The preferential approach to nonmonotonic reasoning was consolidated in depth by Krause, Lehmann and Magidor (KLM) for propositional logic in the early 90's. In recent years, there have been efforts to extend their framework to Description Logics (DLs) and a solid (though preliminary) theoretical foundation has already been established towards this aim. Despite this foundation, the generalisation of the propositional framework to DLs is not yet complete and there are multiple proposals for entailment in this context with no formal system for deciding between these. In addition, there are virtually no existing preferential reasoning implementations to speak of for DL-based ontologies. The goals of this PhD are: to place the preferential approach in context w.r.t. the alternative nonmonotonic reasoning proposals, to provide a complete generalisation of the preferential framework of KLM to the DL ALC, provide a formal understanding of the relationships between the multiple proposals for entailment in this context, and finally, to develop an accompanying defeasible reasoning system for DL-based ontologies with performance that is suitable for use in existing ontology development settings.
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