The aim of the paper is to propose a unified formal account of dialogical cognitive processes so that it allows the analysis of similarities and differences between those processes. Formal dialogue systems constitute two basic categories or paradigms of modelling communication depending on what cognitive process is described by a given system. The first paradigm consists of designing a set of dialogue rules in a similar manner to Lorenzen’s dialogue logic (1978), and according to which players jointly aim to prove (argue) the validity of a formula. In such cases we will say that the system describes formal dialogues and the formal cognitive process of proving the validity of a formula. The second paradigm focuses on building a system similar to Hamblin’s formal dialectics (1970), which “simulates” the real-life communication practice. In the type of dialogues described by those systems, players perform “good” argumentation, i.e. argumentation which fulfils certain requirements of rationality such as e.g. the requirement of not committing a fallacy of circular reasoning (begging the question). In such a case we will be speaking of a natural dialogue and a natural cognitive process of argumentation.