Notre Dame Journal of Formal Logic

LK, LJ, Dual Intuitionistic Logic, and Quantum Logic

Hiroshi Aoyama


In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic (orthologic and orthomodular 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 (a kind of paraconsistent logic). Our study is completely syntactical.

Article information

Notre Dame J. Formal Logic, Volume 45, Number 4 (2004), 193-213.

First available in Project Euclid: 29 October 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B53: Paraconsistent logics 03B60: Other nonclassical logic

LK LJ dual intuitionistic logic paraconsistent logic quantum logic


Aoyama, Hiroshi. LK, LJ, Dual Intuitionistic Logic, and Quantum Logic. Notre Dame J. Formal Logic 45 (2004), no. 4, 193--213. doi:10.1305/ndjfl/1099238445.

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