Reasoning in Defeasible Description Logics with System W and Lexicographic Inference

Description Logics (DLs) are widely applied in AI and database systems. However, like other classical logics, they cannot adequately handle defeasible information. Building on the notion of rational closure - a form of defeasible reasoning originally developed for the propositional setting and later adapted to DLs - we extend this approach by incorporating two further forms of defeasible reasoning: System W and lexicographic closure. Both are well-established entailment relations in the propositional case and are known to satisfy several desirable properties. In this paper, we provide model-theoretic definitions of these extensions for DLs, analyze their behaviour by relating them to their propositional counterparts, and present algorithms for their computation.