中文摘要：

针对基于粗糙集理论的决策信息系统的特点,引入属性常量作为基本符号,对命题模态逻辑进行扩展,给出了扩展命题模态逻辑形式系统及其相关语义描述,说明每个基于粗糙集理论的决策信息系统均可通过扩展命题模态逻辑语义来表示.本文证明了基于扩展命题模态逻辑语义的决策信息系统表示定理,并给出了语义模型中对象的逻辑描述,特别是对基于等价关系的上近似和下近似集的逻辑刻画,为基于粗糙集理论的决策信息系统分析和处理提供了新思路.

英文摘要：

To direct at the characteristic of the decision information system based on Rough Set theory,the propositional modal logic is extended by adding the attribute constants as basic symbols,and the formal system of the extended propositional modal logic as well as its semantics are described.Moreover,the representation theorems of the decision information system by using the semantics of the extended propositional modal logic and the logic descriptions about the objects in the semantics are given.