  Each quiver corresponds to a path semigroup, and such a path semigroup also
corresponds to an associative K-algebra over an algebraically closed field K.
Let Q be a quiver and S_Q, KQ be its path semigroup, path algebra,
respectively. In this paper, we study some properties of the congruence lattice
of S_Q. First, we show that there is a one-to-one correspondence between
congruences on S and certain algebraic ideals of KQ. Based on such a
description, we consider acyclic quivers and show that the congruence latices
of such path semigroups are strong upper semimodular but not necessarily lower
semimodular. Moreover, we provide some equivalent conditions for the congruence
lattices to be modular and distributive.
