Splicing logics: Semantic fibring

    Carnielli, Walter (et al.)

    Pages 91-137

  • Heterogeneous fibring

    Carnielli, Walter (et al.)

    Pages 139-178

  • Fibring non-truth functional logics

    Carnielli, Walter (et al.)

    Pages 179-214

Buy this book

eBook $179.00
price for USA (gross)
  • ISBN 978-1-4020-6782-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-1-4020-6781-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $229.00
price for USA
  • ISBN 978-90-481-7725-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Analysis and Synthesis of Logics
Book Subtitle
How to Cut and Paste Reasoning Systems
Authors
Series Title
Applied Logic Series
Series Volume
35
Copyright
2008
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-6782-2
DOI
10.1007/978-1-4020-6782-2
Hardcover ISBN
978-1-4020-6781-5
Softcover ISBN
978-90-481-7725-7
Series ISSN
1386-2790
Edition Number
1
Number of Pages
XVI, 602
Topics