Quantum modal logic

Kenji Tokuo

doi:10.1093/jigpal/jzae123

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arXiv · 2511.10188

Quantum modal logic

Kenji Tokuo

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Abstract

A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are demonstrated. This framework is intended to serve as a basis for formalizing various modal logics over quantum logic, such as quantum alethic logic, quantum temporal logic, quantum epistemic logic, and quantum dynamic logic.

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Kenji Tokuo. 2025-11-13. Quantum modal logic. https://doi.org/10.1093/jigpal%2Fjzae123

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