Algebraic characterization of temporal logics on forests

We propose a rich class FL(L) of temporal logics, parametrized by a class L of modalities, evaluated over forests, that is, ordered tuples of ordered but unranked finite trees, an algebraic product operation (which we call the Moore product) of forest automata, and show that these logically defined classes of forest languages are characterized precisely via the Moore product. As an application we show that the fragment of the logic CTL which uses only the non-strict EF modality has a polynomial-time decidable definability problem. 1998 ACM Subject Classification F.4.1. Mathematical Logic