Boosting the Correspondence between Description Logics and Propositional Dynamic Logics

One of the main themes in the area of Terminologi cal Reasoning has been to identify description logics DLs that are both very expressive and decidable A recent paper by Schild showed that this issue can be pro tably addressed by relying on a correspondence between DLs and propositional dynamic logics PDL However Schild left open three important problems related to the translation into PDLs of functional re strictions on roles both direct and inverse number restrictions and assertions on individuals The work reported in this paper presents a solution to these problems The results have a twofold signi cance From the standpoint of DLs we derive decidability and complexity results for some of the most expres sive logics appeared in the literature and from the standpoint of PDLs we derive a general methodol ogy for the representation of several forms of program determinism and for the speci cation of partial com