Abstract: Aiming at epistemic role being not capable of expressing bi-directional relationship between individuals, this paper embeds inverse role into description logic ALCK and obtains ALCIK in order to extend expressiveness, models practical problems more conveniently while keeping capturing minimal knowledge and introspecting. It gives semantic and syntax of ALCIK and designs query tableau algorithm on condition that Tbox is empty and Abox is K-free. It also proves that the algorithm which will terminate definitely is sound and complete by induction on structure of ALCIK concept and investigates its computational complexity at last. The theoretical analysis shows that in this situation epistemic query problem is decidable and complexity is in PSpace-hard class.

Key words: epistemic role, inverse role, K operator, query tableau algorithm, complexity

摘要： 针对认知角色不能表达个体间双向关系的问题，在描述逻辑ALCK中加入逆角色得到ALCIK，以扩充其表达能力，在能够捕获最小知识和实现自省推理的同时可以更加方便地对实际问题建模，给出了ALCIK的语法和语义，并且在Tbox为空集，Abox中无K算子的情况下，设计了ALCIK概念的查询表算法，根据概念结构归纳证明了表算法的可靠性和完备性，并且一定会停机，最后讨论了复杂度。理论分析表明，此时认知查询问题是可判定的，并且计算复杂度为PSpace-hard。

关键词: 认知角色, 逆角色, K算子, 查询表算法, 复杂度