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Erschienen in:
2013 | OriginalPaper | Buchkapitel
A Labelled Sequent Calculus for BBI: Proof Theory and Proof Search
verfasst von : Zhé Hóu, Alwen Tiu, Rajeev Goré
Erschienen in: Automated Reasoning with Analytic Tableaux and Related Methods
Verlag: Springer Berlin Heidelberg
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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.