The research presented in this dissertation belongs to the field of Computational Semantics, field which borrows techniques from Artificial Intelligence, formal tools from Logics, and methods and data from Linguistics. This work has been undergone under Mario Borillo's supervision, in the ``Langue, Raisonnement, Calcul'' Group in Toulouse. This group involves both computer scientists from the Institut de Recherche en Informatique de Toulouse (URA CNRS, Université Paul Sabatier, INP) and linguists from the Équipe de Recherche en Syntaxe et Sémantique (URA CNRS, Université Toulouse-Le Mirail).

The aim of this work is the study of logical and semantic phenomena entailed by the presence in natural language of both time and negation concepts. For that purpose, the author undertakes a linguistic study of the French presupposition inducer ne... plus (no/any more). This study leads to the identification of various temporal, aspectual, modal and pragmatic properties of this term. From the aspectuo-temporal point of view, on the one hand, a sensitiveness of the term ne... plus to various factors (aspectual class of the predicate, tenses, temporal adverbials), is observed and described. It is also observed occurrences of modal and/or pragmatic uses of this locution. On the other hand, ne... plus proves to be a fruitful entry point for the study of the presupposition phenomena, especially when it interacts with negation.

From the results of this study, which corresponds to the first part of the dissertation, a formal representation of the relevant properties of ne... plus is proposed, in the framework of Hans Kamp's Discourse Representation Theory (1981: A Theory of Truth and Semantics Representation, Amsterdam; Kamp & Reyle 1993: From discourse to logic, Kluwer). This works gives thus the opportunity to have the DRT confronted with new linguistic and representational data. This formalization is presented in the second part of the dissertation. The author introduces in this second part the DRT and its treatment for time, and then extends it to account for presupposition, using for that purpose Rob van der Sandt's proposition to handle presupposition as anaphora (van der Sandt 1992: Presupposition Projection as Anaphora Resolution, Journal of Semantics, 9(4)).

The third part of the dissertation deals with the formalisation of the whole semantic process, which takes as input syntactic trees of utterances and yields a semantics representation of these utterances, in which are taken into account all the relevant aspectual and presuppositional properties of ne... plus. This DRS construction process is formalised by means of a lambda-calculus inspired from Nicholas Asher's (1993: Reference to Abstract Objects in Discourse, Kluwer), and integrates a formalisation of Rob van der Sandt's algorithm for the ``anaphoric treatment of presupposition''.