On computable automorphisms in formal concept analysis

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 that the computable formal contexts and computable structures actually have the same automorphism groups and groups of computable automorphisms. We construct some examples of formal contexts and concept lattices that have nontrivial automorphisms but none of them could be hyperarithmetical in any hyperarithmetical presentation of these structures. We also show that it could be happen that two formal concepts are automorphic but they are not hyperarithmetically automorphic in any hyperarithmetical presentation.