Description logics (DLs) are a family of logic-based knowledge representation languages used to represent knowledge of an application domain in a structured and well-understood way while providing inference procedures for reasoning about the represented knowledge. DLs form a very active research area, spanning the last 40 years, and which led to a rich variety of description formalisms, with differing expressive power, employed in various application domains (e.g., information systems and databases, natural language processing, semantic web, etc). Standard inference problems (e.g., subsumption, satisfiability, and instance problem), as well as their computational properties (decidability, connection between complexity and expressivity), are now well understood. After a brief introduction to description logics non-standard inferences, this talk will be devoted to presenting description logics augmented with (concept or role) variables. Concepts with variables (also called patterns) have been introduced in description logics since the mid-nineties and led to a highly interesting research stream on the so-called nonstandard reasoning, specifically, matching and unification. The talk will discuss new semantics for variables and highlights new inference problems which can be viewed as generalizations of matching and unification.
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