Boosting the correspondence between description logics and proposit ional ynamic logics

One of the main themes in the area of Terminological 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 profitably 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 restrictions 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 significance. From the standpoint of DLs, we derive decidability and complexity results for some of the most expressive logics appeared in the literature, and from the standpoint of PDLs, we derive a general methodology for the representation of several forms of program determinism and for the specification of partial com-