Hybrid Logics and Ontology Languages

Description Logics (DLs) are a family of logic based knowledge representation formalisms. Although they have a range of applications, they are perhaps best known as the basis for widely used ontology languages such as OIL, DAML+OIL and OWL, the last of which is now a World Wide Web Consortium (W3C) recommendation. SHOIN, the DL underlying OWL DL (the most widely used "species" of OWL), includes familiar features from hybrid logic. In particular, in order to support extensionally defined classes, SHOIN includes nominals: classes whose extension is a singleton set. This is an important feature for a logic that is designed for use in ontology language applications, because extensionally defined classes are very common in ontologies. Binders and state variables are another feature from Hybrid Logic that would clearly be useful in an ontology language, but it is well known that adding this feature to even a relatively weak language would lead to undecidability. However, recent work has shown that this feature could play a very useful role in query answering, where the syntactic structure of queries means that the occurrence of state variables is restricted in a way that allows for decidable reasoning.