Lattice logic, bilattice logic and paraconsistent quantum logic: A unified framework based on monosequent systems
Lattice logic, bilattice logic and paraconsistent quantum logic: A unified framework based on monosequent systems
复制标题
格逻辑、双格逻辑和次相一致量子逻辑：基于单序列系统的统一框架
DOI：
10.1007/s10992-020-09585-2
复制
发表时间：
2021
影响因子：
1.5
通讯作者：
Norihiro Kamide
中科院分区：
文献类型：
--
作者：
近藤和希;関川浩;Norihiro Kamide
格逻辑、双格逻辑和次协调量子逻辑都是基于单量子系统来研究的。次协调量子逻辑是格逻辑的推广，双格逻辑是次协调量子逻辑的推广。Monochronical系统是一种基于限制性代数的代数演算，它的前件和后件都只包含一个公式。已知关于格值语义的完备性定理对于格逻辑的单值系统成立。证明了次协调量子逻辑关于格值语义的完备性定理，证明了双格逻辑关于双格值语义的完备性定理。一些语法性质，包括削减消除和对偶，也研究了这些逻辑的monoclonal系统。
Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect to a lattice-valued semantics is proved for paraconsistent quantum logic, and a completeness theorem with respect to a bilattice-valued semantics is proved for bilattice logic. Some syntactical properties, including cut-elimination and duality, are also investigated for the monosequent systems for these logics.