SAT-Based PAC Learning of Description Logic Concepts

We propose bounded fitting as a scheme for learning description logic concepts in the presence of ontologies. A main advantage is that the resulting learning algorithms come with theoretical guarantees regarding their generalization to unseen examples in the sense of PAC learning. We prove that, in contrast, several other natural learning algorithms fail to provide such guarantees. As a further contribution, we present the system SPELL which efficiently implements bounded fitting for the description logic $\mathcal{ELH}^r$ based on a SAT solver, and compare its performance to a state-of-the-art learner.