Complexity of the Problem of Being Equivalent to Horn Formulas

Abstract

We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, ∀-sentence, ∃-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity k ≥ 2, then each of the problems mentioned is an m-complete \( {\Sigma}_1^0 \) set.