Some IR models make use of an implication to match a document d and a query q, computing either “q implies d”(eg in fuzzy inclusion models) or, the other way,“d implies q”(eg in logical IR models). This paper analyzes, from a theoretical point of view, the IR models using both approaches. Even if the above notations seem to be opposite, it is shown that they sometimes come from different formulations of the same paradigm, which led to mistakes in the literature. Then the paper comes back to fuzzy models based on “q implies d”(q included in d) and shows their efficiency, and compares them to models based on “d implies q”(d included in q). The latter is attractive from a theoretical point of view, but turns out to be less efficient in practice, and is rarely adopted in the literature. At last, attempts to use “d implies q” in a fuzzy model are discussed, and we try to explain their inefficiency.