Remarks on projective unifiers

Abstract

A projective unifier for a unifiable formula a in a logic L is a unifier a for a (i.e. a substitution making a a theorem of L) such that a —L a(x) o x. Using the result of Burris [3] we observe that every discriminator variety has projective unifiers. Several examples of projective unifiers both in discriminator and in non-discriminator varieties are given. As an application we show that logics with projective unifiers are almost structurally complete, i.e. every admissible rule with unifiable premises is derivable.