A labelled sequent calculus for BBI: proof theory and proof search
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Goré, Rajeev
Tiu, Alwen
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Abstract
We present a labelled sequent calculus for Boolean bunched implications (BBI), a classical variant of the logic of Bunched Implications (BI). 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 localized around applications of certain logical rules, thereby localizing 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 show that different semantics for BBI and some axioms in concrete models can be captured modularly simply by adding extra structural rules.
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Journal of Logic and Computation
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28
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4
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© 2018 Oxford University Press. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Logic and Computation following peer review. The definitive publisher-authenticated version A labelled sequent calculus for BBI: proof theory and proof search, Journal of Logic and Computation, Volume 28, Issue 4, June 2018, Pages 809–872 is available online at: https://doi.org/10.1093/logcom/exv033
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Mathematical sciences
Philosophy and religious studies
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Hou, Z; Goré, R; Tiu, A, A labelled sequent calculus for BBI: proof theory and proof search, Journal of Logic and Computation, 2018, 28 (4), pp. 809-872