Abstract
Demonic composition \(*\) is an associative operation on binary relations, and demonic refinement \({\sqsubseteq }\) is a partial order on binary relations. Other operations on binary relations considered here include the unary domain operation D and the left restrictive multiplication operation \(\circ \) given by \(s\circ t=D(s)*t\). We show that the class of relation algebras of signature \(\{\, \sqsubseteq , D, *\, \}\), or equivalently \(\{\, \subseteq , \circ , *\, \}\), has no finite axiomatisation. A large number of other non-finite axiomatisability consequences of this result are also given, along with some further negative results for related signatures. On the positive side, a finite set of axioms is obtained for relation algebras with signature \(\{\, \sqsubseteq , \circ , *\, \}\), hence also for \(\{\, \subseteq , \circ , *\, \}\).
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