Knowledge and Information Systems

, Volume 55, Issue 1, pp 113–139 | Cite as

A many-sorted theory proposal for information retrieval: axiomatization and semantics

  • Loutfi ZerargaEmail author
  • Yassine Djouadi
Regular Paper


Logic-based models have been already proposed for information retrieval purpose. However, there is a need for new formalisms providing more generic frameworks. For this purpose, an information retrieval axiomatic theory is proposed in this paper, independently of any model. Our proposal which mainly relies on many-sorted logic allows to consider various sets in the domain of discourse that provides us a rich framework to model the different items such as documents, index terms, queries. The theory relies on a sound set of axioms driving the retrieval process as proof of theorems. As such the genericity consists of a main motivation; it will be proved that three classical information retrieval models, namely the Boolean model; the fuzzy-set-based extension of the Boolean model; and the vector space model, satisfy the proposed theory, establishing then its consistency. Beyond the genericity, the proposed approach may face concrete problems. Indeed, it is well known that the use of the classical settings of formal concept analysis theory for information retrieval does not allow disjunctions and negations in queries. For this purpose, this paper gives a characterization of these queries forms using appropriates theorems of the theory. Useful algebraic properties (i.e., isomorphisms) are then established for this end.


Information retrieval Axiomatic theory Many-sorted first-order logic Boolean model Vector space model Formal concept analysis 



We thank anonymous reviewers for their constructive comments that helped us to highly improve the quality of the paper.


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© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  1. 1.LIMOSEUniversité de BoumerdèsBoumerdesAlgeria
  2. 2.IRITUniversité Paul SabatierToulouse Cedex 09France

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