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A language grounding problem is considered for nonuniform sets of modal conjunctions consisting of conjunctions extended with more than one modal operator of knowledge, belief or possibility. The grounding is considered in the context of semiotic triangles built from language symbols, communicative cognitive agents and external objects. ; The communicative cognitive agents are assumed to be able to observe external worlds and store the results of observations in internal knowledge bases. It is assumed that the only meaning accessible to these agents and assigned to modal conjunctions can be extracted from these internal knowledge bases. ; Commonsense requirements are discussed for the phenomenon of grounding nonuniform sets of modal conjunctions and confronted with an original idea of epistemic satisfaction relation used to define proper conditions for language grounding. Theorems are formulated and proved to show that the communicative cognitive agents based on the proposed model of grounding fulfill some commonsense requirements given for processing sets of nonuniform modal conjunctions. ; The main result is that the communicative cognitive agents considered can be constructed in a way that makes them rational and intentional as regards the processing of modal conjunctions and from the human point of view.