Logical separability of labeled data examples under ontologies

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental applications such as concept learning, reverse engineering database queries, generating referring expressions, entity comparison knowledge graphs. In this paper, we investigate existence separating for presence an ontology. Both ontology language separation language, concentrate on first-order logic following important fragments thereof: description ALCI, guarded fragment, two-variable negation fragment. For separation, also consider (unions of) conjunctive queries. We several forms separability differ treatment whether or not they admit use additional helper symbols to achieve separation. Our main results are model-theoretic characterizations (all variants separability, power different languages, investigation computational complexity deciding separability.