The Situated Artificial Institution (SAI) model, as proposed in the literature, conceives the regulation of Multi-Agent Systems as based on a constitutive state that is consequence of the institutional interpretation of facts issued by the environment. The different nature of these facts (e.g. past sequence of events, states holding) implies various dynamic behaviours that need to be considered to properly define the life cycle of the constitutive state. This paper aims to bring such a dynamic to SAI. It defines a formal apparatus (i) for the institutional interpretation of environmental facts based on constitutive rules and (ii) for the management of the resulting constitutive state.