SAT-Based Bounded Fitting for the Description Logic ALC

Bounded fitting is a general paradigm for learning logical formulas from positive and negative data examples, that has received considerable interest recently. We investigate bounded fitting for the description logic ALC and its syntactic fragments. We show that the underlying size-restricted fitting problem is NP-complete for all studied fragments, even in the special case of a single positive and a single negative example. By design, bounded fitting comes with probabilistic guarantees in Valiant's PAC learning framework. In contrast, we show that other classes of algorithms for learning ALC concepts do not provide such guarantees. Finally, we present an implementation of bounded fitting in ALC and its fragments based on a SAT solver. We discuss optimizations and compare our implementation to other concept learning tools.