The article addresses the issues of extending a category and updating a lexical concept, and determining its reference. We try to answer the questions: how can an object seen for the first time extend a category or update a concept? How is it possible to determine the reference of a concept that represents a behaviour? Firstly, we discuss the learning of inferential linguistic competence used to update a concept through an approach based on prototype theory. Secondly, we discuss the learning of referential linguistic competence used to determine the reference of a concept through an approach based on embodied cognition. Finally, on the basis of the dual dimension of the praxis of rule-following, we show how it is possible to combine the two approaches into a single model that deals with both the extension of a category and the updating of a concept, and the determination of the reference.