An approach to developing the interpretation of incoming modal conjunctions is proposed. It is assumed that an artificial cognitive receiving agent is given. This agent uses modal conjunctions both to inform about its states of knowledge as well as collects incoming conjunctions produced by other external agents. Each single incoming conjunction is transformed into a set of predefined constraints which are used by the receiving agent to modify its private and subjective opinion on a state of an object. The model for single modal conjunction integration is extended to the case of set of incoming conjunctions. The extension is based on consensus approach. Both models are supported by the theory of modal language grounding.