Putting Non Convex Interval Mutual Relation Models into Practice
Résumé
J.F. Allen's work provides an essential theoretical framework for convex intervals calculus. G. Ligozat extended this fundamental work to the case of non convex intervals. Most of the algebraic properties are preserved. However, the lattice of the relation between non convex intervals is too important for being mastered and used as a whole in practical industrial applications. Within this respect, we select a set of relevant extended relation types(namely ALLEN*) which can apply to non convex intervals while bearing a semantics close to the genuine Allen's one. We provide a formal specification of these relation types and develop a composition calculus that results in transitivity tables. The paper places our work within Ligozat's theory and special properties are enounced about the set ALLEN*. As a conclusion, we evoke practical use cases for our proposal which has been experimented on the occasion of an ANR project.