The learnability of description logics with equality constraints

Although there is an increasing amount of experimental research on learning concepts expressed in first-order logic, there are still relatively few formal results on the polynomial learnability of first-order representations from examples. Most previous analyses in the pac-model have focused on subsets of Prolog, and only a few highly restricted subsets have been shown to be learnable. In this paper, we will study instead the learnability of the restricted first-order logics known as “description logics”, also sometimes called “terminological logics” or “KL-ONE-type languages”. Description logics are also subsets of predicate calculus, but are expressed using a different syntax, allowing a different set of syntactic restrictions to be explored. We first define a simple description logic, summarize some results on its expressive power, and then analyze its learnability. It is shown that the full logic cannot be tractably learned. However, syntactic restrictions exist that enable tractable learning from positive examples alone, independent of the size of the vocabulary used to describe examples. The learnable sublanguage appears to be incomparable in expressive power to any subset of first-order logic previously known to be learnable.