Abstract: This paper aims at establishing a one-to-one correspondence between rough approximation operators in multigranulation space and epistemic operators in knowledge reasoning, and thus providing a more reasonable semantic interpretation for rough approximation operators in multigranulation space. By deeply analyzing the close relationship between the semantic set of a logic formula and that of the formula obtained by adding different epistemic operators, this paper proves that EG, CG, DG are in one-to-one correspondence with rough lower approximation operator in model AIU, rough lower approximation operator in model RU and rough lower approximation operator in model RI, respectively. The obtained results are the generalization of the relationship between modal logic and Pawlak rough set in multi-agent environment.

Key words: multigranulation space, rough approximation, knowledge reasoning

摘要： 旨在建立起多粒度空间中粗糙近似算子与知识推理中认知算子之间的一一对应关系，从而给出多粒度空间中粗糙近似算子更为合理的语义解释。对于任意逻辑公式，通过分析其语义集与加了认知算子后的语义集之间的关系，证明了全知算子EG对应于多粒度空间中模型AIU中的下近似算子，公共知识认知算子CG对应于模型RU中的下近似算子，分配知识认知算子DG对应于模型RI中的下近似算子，所得结论是模态逻辑与Pawlak粗糙集之间对应关系在多当事人环境下的推广。

关键词: 多粒度空间, 粗糙近似, 知识推理