In this paper, we present an abstract framework of many-valued modal logic with the interpretation of atomic propositions and modal operators as predicate lifting over coalgebras for an endofunctor on the category of sets. It generalizes Pattinson's stratification method for colagebraic modal logic to the many-valued setting. In contrast to standard techniques of canonical model construction and filtration, this method employs an induction principle to prove the soundness, completeness, and finite model property of the logics. As a consequence, we can lift a restriction on the previous approach~ \cite{Lin2022} that requires the underlying language must have the expressive power to internalize the meta-level truth valuation operations.
翻译:在本文中,我们提出了一个许多有价值模式逻辑的抽象框架,将原子理论和模式操作者解释为一组子的末端人物的直升直升煤热数。它概括了Pattinson关于代谢模式逻辑的分层法与多值背景的概括。 与典型模型构建和过滤的标准技术相比,这种方法采用了引导原则来证明这些逻辑的健全性、完整性和有限模型属性。 因此,我们可以取消对先前方法~\ cite{Lin22}的限制,因为以前的方法要求基本语言必须具有将现代真理评估操作内化的明示力量。