عنوان

The Semantics and Proof Theory of the Logic of Bunched Implications

(Number (ISBN

9789048160723

(Number (ISBN

9789401700917

Number

b408450

Title Proper

The Semantics and Proof Theory of the Logic of Bunched Implications

General Material Designation

[Book]

First Statement of Responsibility

by David J. Pym.

Place of Publication, Distribution, etc.

Dordrecht :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

2002.

Series Title

Applied Logic Series,

Volume Designation

26

ISSN of Series

1386-2790 ;

Text of Note

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.

0

Text of Note

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.

International Standard Book Number

9789048160723

Title

Springer eBooks

Computer science.

Logic.

Philosophy (General).

Pym, David J.

SpringerLink (Online service)

Date of Transaction

20190307161900.0

Electronic name

[Book]

Y