A modal logic of intentional communication

I propose a propositional modal logic of intentional communication, a circular concept which develops an idea by Airenti, Bara and Colombetti (1993). A communication operator is added to a multi-modal language of individual belief, common belief, and intention, and its possible world semantics is justified through a fixpoint construction. A normal modal system for the communication operator is defined, and shown to be sound and complete. Within this framework, I prove some properties of intentional communication and give sufficient conditions for an action to be communicative.