Practical Reasoning for Defeasible Description Logics
Kody Moodley · 2017
Description Logics (DLs) are a family of logic-based languages for formalisingontologies. They have useful computational properties allowing the developmentof automated reasoning engines to infer implicit knowledge fromontologies. However, classical DLs do not tolerate exceptions to specifiedknowledge. This led to the prominent research area of nonmonotonic or defeasiblereasoning for DLs, where most techniques were adapted from seminalworks for propositional and first-order logic.Despite the topic's attention in the literature, there remains no consensuson what "sensible" defeasible reasoning means for DLs. Furthermore, thereare solid foundations for several approaches and yet no serious implementationsand practical tools. In this thesis, we address the aforementioned issuesin a broad sense. We identify the preferential approach, by Kraus, Lehmannand Magidor (KLM) in propositional logic, as a suitable abstract frameworkfor defining and studying the precepts of sensible defeasible reasoning.We give a generalisation of KLM's precepts, and their arguments motivatingthem, to the DL case. We also provide several preferential algorithmsfor defeasible entailment in DLs; evaluate these algorithms; and the mainalternatives in the literature, against the agreed upon precepts; extensivelytest the performance of these algorithms, and ultimately consolidate our implementation in a software tool called Defeasible-Inference Platform (DIP).We found some useful entailment regimes within the preferential contextthat satisfy all the KLM properties and some that have scalable performancein real world ontologies even without extensive optimisation.