中文摘要：

描述逻辑是包含了概念、角色以及概念和角色构造子的一阶逻辑的子逻辑，具有表达能力强且推理可判定的特征。但现有描述逻辑无法表示概念和角色上的函数，因此在图书馆的概念模型中，有一些问题便不能表示，如图书的本数、借书的条目数等。在现有描述逻辑基础上引入函数来解决这个问题。首先分析现有描述逻辑在图书馆的概念模型中不能表示的一些问题并提出解决方法。然后给出带函数的描述逻辑的语法和形式语义，最后用带函数的描述逻辑形式化表示图书馆概念模型中的一些实际问题。

英文摘要：

Description logics are fragments of the first-order logic,which contain concepts,roles,and concept and role constructors;and have features of strong expressivity and decidable reasoning.But the existing description logics cannot express functions on concepts and roles so that some functions in the conceptual model of libraries cannot be expressed,such as the number of books,the number of borrowed books,and so on.This paper introduces a description logic with functions.Firstly the unexpressed functions are analyzed in the conceptual model of libraries using the existing description logics and a solution is proposed.Sec- ondly the syntax and semantics of the description logic with functions are presented.Finally the description logics with functions to the conceptual model of libraries is applied.