A Lightweight Defeasible Description Logic in Depth: Quantification in Rational Reasoning and Beyond

Description Logics (DLs) are increasingly successful knowledge representation formalisms, useful for any application requiring implicit derivation of knowledge from explicitly known facts. A prominent example domain benefiting from these formalisms since the 1990s is the biomedical field. This area contributes an intangible amount of facts and relations between low- and high-level concepts such as the constitution of cells or interactions between studied illnesses, their symptoms and remedies. DLs are well-suited for handling large formal knowledge repositories and computing inferable coherences throughout such data, relying on their well-founded first-order semantics. In particular, DLs of reduced expressivity have proven a tremendous worth for handling large ontologies due to their computational tractability. In spite of these assets and prevailing influence, classical DLs are not well-suited to adequately model some of the most intuitive forms of reasoning. The capability for abductive reasoning is imperative for any field subjected to incomplete knowledge and the motivation to complete it with typical expectations. When such default expectations receive contradicting evidence, an abductive formalism is able to retract previously drawn, conflicting conclusions. Common examples often include human reasoning or a default characterisation of properties in biology, such as the normal arrangement of organs in the human body. Treatment of such defeasible knowledge must be aware of exceptional cases - such as a human suffering from the congenital condition situs inversus - and therefore accommodate for the ability to retract defeasible conclusions in a non-monotonic fashion. Specifically tailored non-monotonic semantics have been continuously investigated for DLs in the past 30 years. A particularly promising approach, is rooted in the research by Kraus, Lehmann and Magidor for preferential (propositional) logics and Rational Closure (RC). The biggest advantages of RC a