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2004•Notre Dame Journal of Formal LogicOpen access

LK, LJ, Dual Intuitionistic Logic, and Quantum Logic

Hiroshi Aoyama

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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.

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What this paper is about

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.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Quantum logic, Intuitionistic logic, Paraconsistent logic, Intermediate logic, Many-valued logic, Mathematics, Dynamic logic (digital electronics), Dual (grammatical number)

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