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This paper is a contribution to the construction of a general model for information retrieval. As in the paper of Van Rijsbergen ([RIJ86]), the implicit base in all information retrieval systems is considered as a logical implication. The measure of correspondence between a document and a query is transformed into the estimation of the strength (or certainty) of logical implication. The modal logics will show its suitability for representing the behavior of information retrieval systems. In existing Information Retrieval models, several aspects are often mixed. A part of this paper is contributed to separate these aspects to give a clearer view of information retrieval systems. This general model is also compared with some existing models to show its generality.