Some Open Problems in Formal Concept Analysis

This note intends to collect some open problems in Formal Concept Analysis. The ones below have been presented at the International Conference on Formal Concept Analysis (ICFCA 2006) held in Dresden February 2006. Would you like to add some problems to this list, please feel free to send them to [email protected] Problems presented at ICFCA 2006 in Dresden Problem 1 (Minimal generators for Boolean layer cakes). A Boolean layer cake is an ordered set obtained from a Boolean lattice 2 by selecting any number of complete level sets from 2 and endowing their set union with the order inherited from 2. Boolean layer cakes are lattices iff, apart from {0} and {1}, a series of consecutive level sets is selected. Finding minimal generating sets for lattices obtained this way is still open. Is there any contextual description of (minimal) generating sets for a given concept lattice? Related works: Sc99. Boolean layer cakes, Theoret. Comput. Sci. 217 (1999), no.2, 255-278 presented by Jürg Schmid [email protected] Problem 2 (Computing pseudo-intents). Are the problems: Instance: A context (G, M, I), a subset Q ⊆ M Question: Is Q a pseudo-intent? and Instance: A context (G, M, I), a closed subset Q ⊆ M Question: Is there a pseudo-intent P with P ′′ = Q? coNP-complete? Is it possible to compute all pseudo-intents with a (cumulative) polynomial-delay algorithm? Related works: KO06. Counting pseudo-intents and #P-completeness LNAI 3874 (2006), 306-308 Ku04. S.O. Kuznetsov, On Complexity of Computing the Duquenne-Guigues Basis, Journal of Universal Computer Science 10, (2004), no.8, pp. 927-933. presented by Sergei O. Kuznetsov [email protected]