Abstract Mathematical reason of the work is to inspire the activity to build a model of a variable property depending on the stages of knowledge and recognition mapping. An evolent is chosen along which the stages evolve. A generalized recognition mapping is constructed, which varies along the stage evolvent. It is shown that the induced variable domains form the functional spaces and collect exactly those individuals who satisfy the recognition condition. This gives rise to families of subsets that can be treated as generalized concepts. These concept spaces, in turn, can be expressed through families of dependencies on variable concepts. This is achieved by a suitable selection of displaced concepts. The cognitive reason of the work is consistent applying the method of indexical expressions, which allows the semantic model to take into account the stages of knowledge and their evolving. The resulting information graphs, as it turns out, can be interpreted as an environment for the propagation of data streams, which in this sense can control their interference. Using this basis, a toolkit for managing cognitive information can be developed. In addition, in this work, the ideas of modeling information processes by variable domains are largely inherited. The features of process inheritance are taken into account. The model solutions used are also based on the idea of channelized propagation of processes. Finally, the possibilities of jump-like transitions of processes, as well as the effects of entanglement of information processes, potentially causing cognitive interference and its propagation along the network channels, are taken into account.