Action is one of the most important concepts in computer science, and
situation calculus is tile standard formalism for representing and rea
soning about actions and their effects. Situation calculus essentially
could be presented in a logic framework. Based on the framework LR, s
uch a logic framework is given. Minimal action theory is proposed and
studied from the point of view of model theory, By theorems of mathema
tical logic, some results about the definability about the progression
in minimal action theory are obtained.