Reasoning with Intervals on Granules

The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities with respect to the event taken into account. For instance, how to express the inter-war period in terms of a {\em years} interval? This paper presents a new type of intervals, neither open ,nor closed or open-closed and the extension of operations on intervals of this new type, in order to reduce the gap between the discourse related to temporal relationship and its translation into a discretized model of Time

Représentation du temps, relations temporelles et théories des temps verbaux.

Rapport InterneNous présentons un cadre unique de description des différents modèles référentiels et procéduraux de descriptions des temps verbaux, fondé sur la notion de \emph{points spécieux}, associée à celle de neutralité de la forme des extensions temporelles des éléments des modèles. Ce cadre permet à la fois la description et le calcul des relations décrites qui s'expriment sous la forme de S-langages \cite{Schwer2007, DurandSchwer2008} réécrits dans l'esprit de Reichenbach. Nous montrons, à travers l'examen des théories de Port-Royal (1667), de l'Abbé Girard (1747), de Beauzée (1767) et de Reichenbach (1947) comment le système néo-Reichenbachien de Co Vet (2007) s'ancre dans une tradition de définition des temps verbaux du français qui d'une part tend à se dégager des contraintes sur le nombre, la nature et les formes des repères nécessaires à leurs expressions relationnelles et d'autre part donne plus d'importance à ce qu'emporte d'universel l'évenance avec elle, c'est-à-dire non la forme de son extension temporelle (encore présente chez Reichenbach) mais son "aura" temporelle (apportée par Co Vet)

Reasoning with Intervals on Granules

The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enough when the periods are written in terms of coarse granularities with respect to the event taken into account. For instance, how to express the inter-war period in terms of a years interval? This paper presents a new type of intervals, neither open, nor closed or open-closed and the extension of operations on intervals of this new type, in order to reduce the gap between the discourse related to temporal relationship and its translation into a discretized model of Time

Reasoning with Intervals on Granules

The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enough when the periods are written in terms of coarse granularities with respect to the event taken into account. For instance, how to express the inter-war period in terms of a years interval? This paper presents a new type of intervals, neither open, nor closed or open-closed and the extension of operations on intervals of this new type, in order to reduce the gap between the discourse related to temporal relationship and its translation into a discretized model of Time