Description Logics (DLs) are a family of logic-based knowledge representation formalisms with appealing computational properties and a variety of applications at the confluence of modern artificial intelligence and other areas. In particular, DLs are well-suited for representing and reasoning about ontologies and therefore constitute the formal foundations of the Semantic Web. The different DL formalisms that have been proposed in the literature provide us with a wide choice of constructors in the object language. However, these are intended to represent only classical, unquestionable knowledge, being unable to express the different aspects of uncertainty and vagueness that often show up in everyday life. Examples of these comprise the various guises of exceptions, typicality (and atypicality), approximations and many others, as usually encountered in the different forms of human quotidian reasoning. A similar argument can be put forward when moving to the level of entailment, that of the sanctioned conclusions from a knowledge base. DL systems provide for a variety of (standard and non-standard) reasoning services, but the underlying notion of entailment remains classical and therefore, depending on the application one has in mind, DLs inherit most of the criticisms raised in the development of the so-called non-classical logics. In this regard, endowing DLs and their associated reasoning services with the ability to cope with defeasibility is a natural step in their development. Indeed, the past two decades have witnessed the surge of many attempts to introduce non-monotonic reasoning capabilities in a DL setting. These range from preferential approaches to circumscription-based ones, amongst others. In spite of all the progress that has been achieved in the area, the study of non-monotonic reasoning in DLs remains a large avenue for exploration. To witness, the bulk of the effort in this direction has been put in the definition of accounts of defeasible subsumption and in the characterisation of appropriate notions of defeasible entailment relations. This suggests that existing approaches to reasoning with defeasible inheritance and typicality in ontologies may lack constructors that are important from a modelling perspective. Indeed, here we make a case for a number of additional defeasible constructs at the object level enriching the basic DL concept language and propose a corresponding preferential semantics. We show that this does not negatively affect decidability or complexity of reasoning for an important class of DLs, and that existing notions of preferential reasoning can be expressed in terms of our new constructs.

Keywords: Ontologies, Description Logics, Defeasible Reasoning, Preferential Semantics