Bulletin of the Section of Logic 51 (1):73-89 (2022)

Abstract
In this study, new sequent calculi for a minimal quantum logic ) are discussed that involve an implication. The sequent calculus \ for \ was established by Nishimura, and it is complete with respect to ortho-models. As \ does not contain implications, this study adopts the strict implication and constructs two new sequent calculi \ and \ as the expansions of \. Both \ and \ are complete with respect to the O-models. In this study, the completeness and decidability theorems for these new systems are proven. Furthermore, some details pertaining to new rules and the strict implication are discussed.
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DOI 10.18778/0138-0680.2021.22
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References found in this work BETA

Proof Theory for Modal Logic.Sara Negri - 2011 - Philosophy Compass 6 (8):523-538.
Implication Connectives in Orthomodular Lattices.L. Herman, E. L. Marsden & R. Piziak - 1975 - Notre Dame Journal of Formal Logic 16 (3):305-328.
Material Implication in Orthomodular (and Boolean) Lattices.Gary M. Hardegree - 1981 - Notre Dame Journal of Formal Logic 22 (2):163-182.

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