The expressive power of second order Horn logic

Abstract

We investigate second order Horn logic, the restriction of second order logic to formulae whose first order part is a universal Horn formula. It is shown that this logic collapses to its existential fragment. In the presence of a successor relation, second order Horn logic has the same expressive power as fixpoint logic and therefore captures precisely the class of polynomial time computable queries. In the absence of the successor relation this logic is strictly weaker than fixed point logic.