Due to the increasing interested and use of chatbot, its properties and operation possibilities shall be proper realized matching both safety and security issues as well as present the several uses and compositions that this technology supports. This paper focus is on dialogue management since it is considered the core of a chatbot. The dialogue manager is responsible to, more than to transform an input sentence into an output one, hold the illusion of a human conversation. In this sense, it is presented an inceptive theoretical framework through a formal way for chatbots that can be used as a reference to explore, compose, build and discuss chatbots. The discussion is performed mostly on ELIZA since, due to its historical records, it can be considered an important reference chatbot, nevertheless, the proposed theory is compatible with the most recent technologies such those using machine and deep learning. The paper then presents some sketchy instances in order to explore the support provided by the theory.