A labelled sequent calculus for BBI: Proof theory and proof search

Zhé Hóu, Rajeev Goré, Alwen Tiu

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    1 Citation (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)809-872
    Number of pages64
    JournalJournal of Logic and Computation
    Volume28
    Issue number4
    DOIs
    Publication statusPublished - 7 Jun 2018

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