Abstract. Directoids are groupoids defined on every upward directed poset. They fully characterize these posets. Hence, in order to study conguences on directed posets, we can convert the poset into a directoid and study congruences on it. The paper is devoted to several characterizations of congruences on directoids, on directoids with an antitone involution, on directoids with sectionally antitone involutions and on double directoids.

AMS Subject Classification (1991): 06A06, 06B10, 08A30

Keyword(s): directoid, poset, congruence relation, filter, antitone involution, double directoid

Received October 11, 2011, and in revised form April 14, 2012. (Registered under 53/2011.)