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

Abstract : 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).
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https://hal.archives-ouvertes.fr/hal-01394116
Contributor : Karam Abdulahhad <>
Submitted on : Tuesday, November 8, 2016 - 4:37:57 PM
Last modification on : Wednesday, August 5, 2020 - 3:01:46 AM

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Karam Abdulahhad, Jean-Pierre Chevallet, Catherine Berrut. Logics, Lattices and Probability: The Missing Links to Information Retrieval. The Computer Journal, Oxford University Press (UK), 2016, ⟨10.1093/comjnl/bxw034⟩. ⟨hal-01394116⟩

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