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Logical forgetting is NP-complete even in the simple case of propositionalHorn formulae, and may exponentially increase their size. A way to forget is toreplace each variable to forget with the body of each clause whose head is thevariable. It takes polynomial time in the single-head case: each variable is atmost the head of a clause. Some formulae are not single-head but can be made soto simplify forgetting. They are single-head equivalent. The first contributionof this article is the study of a semantical characterization of single-headequivalence. Two necessary conditions are given. They are sufficient when theformula is inequivalent: it makes two sets of variables equivalent only if theyare also equivalent to their intersection. All acyclic formulae areinequivalent. The second contribution of this article is an incompletealgorithm for turning a formula single-head. In case of success, forgettingbecomes possible in polynomial time and produces a polynomial-size formula,none of which is otherwise guaranteed. The algorithm is complete oninequivalent formulae.

One head is better than two: a polynomial restriction for propositional definite Horn forgetting