Human-machine interaction is among the most complex problems in the field of artificial intelligence. Indeed, software that cooperates with dependent people must have contradictory qualities such as speed and expressiveness, or even precision and generality. This requires a radical paradigm shift from standard approaches, which, while effective, are often but rigid. The objective is then to design tools capable of generating intermediate solutions that sometimes get very useful for certain problems. These solutions make it possible to expand the possibilities of adaptation in a fluid and continuous way. With this idea, the role of explainability in the resolution process is a decisive criterion for obtaining flexible systems. Thus, the search at all costs for a complete and optimal response has overshadowed the usefulness of these models.

Mathematics offers the best tools for formalization. However, it appears that the foundation of mathematics is defined by an implicit circularity. This defect reveals a lack of rigor in describing the basic concepts used in mathematics. It is therefore sufficient to recognize the need for a formalism based on a precursor language. In the absence of alternatives, natural language is a precursor to a new formalism. This is inspired by lambda calculus as well as type theory. From basic concepts, defined by explicit circularity, it is then possible to reconstruct classical mathematical concepts as well as other tools and structures very useful what is following.

By using this formalism, it becomes possible to axiomatize an endomorphic metalanguage. This one manipulates a dynamic grammar capable of adjusting its semantics to exploitation. The recognition of basic structures allows this language to avoid using keywords. This, combined with a new model of knowledge representation, supports the construction of a very expressive description logic.

With this language and this formalism, it becomes possible to create frameworks in fields that were previously heterogeneous. For example, in automatic planning, the classic state-based model makes it impossible to unify the representation of planning domains. The interest of such tools on planning and its multiple paradigms is illustrated. This results in a general planning framework that allows all types of domains to be expressed.

Concrete algorithms are then created that show the principle of intermediate solutions. Two new approaches to real-time planning are presented and evaluated. The first is based on a usefulness heuristic of planning operators to repair existing plans. The second uses hierarchical task networks to generate valid plans that are abstract and intermediate solutions. These plans allow for a much shorter execution time for any use that does not require a detailed plan.

We then illustrate the use of these plans on intent recognition by reverse planning. Indeed, in this field, the fact that no plan libraries are required makes it much easier to design recognition models. By exploiting abstract plans, it becomes possible to create a system theoretically more efficient than those using complete planning.