Skip to main content
SpringerLink
Log in
Book cover

The Semantics and Proof Theory of the Logic of Bunched Implications

  • Book
  • © 2002

Overview

Authors:
  1. David J. Pym

    1. University of Bath, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Applied Logic Series (APLS, volume 26)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xlix
    Download chapter PDF

  2. Propositional BI

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction to Part I

      • David J. Pym
      Pages 3-12

    3. Natural Deduction for Propositional BI

      • David J. Pym
      Pages 13-31

    4. Algebraic, Topological, Categorical

      • David J. Pym
      Pages 33-49

    5. Kripke Semantics

      • David J. Pym
      Pages 51-66

    6. Topological Kripke Semantics

      • David J. Pym
      Pages 67-87

    7. Propositional BI as a Sequent Calculus

      • David J. Pym
      Pages 89-95

    8. Towards Classical Propositional BI

      • David J. Pym
      Pages 97-106

    9. Bunched Logical Relations

      • David J. Pym
      Pages 107-119

    10. The Sharing Interpretation, I

      • David J. Pym
      Pages 121-144

  3. Predicate BI

    1. Front Matter

      Pages 145-145
      Download chapter PDF

    2. Introduction to Part II

      • David J. Pym
      Pages 147-156

    3. The Syntax of Predicate BI

      • David J. Pym
      Pages 157-162

    4. Natural Deduction and Sequent Calculus

      • David J. Pym
      Pages 163-177

    5. Kripke Semantics for Predicate BI

      • David J. Pym
      Pages 179-199

    6. Topological Kripke Semantics for Predicate BI

      • David J. Pym
      Pages 201-205

    7. Resource Semantics, Type Theory and Fibred Categories

      • David J. Pym
      Pages 207-261

    8. The Sharing Interpretation, II

      • David J. Pym
      Pages 263-269

  4. Back Matter

    Pages 271-290
    Download chapter PDF
Back to top

Keywords

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)

Authors and Affiliations

  • 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

Publish with us

Policies and ethics

Back to top

Search

Navigation