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arXiv · 2010.08352

Focused Proof-search in the Logic of Bunched Implications

Alexander Gheorghiu·Sonia Marin
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Abstract

The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof theory, proof-search in BI has always been a difficult problem. The focusing principle is a restriction of the proof-search space that can capture various goal-directed proof-search procedures. In this paper, we show that focused proof-search is complete for BI by first reformulating the traditional bunched sequent calculus using the simpler data-structure of nested sequents, following with a polarised and focused variant that we show is sound and complete via a cut-elimination argument. This establishes an operational semantics for focused proof-search in the logic of Bunched Implications.

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Alexander Gheorghiu, Sonia Marin. 2020-10-16. Focused Proof-search in the Logic of Bunched Implications. https://arxiv.org/abs/2010.08352

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