This paper presents a method for the decomposition of HML formulas. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulas, obtained by decomposing the original formula. The method uses the structural operational semantics of the process algebra. The main contribution of this paper is the extension of an earlier decomposition method for the De Simone format from the Ph.D. thesis of Larsen in 1986, to more general formats.
Fokkink, W., Van Glabbeek, R., & De Wind, P. (2006). Compositionality of Hennessy-Milner logic by structural operational semantics. In Theoretical Computer Science (Vol. 354, pp. 421–440). https://doi.org/10.1016/j.tcs.2005.11.035