Logics, Lattices and Probability: The Missing Links to Information Retrieval

International audience; Logic-based information retrieval (IR) models represent the retrieval decision as an implication d→q between a document d and a query q, where d and q are logical sentences. However, d→q is generally a binary decision, thus we need a measurement to estimate the degree to which d implies q, denoted U(d→q). Most of the existing logic-based IR models either do not precisely define the implication d→q or use non-classical definitions. Some models also define the uncertainty U in informal ways. More importantly, they use two non-related frameworks to define d→q and its uncertainty U, even though the two notions are intrinsically related. The goal of this study is to propose a new logic-based IR model, which overcome these shortcomings. To this end, we first propose to replace the implication d→q by the validity of material implication ⊨d⊃q. Second, we redefine and adapt the mathematical relationship between logics, lattices and probability. Our new IR model presents a possible formalism for van Rijsbergen's intuition about replacing U(d→q) by P(q∣d).