This tutorial will present formal structures which often structure the development of ideospheres in Human Sciences. An ideosphere (Barthes77) is initiated by a founding speech and helps establish correspondences to other such speeches and take commitment and refusal positions in a system that is inachieved. In pedopsychiatry, an ideosphere is focus on early interactions between the infant and his environment, and examine the processes of semiotization, as well as the use of representation abilities as a means to communicate (Golse 99,07) (Dor 02}.

These structures and their organization within a general system can be formalized with category theory, as is done for instance when modeling computation systems and relating different models. We show under what conditions they correspond to a formalization within modal logic of the system in use; at this point we will make a comparison with what is done with categorial models which relate various logics. Finally we develop the concepts of autonomy and learning, and use them to illustrate the presented mathematical tools and methods; this will help model zig-zag processes between various formalizations

Bibliography:

Barthes R., Le Neutre, Cours au collège de France 1977-1978.

Dor J., Introduction à la lecture de Lacan : l'inconscient structuré comme un langage, Espace analytique , Denoel 2002.

Golse B., Du corps à la pensée, Le fil rouge, PUF, 1999. .

Golse B, l'être-bébé, Le fil rouge PUF 2007.