Possibilistic operators in Formal Concept Analysis as Kan extensions
arXiv:2607.26776
The paper shows that the eight Dubois‑Prade possibilistic operators used in Formal Concept Analysis can be derived as Kan extensions of a Boolean profunctor, and uses this insight to characterize closure operators and construct new ones.
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 -pairs are the formal concepts of the complement context. We further prove that the FCA closure operator and the -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.
10 pages, comments are welcome!