The Semantics and Proof Theory of the Logic of Bunched Implications

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Springer Science & Business Media, 31 juil. 2002 - 290 pages
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.
 

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Table des matières

I
xxi
II
1
III
3
IV
13
V
33
VI
51
VII
67
VIII
89
XI
121
XII
145
XIII
147
XIV
157
XV
163
XVI
179
XVII
201
XVIII
207

IX
97
X
107

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Page ii - Department of Computer Science, King's College, London, UK SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing...
Page i - Pym. The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series. Kluwer Academic Publishers, 2002.

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