Keys, Nominals, and Concrete Domains

Abstract

Many description logics (DLs) combine knowledge representation on an abstract, logical level with an interface to 'concrete' domains such as numbers and strings with built-in predicates such as <, +, and prefix-of. These hybrid DLs have turned out to be quite useful for reasoning about conceptual models of information systems, and as the basis for expressive ontology languages. We propose to further extend such DLs with key constraints that allow the expression of statements like 'US citizens are uniquely identified by their social security number'. Based on this idea, we introduce a number of natural description logics and perform a detailed analysis of their decidability and computational complexity. It turns out that naive extensions with key constraints easily lead to undecidability, whereas more careful extensions yield NEXPTIME-complete DLs for a variety of useful concrete domains.