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逻辑的表达力及其推理问题的计算复杂性一直以来都是逻辑研究的两个重点。描述逻辑是一族重要的知识表示语言，目前国内外对其计算复杂性的研究成果比较丰富。相对而言，对其表达力的研究较少。从逻辑语义的角度看，解释之间的互模拟关系是刻画表达力的一个有效途径，其较具代表性的结论是刻画命题模态逻辑表达力的van Benthem 定理。文中主要研究了包含顶概念、原子概念、原子概念否定、概念交和完全存在约束等 5 个概念构造子的描述逻辑 ，给出了 模拟关系，建立了刻画 表达力的 van Benthem 定理。在 基础之上，再增加概念并构造子，还给出刻画 表达力的 vanBenthem 定理。在这些工作的基础上,给出了EL、EL和ELU等 4 个系统表达力之间的比较结果.结合上述 4 个系统及 在概念之间包含关系推理问题的计算复杂性,明确了如下结论:在表达力要求不高的情形下,可以优先选择 作为本体的表示语言.而对表达力要求较高的情形下,应该优先选择 作为本体的表示语言.同时,在没有特殊要求的情况下,应尽量避免使用EL-、ELY和ELY-作为本体的表示语言.
The logic of expression and the computational complexity of its reasoning problems have long been the two focuses of logical research. Description logic is a family of important knowledge representation languages. At present, the research results of computational complexity at home and abroad are rich. Relatively speaking, less research on its expression. From the point of view of logic and semantics, the inter-simulative relationship between interpretations is an effective way to express expressive force. The more representative conclusion is the van Benthem theorem that expresses the expressive power of propositional modal logic. In this paper, five description constructors including top concept, atomic concept, negative concept of atomic concept, conceptual concept and complete existence constraint are mainly studied. The van Benthem theorem is established to describe the expressive power. On top of that, add concepts and construct children, and also give van Benthem’s theorem that portrays expressiveness. On the basis of these work, the comparison results between the four system expressions such as EL, EL and ELU are given.According to the above four systems and the computational complexity of including the relationship reasoning among the concepts, the following conclusions are made clear : In the case of less expressive power, you can give priority to as the body of the language, while the expression of the higher requirements of the situation, we should give priority to as the body of the language.At the same time, without special requirements, Try to avoid using EL-, ELY, and ELY- as ontology languages.