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arXiv · 2607.26776

Possibilistic operators in Formal Concept Analysis as Kan extensions

Torgeir Aambø
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Abstract

In this paper we prove that Dubois--Prade's eight possibilistic operators in Formal Concept Analysis arise canonically from Kan extensions of the underlying boolean profunctor. This provides a conceptual explanation for the result that $N\Pi$-pairs are the formal concepts of the complement context. We further prove that the FCA closure operator and the $N\Pi$-pairs are the only symmetric or asymmetric operator compositions that give formal concepts. Finally we use these eight possibilistic operators to construct new closure operators on a formal context via standard categorical arguments.

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BibTeXRIS

Torgeir Aambø. 2026-07-29. Possibilistic operators in Formal Concept Analysis as Kan extensions. https://arxiv.org/abs/2607.26776

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