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Labelled Connection-based Proof Search for Multiplicative Intuitionistic Linear Logic

Didier Galmiche 1 Daniel Méry 1 
1 TYPES - Logic, Proof Theory and Programming
LORIA - FM - Department of Formal Methods
Abstract : We propose a connection-based characterization for multiplicative intuitionistic linear logic ({\MILL}) which is based on labels and constraints that capture Urquhart's possible world semantics of the logic. We first briefly recall the purely syntactic sequent calculus for {\MILL}, which we call LMILL. Then, in the spirit of our previous results on the Logic of Bunched Implications (BI), we present a connection-based characterization of MILL provability. We show its soundness and completeness without the need for any notion of multiplicity. From the characterization, we finally propose a labelled sequent calculus for MILL.
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Submitted on : Wednesday, October 28, 2020 - 4:27:53 PM
Last modification on : Monday, February 7, 2022 - 10:04:06 AM


  • HAL Id : hal-02982539, version 1



Didier Galmiche, Daniel Méry. Labelled Connection-based Proof Search for Multiplicative Intuitionistic Linear Logic. International Workshop on Automated Reasoning in Quantified Non-Classical Logics, ARQNL 2018, 2018, Oxford, United Kingdom. pp.49-63. ⟨hal-02982539⟩



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