Soundness and Completeness of Relational Concept Analysis

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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