  A recently published paper (Schmid, Rozowski, Silva, and Rot, 2022) offers a
(co)algebraic framework for studying processes with algebraic branching
structures and recursion operators. The framework captures Milner's algebra of
regular behaviours (Milner, 1984) but fails to give an honest account of a
closely related calculus of probabilistic processes (Stark and Smolka, 1999).
We capture Stark and Smolka's calculus by giving an alternative framework,
aimed at studying a family of ordered process calculi with inequationally
specified branching structures and recursion operators. We observe that a
recent probabilistic extension of guarded Kleene algebra with tests (Rozowski,
Kozen, Kappe, Schmid, Silva, 2022) is a fragment of one of our calculi, along
with other examples. We also compare the intrinsic order in our process calculi
with the notion of similarity in coalgebra.
