This paper discusses the epistemological and methodological bases of a scientific theory of meaning and proposes a detailed version of a formal theory of argumentation based on Anscombre and Ducrot's conception. Argumentation is shown to be a concept which is not exclusively pragmatic, as it is usually believed, but has an important semantic body. The bridge between the semantic and pragmatic aspects of argumentation consists in a set of gradual inference rules, called topoi, on which the argumentative movement is based. (...) The content of each topos is determined at the pragmatic level, while the constraints on the forms of the topoi attached to a sentence are determined at the semantic level. Applications and possible applications toartificial intelligence and to cognitive sciences are discussed. In particular, the gradual models used to account for argumentation are shown to be extremely promising for Knowledge management, a discipline which includes knowledge acquisition, knowledge representation, transmission of knowledge (communication, interfaces, etc.), knowledge production (decision help, reasoning, etc.). A first formal model is presented and discussed: it is shown in details how it accounts for most of the argumentative features of sentences containing but, little and a little, and how it can be extended to describe sentences containing other argumentative connectives. However, this model is shown to be too simple and to violate the compositionality principle, which is shown, in the first section, to bean important methodological principle for any scientific theory. After a detailed analysis of the possible reasons for this violation, an improved model is proposed and its adequacy is discussed. (shrink)