  We give a definition of representability for distributive quasi relation
algebras (DqRAs). These algebras are a generalisation of relation algebras and
were first described by Galatos and Jipsen (2013). Our definition uses a
construction that starts with a poset. The algebra is concretely constructed as
the lattice of upsets of a partially ordered equivalence relation. The key to
defining the three negation-like unary operations is to impose certain symmetry
requirements on the partial order. Our definition of representable distributive
quasi relation algebras is easily seen to be a generalisation of the definition
of representable relations algebras by Jonsson and Tarski (1948). We give
examples of representable DqRAs and give a necessary condition for an algebra
to be finitely representable. We leave open the questions of whether every DqRA
is representable, and also whether the class of representable DqRAs forms a
variety. Moreover, our definition provides many other opportunities for
investigations in the spirit of those carried out for representable relation
algebras.
