论文标题
多价值煤层模态逻辑的归纳构造
An Inductive Construction for Many-Valued Coalgebraic Modal Logic
论文作者
论文摘要
在本文中，我们介绍了一个多价值模态逻辑的抽象框架，并将原子命题和模态算子解释为谓语上的谓语，以在集合类别上进行内膜。它将帕丁森的分层方法推广到colagebraic模态逻辑上，以列为多价值设置。与规范模型构建和过滤的标准技术相反，该方法采用归纳原理来证明逻辑的健全性，完整性和有限模型属性。结果，我们可以限制对先前的方法〜\ cite {lin2022}，需要基础语言必须具有表达能力来内部化元级真实估值操作。
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.
