The Semantics and Proof Theory of the Logic of Bunched Implications by David J. PymThe Semantics and Proof Theory of the Logic of Bunched Implications by David J. Pym

The Semantics and Proof Theory of the Logic of Bunched Implications

byDavid J. Pym

Paperback | December 4, 2010

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This monograph provides a thorough account of the model theory, proof theory and computational interpretations of BI, the logic of bunched implications, which freely combines intuitionistic logic and multiplicative intuitionistic linear logic. Starting, on the one hand, from elementary observations about modelling resources and, on the other, from a desire to develop a system of logic within which additive (or extensional) and multiplicative (or intensional) implications co-exist with equal logical status, we give natural deduction, lambda-calculi, sequent calculus, categorical semantics, Kripke models, topological models, logical relations and computational interpretations for both propositional and predicate BI, within which both additive and multiplicative quantifiers also co-exist.This monograph will be of interest to graduate students and researchers in mathematical logic, philosophical logic, computational logic and theoretical computer science.
Title:The Semantics and Proof Theory of the Logic of Bunched ImplicationsFormat:PaperbackDimensions:339 pages, 9.45 × 6.3 × 0 inPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048160723

ISBN - 13:9789048160723

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Table of Contents

List of Figures. List of Tables. Preface. Acknowledgments. Foreword. Introduction; David J. Pym. Part I: Propositional BI. 1. Introduction to Part I. 2. Natural Deduction for Propositional BI. 3. Algebraic, Topological, Categorical. 4. Kripke Semantics. 5. Topological Kripke Semantics. 6. Propositional BI as a Sequent Calculus. 7. Towards Classical Propositional BI. 8. Bunched Logical Relations. 9. The Sharing Interpretation, I. Part II: Predicate BI. 10. Introduction to Part II. 11. The Syntax of Predicate BI. 12. Natural Deduction & Sequent Calculus For Predicate BI. 13. Kripke Semantics for Predicate BI. 14. Topological Kripke Semantics for Predicate BI. 15. Resource Semantics, Type Theory & Fibred Categories. 16. The Sharing Interpretation, II. Bibliography. Index.

Editorial 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)