In this thesis, we address the issue of building an "algebra" of discourse relations (or rhetorical relations) -inspired from Allen's (1983) temporal algebra - consisting of a set of discourse relations inference rules. In the context of automatic discourse analysis, these rules can help the inference of implicit information in manual or automatic annotation and the comparison of multiple annotations of the same discourse. However, there is little or no definition of such rules in the existing theories for discourse analysis. The thesis therefore focuses on this question. We address ail the issues raised by the construction of a discourse relations algebra, which are related to the properties of discourse structures, relations, and sets of relations. After adopting a set of relations, we propose a methodology for identifying the set of relations that can be established between a and c, starting from two relations R1 (a, b) and R2 (b, c). The methodology combines the examination of semantic links associated with the relations involved, the analysis of theoretical and empirical data, acquired automatically by the presence of discourse connectives. For data analysis, linguistic tests are used to determine if the units a and c are connected rhetorically, and if so, by which relation. This methodology is applied on a set of premises involving interactions between different "groups" of relations: temporal, causal, and adversative relations.
