This paper is at the same time a first step towards an "implementation" of the inferentialist view of meaning and a first proposal for a logical structure which describes an argumentation. According to inferentialism the meaning of a statement lies in its argumentative use, its justifications, its refutations and more generally its deductive relation to other statements. In this first step we design a simple notion of argumentative dialogue. Such dialogues can be either carried in purely logical terms or in natural language. Indeed, a sentence can be mapped to logical formulas representing the possible meanings of the sentence, as implemented with some categorial parsers. We then present our version of dialogical logic, which we recently proved complete for first order classical logic. Next we explain, through examples, how argumentative dialogues can be modeled within our version of dialogical logic.Finally, we discuss how this framework can be extended to real argumentative dialogues, in particular with a proper treatment of axioms.