Quantum modal logic
Logic in Computer Science
2025-11-14 v1 Logic
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.
Cite
@article{arxiv.2511.10188,
title = {Quantum modal logic},
author = {Kenji Tokuo},
journal= {arXiv preprint arXiv:2511.10188},
year = {2025}
}