表达式的覆盖、分解与划分

COVERING, DECOMPOSITION,AND PARTITION OF EXPRESSIONS

本文把简单表达式（项和原子）视为语言Ｌ的Ｈｅｒｂｒａｎｄ域或Ｈｅｒｂｒａｎｄ基中的集合．作者提出覆盖表达式的概念，得到２个表达式之间覆盖关系的判别准则．对多个表达式，作者提出表达式的分解概念及相应的分解算法，在此基础上，本文给出卫个表达式覆盖多个表达式的等价条件．根据集合的划分公式，得到划分表达式的方法．最后定义１个变换把合取式转换为简单表达式，从而方便地把简单表达式的结果推广到合取式．本文是作者提出的一种标记逻辑程序的过程语义的理论基础．

In this paper,a simple expression E,i.e.,a term or an atom,is viewed as a set,the'so-called'generated set of E,of the Herbrand universe U.or Herbrand base BLof the language L.The authors give a criteria to determine whether an expression coversanother one,and present the notion of decomposition expressions and the decomposition algorithm on which a necessary and sufficient condition for the covering relation between one and several other expressions is based.Then,they show how to partition a union of the sets generated by the simple expressions according to the partition formula in the set theory.Finally,they generalize generis these above results into the conjunctions through defining a transformation which converts a conjunction into a simple expression.This paper provides the theoretic foundation of the procedural semantics of authors'annotated logic program.