  G. Plotkin and the author have worked out the equivalence between state
transformer semantics and predicate transformer semantics in a domain
theoretical setting for programs combining nondeterminism and probability.
Works of C. Morgan and co-authors, Keimel, Rosenbusch and Streicher, already go
in the same direction using only discrete state spaces. It is the aim of this
paper to exhibit a general framework in which one can hope that state
transformer semantics and predicate transformer semantics are equivalent. We
use a notion of entropicity borrowed from universal algebra and a relaxed
setting adapted to the domain theoretical situation.
