大学水平的“数学分析知识”的获取和分析研究

在过去的几十年里,数学软件系统变得越来越强大和复杂.各种数学系统的集成变得非常有意义.基于Web的分布式数学平台使得与数学相关的活动（称之为数学服务）都可以在Web上得以实现.所有这些都需要一个底层的、可共享的、面向内容的知识库作为支撑.本文介绍一个大学水平的、可共享的数学分析知识库的获取和分析方法.NKIMath采用基于本体、框架、逻辑和类型的形式表示,采用面向概念的知识获取方法,从一套大学本科数学分析课本（2本）中获取了所有主要概念和定理.本文还总结和分析了知识获取过程中出现的错误.

Acquisition and Analysis of University-Level Knowledge of Mathematical Analysis

Over the past decades mathematical software systems have become increasingly powerful and complex. The integration of mathematical formal systems is highly desirable. Web-oriented platforms of distributed mathematical services enable mathematical activities to be implemented on the Web. All those require an underlying, shareable, and content-oriented mathematical repository. In this paper, based on ontology, frame representation, predicate logic and type, we present a knowledge representation for mathematical analysis. A concept-oriented knowledge acquisition has been developed and with the method we have extracted all the main concepts and theorems from a university-level textbook on mathematical analysis. The paper will also discuss possible errors that a knowledge engineer may commonly make in acquiring mathematical knowledge.