V.: Two-dimensional description logics for context-based semantic interoperability

Description Logics (DLs) provide a clear and broadly accepted paradigm for modeling and reasoning about terminological knowledge. However, it has been often noted, that although DLs are well-suited for represent-ing a single, global viewpoint on an application domain, they offer no formal grounding for dealing with knowl-edge pertaining to multiple heterogeneous viewpoints — a scenario ever more often approached in practical applications, e.g. concerned with reasoning over dis-tributed knowledge sources on the Semantic Web. In this paper, we study a natural extension of DLs, in the style of two-dimensional modal logics, which supports declarative modeling of viewpoints as contexts, in the sense of McCarthy, and their semantic interoperability. The formalism is based on two-dimensional semantics, where one dimension represents a usual object domain and the other a (possibly infinite) domain of viewpoints, addressed by additional modal operators and a metalan-guage, on the syntactic level. We systematically intro-duce a number of expressive fragments of the proposed logic, study their computational complexity and con-nections to related formalisms