基于Rough集理论的模态逻辑与Rough逻辑

MODAL LOGIC AND Rough LOGIC BASED ON Rough SETTHEORY

在介绍Ｒｏｕｇｈ集的基础上，定义了Ｒｏｕｇｈ下（Ｌ）和上（Ｈ）近似算子，建立了基于Ｒｏｕｇｈ集理论的模态逻辑和Ｒｏｕｇｈ逻辑。阐述了这两种逻辑能在Ｒｏｕｇｈ集公理化基础上被统一起来，并且随着不同性质的关系Ｒ，能得到与模态逻辑相平行的各种Ｒｏｕｇｈ逻辑模型。

This paper defines rough lower (L) and upper (H) approximate operatores,and establishes modal logic and rough logic based on rough setstheory.It describes the uniformity of two logic on the basis of rough set axiomatization.And we have various similar deductive models of rough logic to modal logic according to different properties of relation R.