Journal of Philosophical Logic 47 (2):301-324 (2018)

Abstract
Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.
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DOI 10.1007/s10992-017-9428-z
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References found in this work BETA

The Logic of Quantum Mechanics.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-45.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible Falsity and Inexact Predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Semantic Analysis of Orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.

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Citations of this work BETA

The Philosophy of Logical Practice.Ben Martin - 2022 - Metaphilosophy 53 (2-3):267-283.

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