Although BDI approach is currently a subject of much ongoing research, less relative works about modeling communication have been involved. The aim of this paper is to extend classical BDI logic for representing and reasoning about speech act interactions between multi agents. A many-sorted, quantified, first-order, multi-modal logic with branching time structure is presented, including standard BDI modal and temporal operators like belief, goal, intention, etc. In addition, some operators and constructs are introduced for characterizing agents' “know-how” or having plans about how to achieve their intentions and for interpreting the pragmatic meanings of inter-agent communication. While discussing the syntax and semantics of the logic, some kinds of illocutionary speech acts are logically classified and interpreted.