Extending Description Logics with Generic Concepts - the Case of Terminologies

We propose an extension of Description Logics (DLs) with generic concepts and conditional axioms. Inspired by object-oriented languages, generic concepts allow a compact definition of concepts with similar structures. For example, one can define a generic concept Owner[X] to describe objects that own another object from X, and later use a specific replacement of the parameter X, such as Owner[Pet] representing pet owners. Conditional axioms can be used to set bounds on the values that replace the generic parameters. For example, we could restrict replacements of X in a concept Keeper[X] to only subconcepts of Pet. As the set of possible parameter replacements can be infinite and even uncountable, the generic extensions are, in general, undecidable. To identify decidable generic DLs, we focus on the case of terminologies, requiring that variables are only used in definitions of generic concepts. We formulate restrictions that allow a reduction of generic entailment to classical entailment and further conditions that ensure decidability.