Abstract. The dual discriminator function was introduced in connection with weakly associative lattices, a structure where the transitivity of the ``partial ordering'' is forgotten, but least upper bounds and greatest lower bounds exist. In this paper we investigate a more general structure where ``join'' is just one of the upper bounds and ``meet'' is just one of the lower bounds in a directed graph. Our goal is to find a dual discriminator term in this larger variety.

AMS Subject Classification (1991): 08A40, 05C75

Keyword(s): dual discriminator, congruence distributivity, varieties, generalizations of distributive lattices, directed graph

Received July 19, 2000, and in revised form January 25, 2001. (Registered under 2797/2009.)