ExpTime Tableaux with Global Caching for Graded Propositional Dynamic Logic

Abstract

We present the first direct tableau decision procedure for graded PDL, which uses global caching and has ExpTime (optimal) complexity when numbers are encoded in unary. It shows how to combine checking fulfillment of existential star modalities with integer linear feasibility checking for tableaux with global caching. As graded PDL can be used as a description logic for representing and reasoning about terminological knowledge, our procedure is useful for practical applications.