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.
"LK, LJ, Dual Intuitionistic Logic, and Quantum Logic." Notre Dame J. Formal Logic 45 (4) 193 - 213, 2004. https://doi.org/10.1305/ndjfl/1099238445