2026/07/29 by Torgeir Aambø
Mathematics · Computer Science · #math.CT #cs.LO #msc:18A40 #msc:06A15 #msc:68T30
10 pages, comments are welcome!
arxiv created 2026/07/29 · arxiv updated 2026/07/30
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 NΠ-pairs are the formal concepts of the complement context. We further prove that the FCA closure operator and the NΠ-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.