The Representation of Structured Objects in DLs using Description Graphs

Applications of description logics (DLs) often require the representation of and reasoning with structured objects—that is, objects composed of parts connected in complex ways. Although DLs are general and powerful languages, they cannot describe arbitrarily connected structures. The description of structured objects in DLs can thus be underconstrained, which reduces the number of entailments and can even cause performance problems for reasoning. Hence, we propose an extension of DLs with description graphs, which allow structured objects to be described in a simple and precise way. To represent conditional aspects of the domain, we also allow for Horn rules over description graphs. Extending DLs with axioms that can enforce arbitrary structures easily leads to undecidability [5]. Our formalism, however, is decidable because it can represent only structured objects whose number of parts is bounded. In practice, structured objects are usually modeled up to a certain level of granularity, which naturally determines this bound. We present a reasoning algorithm for the case where the DL part is expressed in SHIQ [3]. We thus obtain a powerful, decidable, and practicable language that combines two complementary formalisms: unbounded but tree-like structures can be described using standard DL axioms, and the naturally bounded structured parts can be described using arbitrarily connected description graphs and rules. Due to lack of space, we cannot present the correctness proofs in this paper; we refer the interested reader to [6]. We have implemented our procedure in the HermiT reasoner. Furthermore, we have extracted description graphs from the GALEN and FMA ontologies, classified them successfully, and even detected a modeling error in GALEN.