The Semantics and Proof Theory of the Logic of Bunched Implications
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 monograph 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 development for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated computational 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.
1139950820
The Semantics and Proof Theory of the Logic of Bunched Implications
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 monograph 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 development for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated computational 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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The Semantics and Proof Theory of the Logic of Bunched Implications

The 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

The Semantics and Proof Theory of the Logic of Bunched Implications

by David J. Pym

Overview

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 monograph 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 development for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated computational 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.

Product Details

ISBN-13: 9789048160723
Publisher: Springer Netherlands
Publication date: 12/04/2010
Series: Applied Logic Series , #26
Edition description: Softcover reprint of hardcover 1st ed. 2002
Pages: 290
Product dimensions: 6.30(w) x 9.45(h) x 0.03(d)

Table of Contents

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.- II Predicate BI.- 10. Introduction to Part II.- 11. The Syntax of Predicate BI.- 12. Natural Deduction & Sequent Calculus.- 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.
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