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Classical BI: A logic for reasoning about dualising resources

Brotherston, J; Calcagno, C; (2009) Classical BI: A logic for reasoning about dualising resources. In: Shao, Z and Pierce, BC, (eds.) POPL '09: Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages. (pp. 328 - 339). Association for Computing Machinery (ACM): New York, NY, United States.

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We show how to extend O'Hearn and Pym's logic of bunched implications, BI, to classical BI (CBI), in which both the additive and the multiplicative connectives behave classically. Specifically, CBI is a non-conservative extension of (propositional) Boolean BI that includes multiplicative versions of falsity, negation and disjunction. We give an algebraic semantics for CBI that leads us naturally to consider resource models of CBI in which every resource has a unique dual. We then give a cut-eliminating proof system for CBI, based on Belnap's display logic, and demonstrate soundness and completeness of this proof system with respect to our semantics.

Type: Proceedings paper
Title: Classical BI: A logic for reasoning about dualising resources
Event: Principles of Programming Languages (POPL)
ISBN-13: 9781605583792
DOI: 10.1145/1480881.1480923
Publisher version: http://dx.doi.org/10.1145/1480881.1480923
Language: English
Additional information: ACM New York, NY, USA © 2009.
Keywords: Classical BI, display logic, semantics, resource models, completeness, cut-elimination, bunched implications
UCL classification: UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Engineering Science
URI: http://discovery.ucl.ac.uk/id/eprint/1353145
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