@article{discovery10134566, publisher = {SPRINGER BASEL AG}, year = {2021}, title = {Axioms for signatures with domain and demonic composition}, journal = {Algebra universalis}, month = {May}, number = {2}, volume = {82}, note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.}, keywords = {Demonic composition, demonic refinement, binary relation, non-deterministic program, total correctness, axiomatisation.}, url = {https://doi.org/10.1007/s00012-021-00719-4}, author = {Hirsch, R and Stokes, T}, abstract = {Demonic composition ? is an associative operation on binary relations, and demonic refinement ? 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 \{?,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 \{?,{$\circ$},?\}, hence also for \{{$\subseteq$},{$\circ$},?\}.} }