Représentation mathématique du temps: après Reichenbach

Abstract

This paper proposes an innovative way of modelising time with mathematical tools. Based on the classical formalism of Reichenbach and on the numerous linguistic approaches that endorse a Reichenbach-like relational-referential view, our formalism is taken from what is generally called S-languages. This model has three main advantages, which are advocated for in this paper, through a discussion of a number of linguistic approaches to time: The S-languages model i) captures the two fundamental relations of precedence and simultaneity, ii) allows to represent the discrete or continuous property of linguistic verbal objects, and iii) provides the algebraic operators required by temporal reasoning without recourse to a logically defined notion of 'time'.