Soundness and Completeness of Relational Concept Analysis

Amine Mohamed Rouane Hacene 1 Marianne Huchard 2 Amedeo Napoli 3 Petko Valtchev 1
2 MAREL - Models And Reuse Engineering, Languages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : Relational Concept Analysis (RCA) is an extension of Formal Concept Analysis (FCA) to the processing of relational datasets, i.e., made of (objects X properties) contexts and (objects X objects) relations. RCA constructs a set of fixpoint concept lattices by iteratively expanding the lattices of the initial contexts. To that end, at each iteration a scaling mechanism translates the inter-object links into relational attributes that reflect the available conceptual structures. The output of a RCA task has so far only been described operationally. We propose here an analytic characterization thereof, i.e., a completeness and consistence result connecting fixpoint extents to particular relational structures in the input data.
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Amine Mohamed Rouane Hacene, Marianne Huchard, Amedeo Napoli, Petko Valtchev. Soundness and Completeness of Relational Concept Analysis. ICFCA: International Conference on Formal Concept Analysis, May 2013, Dresden, Germany. pp.228-243, ⟨10.1007/978-3-642-38317-5_15⟩. ⟨lirmm-00833506⟩

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