Defeasible Reasoning for Description Logics
Description Logics (DLs) are a family of logic-based knowledge representation formalisms with interesting computational properties and a variety of applications at the confluence of modern artificial intelligence and databases. 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 25 years have witnessed many attempts to introduce non-monotonic reasoning capabilities in Description Logics. These range from preferential approaches to circumscription-based ones, amongst others.
The goal of this tutorial is two-fold: (1) to provide an overview of the development of non-monotonic approaches to description logics from the past 25 years, in particular pointing out the difficulties that arise when naïvely transposing the traditional propositional approaches to the DL case, and (2) present the latest results in the area, especially those based on the preferential approach, as well as the new directions for investigation that these have opened.