Abstract:

Formal concept analysis is a partial order theory for conceptual analysis and visualization. Decision implications are the knowledge representation for decision-making in formal concept analysis. From the logical perspective, the semantic description and syntactic description have been given, with a complete set of inference rules for the syntactic aspect: the augmentation inference rule and the combination inference rule. Based on this, a new inference rule, consequence combination, is proposed and proven to be sound in this paper; furthermore, augmentation and consequence combination are proven to be complete with respect to the semantical aspect and non-redundant with respect to each other. Finally, the properties of augmentation and consequence combination inference rules are studied, and then deduction process is studied for deriving its closed set from a complete set using the inference rules. These conclusions are research basis for the future algorithm research and application, also the base for the deeper theoretic research.

Key words: formal concept analysis, decision implication, inference rule

摘要：

形式概念分析是用于概念分析和可视化的偏序集理论。决策蕴涵是形式概念分析在决策情形下的知识表示。已有研究从逻辑角度分析了决策蕴涵，并给出了完整的语义描述和语构描述，其中在语构方面已经有一个完备的推理规则集，即扩增推理规则和合并推理规则。在此基础上，提出了新的推理规则——后件合并推理规则，证明了其合理性，以及与扩增推理规则组成的推理规则集的完备性和无冗余性；通过研究扩增推理规则和后件合并推理规则的性质，给出了使用这两条推理规则从完备集推导其对应封闭集的有效方法等理论结果，为进一步的算法研究与应用以及更深入的理论研究工作奠定基础。

关键词: 形式概念分析, 决策蕴涵, 推理规则