We focus on the ramification problem in the setting of the situation
calculus. Our analysis is restricted to theories (or domains)
consisting of effect propositions and (ramification) constraints.
For these domains, we first identify the class of models we are interested in
characterizing. In the case of finite domains, we provide a set of
second order formulas defining the models we are interested in, and
show how sometimes such formulas can be reduced to a first order
theory. When a domain (in the situation calculus) ``corresponds'' to
a domain description in the high level action description language
${\cal AR}$, we show that these two formalizations yield the same conclusions.