  Relation algebra and its reducts provide us with a strong tool for reasoning
about nondeterministic programs and their partial correctness. Demonic
calculus, introduced to model the behaviour of a machine where the demon is in
control of nondeterminism, has also provided us with an extension of that
reasoning to total correctness.
  We formalise the framework for relational reasoning about total correctness
in nondeterministic programs using semigroups with ordinary composition and
demonic lattice operations. We show that the class of representable demonic
join semigroups is not finitely axiomatisable and that the representation class
of demonic meet semigroups does not have the finite representation property for
its finite members.
  For lattice semigroups (with composition, demonic join and demonic meet) we
show that the representation problem for finite algebras is undecidable,
moreover the finite representation problem is also undecidable. It follows that
the representation class is not finitely axiomatisable, furthermore the finite
representation property fails.
