  In this paper we consider, from a computational point of view, the problem of
classifying logics within the Leibniz and Frege hierarchies typical of abstract
algebraic logic. The main result states that, for logics presented
syntactically, this problem is in general undecidable. More precisely, we show
that there is no algorithm that classifies the logic of a finite consistent
Hilbert calculus in the Leibniz and in the Frege hierarchies.
