LK, LJ, Dual Intuitionistic Logic, and Quantum Logic

Notre Dame Journal of Formal Logic 45 (4):193-213 (2004)
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Abstract

In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical

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10.1305/ndjfl/1099238445

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Citations of this work

Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.

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References found in this work

Semantic analysis of orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
On Closed Elements in Closure Algebras.J. C. C. Mckinsey & Alfred Tarski - 1946 - Annals of Mathematics, Ser. 2 47:122-162.
Dual-Intuitionistic Logic.Igor Urbas - 1996 - Notre Dame Journal of Formal Logic 37 (3):440-451.
The Logic of Contradiction.Nicolas D. Goodman - 1981 - Mathematical Logic Quarterly 27 (8‐10):119-126.

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