The Semantics and Proof Theory of the Logic of Bunched Implications (2002) (Applied Logic Series #26)

Synopsis

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.

Copyright:

2002

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9789401700917

Related ISBNs:

9781402007453

Publisher:

Springer Netherlands

Date of Addition:

08/19/22

Copyrighted By:

N/A

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Computers and Internet, Mathematics and Statistics, Philosophy

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.