, Volume 33, Issue 1, pp 103-113

Proof theory for minimal quantum logic I

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In this paper we give a sequential system of minimal quantum logic which enjoys cut-freeness naturally. The duality theorem, the cut-elimination theorem, and the completeness theorem with respect to the relational semantics of R. I. Goldblatt are presented. Due to severe limitations of space, technically heavy proofs of the first two theorems are relegated to a subsequent paper.