量子模态逻辑
Quantum modal logic
Kenji Tokuo
arXiv
2025年11月13日
基于量子逻辑的模态逻辑以最简单的形式形式化。 具体来说,提供了关系语义和隐性微积分,并证明了连接这两个概念的健全性和完整性定理。 该框架旨在作为将量子逻辑的各种模态逻辑形式化的基础,例如量子极化逻辑、量子时间逻辑、量子认识论逻辑和量子动态逻辑。
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.