By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the Lin-Zhao theorem remains correct even if we restrict loop formulas to a special class of loops called ``elementary loops.'' In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop for nondisjunctive programs, but is simpler, and, unlike elementary loops, can be extended to disjunctive programs without producing unintuitive results. We show that the maximal unfounded elementary sets for the ``relevant'' part of a program are exactly the minimal sets among the nonempty unfounded sets. We also present a graph-theoretic characterization of elementary sets for nondisjunctive programs, which is simpler than the one proposed in (Gebser & Schaub 2005). Unlike the case of nondisjunctive programs, we show that the problem of deciding an elementary set is coNP-complete for disjunctive programs.

提出了循环和循环公式的概念，证明了非不相交逻辑程序的答案集恰好是满足所有循环的Clark完成模型。简化和概括了基本循环的概念，并阐明了其作用。提出了基本集合的概念，对于非不相交程序几乎等价于基本循环的概念，但更简单，并且可以扩展到包含分离项的程序而不产生令人费解的结果。证明了“相关”部分的最大无根基本集合正好是非空的最小无根集合。提出了用于非不相交程序的基本集合的图论刻画，相对于(Gebser & Schaub 2005)提出的刻画更为简单。同时，对于分离项程序，决定一个基本集合的问题是coNP完备的。

逻辑编程的基本集合