中文摘要：

以往的粗糙描述逻辑（RDL）都是基于传统的粗糙集理论。实际上,经常会出现用形式概念表示一个概念的情况,此时一个自然的问题就是如何处理可能出现的不确定概念。把形式概念分析与粗糙集理论联系起来做为基础,给出可定义概念和不可定义概念的定义,并给出不可定义概念的上近似和下近似,这里的近似定义虽然不同于传统的粗糙近似算子形式,但是有很好的实用性。基于新的上下近似定义,把一组近似算子引入到描述逻辑的结构中,形成一种新的粗糙描述逻辑。给出了相应的语法和语义,最后还给出了扩展的Tableau算法,可以用来解决相应的推理问题。

英文摘要：

The existing rough description logic （RDL） is based on the classical rough set theory. In fact, one often encounters a case that there is a formal concept structure on the domain of objects. A natural question is how to deal with the possibly occurring uncertain concepts. In the paper, based on a combination of the formal concept analysis and the rough set theory, we provide the notion of a definable concept. For an un-definable concept （a rough set）, the upper and lower approximations of a rough set based on formal concept are also given. The notions are very different from their classical forms, but they are pretty practical. Based on the novel notions of the upper and lower approximations, we add the approximation operators to the structure of description logic. Then a new RDL is established. The cor- responding semantic meaning and syntax are given. Finally, an extended Tableaux algorithm is given, which can be used to solve some related reasoning problems.