For us, the relations of dependence between expression and content can be representational (one object which is put in place of another for a certain purpose), instrumental (an object uses another as an instrument) and structural (two or more objects make up a system from which new objects emerge). In this way, semiotic functions and the associated mathematical ontology, take into account the essentially relational nature of mathematics and radically generalize the notion of representation. The role of representation is not exclusively undertaken by language: in accordance with Peirce’s semiotic, we assume the different types of objects (problem-situations, procedures, definitions, propositions and arguments) can also be expression or content of the semiotic functions.