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Fixed-point semantics for barebone relational concept analysis

Jérôme Euzenat 1
1 MOEX - Evolution de la connaissance
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : Relational concept analysis (RCA) extends formal concept analysis (FCA) by taking into account binary relations between formal contexts. It has been designed for inducing description logic TBoxes from ABoxes, but can be used more generally. It is especially useful when there exist circular dependencies between objects. In this case, it extracts a unique stable concept lattice family grounded on the initial formal contexts. However, other stable families may exist whose structure depends on the same relational context. These may be useful in applications that need to extract a richer structure than the minimal grounded one. This issue is first illustrated in a reduced version of RCA, which only retains the relational structure. We then redefine the semantics of RCA on this reduced version in terms of concept lattice families closed by a fixed-point operation induced by this relational structure. We show that these families admit a least and greatest fixed point and that the well-grounded RCA semantics is characterised by the least fixed point. We then study the structure of other fixed points and characterise the interesting lattices as the self-supported fixed points.
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https://hal.archives-ouvertes.fr/hal-03426547
Contributor : Jérôme Euzenat Connect in order to contact the contributor
Submitted on : Friday, November 12, 2021 - 1:04:19 PM
Last modification on : Thursday, January 20, 2022 - 5:29:00 PM

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Jérôme Euzenat. Fixed-point semantics for barebone relational concept analysis. ICFCA - 16th international conference on formal concept analysis, Jul 2021, Strasbourg, France. pp.20-37, ⟨10.1007/978-3-030-77867-5_2⟩. ⟨hal-03426547⟩

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