中文摘要：

着重介绍NKIMath中数学概念的知识表示方法．首先给出了NKIMath知识系统的体系结构，分析了获取数学知识的不同用途．在次基础上给出了一种融合了本体、框架和逻辑综合的知识表示方法，将知识分为滑词逻辑层、知识描述层和概念关系层，不同层次可以满足不同用途的需求，详细给出了数学概念知识表示的基本模式以及参数表示形式．NKIMath可以很容易地实现与W3C推荐的数学文档标注语言OMDoc之间的相互转换，同时在知识表示的多粒度、多语言版本知识自动生成等方面优于OMDoc．

英文摘要：

Mathematical knowledge representation and acquisition are major tasks in many mathematical applications, including knowledge-based automated theorem proving, integration of different mathematical software systems, mathematical semantic Web, and high-level mathematical instruction. Formally launched in early 2000 in the Institute of Computing Technology, Chinese Academy of Sciences, the project of National Knowledge Infrastructure （NKI） aims to build a multi-domain knowledge base to be shared by various knowledge-intensive sophisticated applications, such as natural language understanding, speech understanding, planning and diagnosis, through a standard knowledge application programming interface. In 2001, a subproject called NKIMath was initiated to build a multi-branch mathematical knowledge base as a component of NKI. So far, thousands of mathematical concepts and assertions have been acquired, covering algebra, set theory, number theory, graph theory, etc. The knowledge representation method for mathematical concepts in NKIMath is addressed, which has three levels： predicate logic level, knowledge statement level, and conceptual relation level. The different knowledge levels have different purposes, for example, the predicate logical is machine-oriented, which i＇s used to knowledge reasoning in mathematical software system, and the knowledge statement level is human-oriented, which is used to knowledge instruction and query for different users. The representation system has several features, such as multi-granularity representation for concepts, knowledge sharing and reuse, transformation between knowledge formats.