Language Models and Uncertain Inference in Information Retrieval

In the logical view on IR systems, retrieval is interpreted as implication [Rijsbergen 86]: Let d denote a document (represented as logical formula) and q a query, then retrieval deals with the task of finding those documents which imply the query, i.e. for which the formula d → q is true. Due to the intrinsic uncertainty and vagueness of IR, we have to switch to uncertain inference. Using a probabilistic approach, the probability P (d → q) that the implication goes through should be computed as the conditional probability P (q|d), as pointed out by Rijsbergen.