基于K4的超模态逻辑

A Hypermodal Logic Based on K4

D.M.Gabbay在"超模态逻辑理论:模态逻辑中的模转换"一文中建立了基于任意框架上的超模态逻辑语义学以及第一个超模态逻辑Hs i。该文旨在于扩充语义学,将任意框架上的超模态逻辑语义学扩充到传递框架上,并尝试构建一个K4以上的超模态逻辑K4[T,K],主要研究K4、S4超模态算子性质,特别是关于它叠置的归约问题。

In'A theory of hypermodal logics: Mode shifting in modal logic'D. M. Gabbay founded a semantics of hypermodal logics based on any frame. He is the first one who founded a hypermodal logicHs i,. Well,Following Gabbay's paradigm,my thesis is to expand the semantics to transitive frames,based on which we are going to found a logic K4[T,K]. There,we are going to study the properties of two kinds of hypermodalities K4 and S4,espectially of the problem of nested hypermodalities.