In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of weakly-related or independent components. However, a theory may represent knowledge that is subject to change due to execution of actions that have effects on some properties mentioned in the theory. Having once computed a decomposition of a theory, one would like to know whether a decomposition has to be computed again in the theory obtained from taking into account changes resulting from execution of an action. In the paper, we address this problem in the scope of the situation calculus, where a change of an initial theory is related to the notion of progression. We undertake a study of the decomposability and inseparability properties known from the literature. We contribute by studying these properties wrt progression and the related notion of forgetting. We provide negative examples and identify cases when these properties are preserved under progression of initial theories and under forgetting in local–effect basic action theories of the situation calculus.