We propose an approach to the operational semantics aimed at describing the behavior of an interpreter (or, anyway, of an implementation) of agent-oriented logic programming languages. We define a formal dialogue game framework that focuses on rules of dialogue that the players of the game, i.e., the components of the language interpreter, can be assumed to adopt in playing an “innocent” game that finalized to creating the interpreter behavior. The approach leads to a natural, uniform and modular way of modeling all the components of an interpreter, including the communication component and the communication protocol, and allows several properties to be formally proved.