Unifying Class-Based Representation Formalisms
  The notion of class is ubiquitous in computer science and is central in many
formalisms for the representation of structured knowledge used both in
knowledge representation and in databases. In this paper we study the basic
issues underlying such representation formalisms and single out both their
common characteristics and their distinguishing features. Such investigation
leads us to propose a unifying framework in which we are able to capture the
fundamental aspects of several representation languages used in different
contexts. The proposed formalism is expressed in the style of description
logics, which have been introduced in knowledge representation as a means to
provide a semantically well-founded basis for the structural aspects of
knowledge representation systems. The description logic considered in this
paper is a subset of first order logic with nice computational characteristics.
It is quite expressive and features a novel combination of constructs that has
not been studied before. The distinguishing constructs are number restrictions,
which generalize existence and functional dependencies, inverse roles, which
allow one to refer to the inverse of a relationship, and possibly cyclic
assertions, which are necessary for capturing real world domains. We are able
to show that it is precisely such combination of constructs that makes our
logic powerful enough to model the essential set of features for defining class
structures that are common to frame systems, object-oriented database
languages, and semantic data models. As a consequence of the established
correspondences, several significant extensions of each of the above formalisms
become available. The high expressiveness of the logic we propose and the need
for capturing the reasoning in different contexts forces us to distinguish
between unrestricted and finite model reasoning. A notable feature of our
proposal is that reasoning in both cases is decidable. We argue that, by virtue
of the high expressive power and of the associated reasoning capabilities on
both unrestricted and finite models, our logic provides a common core for
class-based representation formalisms.
