LSV Seminar

Date

28.01.2020, 11:00

Place

Pavillon des Jardins

Speaker

Ivan Varzinczak (CRIL)

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 artificial intelligence, databases and other areas. In particular, DLs are well-suited for representing and reasoning about ontologies and therefore they stand as 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. Nevertheless, these are intended to represent only classical, unquestionable knowledge, and are therefore unable to express and cope with 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 an ontology. 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 talk, I make a case for endowing DLs and their associated reasoning services with the ability to cope with defeasibility. I start by introducing the notion of defeasible class subsumption, which allows for the specification of and reasoning about defeasible inheritance, and give it an intuitive semantics in terms of preference relations. Next I show how to take defeasibility to the level of entailment through the notion of rational closure of a defeasible ontology. Of particular interest is the fact that our constructions do not negatively affect decidability or complexity of reasoning for an important class of DLs. Finally, I show how our semantic definitions are fruitful in extending DLs with further defeasible constructs at the object level and in providing a notion of contextual defeasible subsumption. These allow for an even more fine-grained treatment of exceptions in reasoning with defeasible inheritance.