A Uniform Framework for Concept Definitions in Description Logics
  Most modern formalisms used in Databases and Artificial Intelligence for
describing an application domain are based on the notions of class (or concept)
and relationship among classes. One interesting feature of such formalisms is
the possibility of defining a class, i.e., providing a set of properties that
precisely characterize the instances of the class. Many recent articles point
out that there are several ways of assigning a meaning to a class definition
containing some sort of recursion. In this paper, we argue that, instead of
choosing a single style of semantics, we achieve better results by adopting a
formalism that allows for different semantics to coexist. We demonstrate the
feasibility of our argument, by presenting a knowledge representation
formalism, the description logic muALCQ, with the above characteristics. In
addition to the constructs for conjunction, disjunction, negation, quantifiers,
and qualified number restrictions, muALCQ includes special fixpoint constructs
to express (suitably interpreted) recursive definitions. These constructs
enable the usual frame-based descriptions to be combined with definitions of
recursive data structures such as directed acyclic graphs, lists, streams, etc.
We establish several properties of muALCQ, including the decidability and the
computational complexity of reasoning, by formulating a correspondence with a
particular modal logic of programs called the modal mu-calculus.
