The aim of this paper is to formalize, from linguistic markers, the on-line modifications of decision processes in terms of detachments from the spatio-temporal situation. For that, a 10-year-old's verbal protocol, obtained during four successive trials on the Tower of Hanoi puzzle, is analyzed in the line of current cognitive linguistics, notably Culioli's theory of enunciative operations. A first modification is inherent to decision process themselves according to their status, defining a distribution of representations between internal vs external problem spaces. That is marked by the presence or not of aggregates and of "starting terms". A second kind of modifications is marked by modal terms. The formalization relies on a cognitive interpretation of enunciative operations involved in these detachments and suggests a new approach of information processing. Results show a progressive identification of constraints, and the reconstruction of the spatio-temporal situation at detached levels. Several kinds of partial articulations and compositions intervene in the on-line construction of elementary classes and between declarative and procedural aggregates.