English

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.

Keywords

Cite

@article{arxiv.2511.10188,
  title  = {Quantum modal logic},
  author = {Kenji Tokuo},
  journal= {arXiv preprint arXiv:2511.10188},
  year   = {2025}
}