  We study a many-valued generalization of Propositional Dynamic Logic where
formulas in states and accessibility relations between states of a Kripke model
are evaluated in a finite FL-algebra. One natural interpretation of this
framework is related to reasoning about costs of performing structured actions.
We prove that PDL over any finite FL-algebra is decidable. We also establish a
general completeness result for a class of PDLs based on commutative integral
FL-algebras with canonical constants.
