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.

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"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)

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University of Bath, UK

David J. Pym

Bibliographic Information

Book Title: The Semantics and Proof Theory of the Logic of Bunched Implications
Authors: David J. Pym
Series Title: Applied Logic Series
DOI: https://doi.org/10.1007/978-94-017-0091-7
Publisher: Springer Dordrecht
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media B.V. 2002
Hardcover ISBN: 978-1-4020-0745-3Published: 31 July 2002
Softcover ISBN: 978-90-481-6072-3Published: 04 December 2010
eBook ISBN: 978-94-017-0091-7Published: 17 April 2013
Series ISSN: 1386-2790
Edition Number: 1
Number of Pages: XLIX, 290
Topics: Mathematical Logic and Foundations, Logic, Programming Languages, Compilers, Interpreters

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Table of contents (16 chapters)

Front Matter

Propositional BI

Front Matter

Predicate BI

Front Matter

Back Matter

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University of Bath, UK

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