A Labelled Sequent Calculus for BBI: Proof Theory and Proof Search

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Hou, Zhe
Tiu, Alwen
Goré, Rajeev
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Galmiche, D

LarcheyWendling, D

Date
2013
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Nancy, France

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Abstract

We present a labelled sequent calculus for Boolean BI (BBI), a classical variant of the logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination. We show that all the structural rules in the calculus, i.e., those rules that manipulate labels and ternary relations, can be localised around applications of certain logical rules, thereby localising the handling of these rules in proof search. Based on this, we demonstrate a free variable calculus that deals with the structural rules lazily in a constraint system. We propose a heuristic method to quickly solve certain constraints, and show some experimental results to confirm that our approach is feasible for proof search. Additionally, we conjecture that different semantics for BBI and some axioms in concrete models can be captured by adding extra structural rules.

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Lecture Notes in Computer Science

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8123

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© Springer-Verlag Berlin Heidelberg 2013. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.The original publication is available at www.springerlink.com

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Theory of computation

Science & Technology

Computer Science, Artificial Intelligence

Computer Science, Software Engineering

Logic

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Hou, Z; Tiu, A; Goré, R, A Labelled Sequent Calculus for BBI: Proof Theory and Proof Search, Lecture Notes in Computer Science, 2013, 8123, pp. 172-187