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Conference Papers Year : 2018

Labelled Connection-based Proof Search for Multiplicative Intuitionistic Linear Logic

Didier Galmiche
Daniel Méry

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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Dates and versions

hal-02982539 , version 1 (28-10-2020)

Identifiers

  • HAL Id : hal-02982539 , version 1

Cite

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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