## Notre Dame Journal of Formal Logic

### LK, LJ, Dual Intuitionistic Logic, and Quantum Logic

Hiroshi Aoyama

#### Abstract

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

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

Dates
First available in Project Euclid: 29 October 2004

http://projecteuclid.org/euclid.ndjfl/1099238445

Digital Object Identifier
doi:10.1305/ndjfl/1099238445

Mathematical Reviews number (MathSciNet)
MR2130478

Zentralblatt MATH identifier
02186745

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

#### Citation

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. http://projecteuclid.org/euclid.ndjfl/1099238445.

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