Article,
On computable automorphisms in formal concept analysis
Siberian Mathematical Journal, 51 (2): 289--295 (March 2010)
Abstract
Abstract Under study are the automorphism groups of computable formal contexts. We give a general method to transform results on the
automorphisms of computable structures into results on the automorphisms of formal contexts. Using this method, we prove thatthe computable formal contexts and computable structures actually have the same automorphism groups and groups of computableautomorphisms. We construct some examples of formal contexts and concept lattices that have nontrivial automorphisms but noneof them could be hyperarithmetical in any hyperarithmetical presentation of these structures. We also show that it could behappen that two formal concepts are automorphic but they are not hyperarithmetically automorphic in any hyperarithmeticalpresentation.
