article

Possible worlds and resources: the semantics of BI

Authors:

Peter W. O'Hearn,

Hongseok YangAuthors Info & Claims

Theoretical Computer Science, Volume 315, Issue 1

Pages 257 - 305

https://doi.org/10.1016/j.tcs.2003.11.020

Published: 05 May 2004 Publication History

Abstract

The logic of bunched implications, BI, is a substructural system which freely combines an additive (intuitionistic) and a multiplicative (linear) implication via bunches (contexts with two combining operations, one which admits Weakening and Contraction and one which does not). BI may be seen to arise from two main perspectives. On the one hand, from proof-theoretic or categorical concerns and, on the other, from a possible-worlds semantics based on preordered (commutative) monoids. This semantics may be motivated from a basic model of the notion of resource. We explain BI's proof-theoretic, categorical and semantic origins. We discuss in detail the question of completeness, explaining the essential distinction between BI with and without ⊥ (the unit of V). We give an extensive discussion of BI as a semantically based logic of resources, giving concrete models based on Petri nets, ambients, computer memory, logic programming, and money.

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Possible worlds and resources: the semantics of BI

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Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 315, Issue 1

Mathematical foundations of programming semantics

5 May 2004

300 pages

ISSN:0304-3975

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Elsevier Science Publishers Ltd.

United Kingdom

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Published: 05 May 2004

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