Learnability of the Classic Knowledge Representation Language

Much of the work in inductive learning considers languages that represent hypotheses using some restricted form of propositional logic; an important research problem is extending propo-sitional learning algorithms to use more expressive rst-order representations. Further, it is desirable for these algorithms to have solid theoretical foundations, so that their behavior is reliable and predictable. This paper uses the tools of computational learning theory to explore the learnability of a class of restricted rst-order logics known as description logics which have been developed by the knowledge representation community. In particular, we will consider the learnability of various subsets of the description logic used in Classic, a knowledge representation system that has been implemented and used in real applications. We identify obstacles to eecient learnability and then describe syntactic restrictions on the Classic description logic that include a large percentage of the tasks to which Classic has been applied, yet yield eeciently learnable sublanguages.