A Unified Framework for Non-standard Reasoning Services in Description Logics

Non-standard reasoning in Description Logics (DLs) comprises computing a Least Common Subsumer (LCS), a Concept Difference, a Concept Unifier, or an Interpolant Concept, to name a few. Although some reasoning services have been unified already (e.g., LCS and Most Specific Concept), the definition of non-standard problems and the computation that solve them are very different from each other. We propose to unify the definitions of non-standard services as special Second-order sentences in DLs; when the solution concepts are optimal with respect to some preferences, a fixpoint replaces the Second-order quantification. Moreover, we propose to combine the well-known Tableaux calculi for DLs with rules that compute substitutions of Concept Variables. We prove soundness and completeness of the combined calculus and we give a sufficient condition for termination, which covers some non-trivial cases.

• Type: Conference
• Year: 2010
• Where: ECAI
• Authors: Simona Colucci, Tommaso Di Noia, Eugenio Di Sciascio, Francesco M. Donini, Azzurra Ragone
• Keywords: Artificial Intelligence, ECAI 2010, Most Specific Concept, Non-standard, Non-standard Reasoning