Symmetric paraconsistent quantum logic
Symmetric paraconsistent quantum logic
复制标题
对称次相容量子逻辑
DOI：
10.1109/ismvl51352.2021.00014
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Norihiro Kamide
中科院分区：
文献类型：
--
作者：
山下真;Tim J. Mullin;Sena Safarina;T. Maehara and K. Ando;Norihiro Kamide
本文引入了一种新的逻辑--对称次协调量子逻辑（SPQL），它是一个对偶单序列系统，是一个限制的、有指标的量子演算。SPQL逻辑是Dalla Chiara和Giuntini的次协调量子逻辑（PQL）的推广和推广。证明了在句法和语义上将SPQL嵌入到PQL中以及将PQL嵌入到SPQL中的定理。此外，还证明了SPOL的割消定理、逆消定理、逆消定理和代数完备定理。
In this study, a new logic called symmetric paracon-sistent quantum logic (SPQL) is introduced as a dual monose-quent system, which is a restricted and indexed sequent calculus. The logic SPQL is regarded as an extension and generalization of Dalla Chiara and Giuntini's paraconsistent quantum logic (PQL). Theorems for syntactically and semantically embedding SPQL into PQL and vice versa are proved. Additionally, cut-elimination, symmetry-elimination, contraposition-elimination, and algebraic-completeness theorems are proved for SPOL.