We investigate Mal’cev conditions described by those equations whose variables runs over the set of all compatible reflexive relations. Let \(p \le q\) be an equation for the language \(\{\wedge , \circ ,+\}\). We give a characterization of the class of all varieties which satisfy \(p \le q\) over the set of all compatible reflexive relations. The aim is to find an analogon of the Pixley–Wille algorithm for conditions expressed by equations over the set of all compatible reflexive relations, and to characterize when an equation \(p \le q\) expresses the same property when considered over the congruence lattices or over the sets of all compatible reflexive relations of algebras in a variety.

我们研究了由方程式描述的Mal'cev条件，这些方程式的变量在所有兼容的自反关系的集合上运行。令\（p \ le q \）是语言\（\ {\ wedge，\ circ，+ \} \）的方程式。我们给出在所有兼容的自反关系的集合上满足\（p \ le q \）的所有品种的类别的表征。目的是找到一个Pixley-Wille算法的类似物，用于在所有兼容自反关系的集合上由方程表示的条件，并表征当考虑全等时方程\（p \ le q \）表示相同的性质格或各种代数的所有兼容反射关系的集合。