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Outstanding Contributions to Logic

J. Michael Dunn on Information Based Logics

Editors: Bimbó, Katalin (Ed.)

  • Highlights contemporary developments in formal logic resulting from the focus on information and its role in inferences 
  • Presents a collection of papers addressing the central theme of J. Michael Dunn's research over the past half century 
  • Offers new research findings, overviews, and fresh presentations of earlier results brought together in a collection selected by experts in nonclassical logics
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  • ISBN 978-3-319-29300-4
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About this book

This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information.

The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics.

The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.

About the authors

Professor Katalin Bimbó is a logician working in the field of non-classical logics. Her main research interests and findings are in the areas of relevance and combinatory logics. She is the author of three books and numerous journal articles. Professor Bimbó held academic positions in the USA, New Zealand and Australia before moving to Canada, where she works at the University of Alberta, in Edmonton.

Table of contents (19 chapters)

  • Introduction: From Information at Large to Semantics of Logics

    Bimbó, Katalin

    Pages 1-14

  • $$\mathbf {RM}$$ and its Nice Properties

    Avron, Arnon

    Pages 15-43

  • Wedge Sum, Merge and Inconsistency

    Mortensen, Chris

    Pages 45-51

  • Single Axioms and Axiom-Pairs for the Implicational Fragments of $$\mathbf {R}$$ , R-Mingle, and Some Related Systems

    Ulrich, Dolph

    Pages 53-80

  • LC and Its Pretabular Relatives

    Maksimova, Larisa

    Pages 81-91

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-29300-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-29298-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
J. Michael Dunn on Information Based Logics
Editors
  • Katalin Bimbó
Series Title
Outstanding Contributions to Logic
Series Volume
8
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29300-4
DOI
10.1007/978-3-319-29300-4
Hardcover ISBN
978-3-319-29298-4
Series ISSN
2211-2758
Edition Number
1
Number of Pages
XLIII, 436
Number of Illustrations and Tables
21 b/w illustrations
Topics