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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.
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Recensione
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)
Contenuti
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.
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- EditoreSpringer
- Data di pubblicazione2010
- ISBN 10 9048160723
- ISBN 13 9789048160723
- RilegaturaCopertina flessibile
- LinguaInglese
- Numero di pagine340
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The Semantics and Proof Theory of the Logic of Bunched Implications (Applied Logic Series)
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The Semantics and Proof Theory of the Logic of Bunched Implications
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ISBN 10: 9048160723
ISBN 13: 9789048160723
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 340 pp. Englisch. Codice articolo 9789048160723
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The Semantics and Proof Theory of the Logic of Bunched Implications (Applied Logic Series)
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The Semantics and Proof Theory of the Logic of Bunched Implications
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Springer Netherlands, Springer Netherlands, 2010
ISBN 10: 9048160723
ISBN 13: 9789048160723
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9789048160723
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The Semantics and Proof Theory of the Logic of Bunched Implications (Applied Logic Series)
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