A New Lattice-Based Information Retrieval Theory

Karam Abdulahhad 1 Jean-Pierre Chevallet 1 Catherine Berrut 1
1 MRIM - Modélisation et Recherche d’Information Multimédia [Grenoble]
LIG - Laboratoire d'Informatique de Grenoble, Inria - Institut National de Recherche en Informatique et en Automatique
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 a bi- nary decision, we thus need a measure to estimate the degree to which d implies q, noted P(d → q). The main problems in the logic-based IR models are the difficulties to implement the decision algorithms and to define the uncertainty measure P as a part of the logic. In this study, we chose the Propositional Logic (PL) as the underlying framework. We propose to replace the implication d → q by the material implication d ⊃ q. However, we know that there is a mapping between PL and the lattice theory. In addition, Knuth [13] introduced the notion of degree of inclusion to quantify the ordering relations defined on lattices. There- fore, we position documents and queries on a lattice, where the ordering relation is equivalent to the material implication. In this case, the impli- cation d → q is replaced by an ordering relation between documents and queries, and the uncertainty P(d → q) is redefined using the degree of inclusion measure. This new IR model is: 1- general where it is possible to instantiate most of classical IR models depending on our lattice-based model, 2- capable to formally prove the intuition of Rijsbergen about replacing P (d → q) by P (q|d), and 3- easy to implement.
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Karam Abdulahhad, Jean-Pierre Chevallet, Catherine Berrut. A New Lattice-Based Information Retrieval Theory. [Research Report] RR-LIG-038, 2013, pp.24. ⟨hal-00953097⟩

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