@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 \{{$\subseteq$},{$\circ$},?\}.}
}