2020/07/03 by Jean Christoph Jung, Carsten Lutz, Jung, Jean Christoph +5 · 7 citations
Computer Science · #Advanced Database Systems and Queries #Artificial Intelligence (cs.AI) #F.4.1 #FOS: Computer and information sciences #I.2.4 #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2007.01610
openalex publication_date 2020/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, generating referring expressions, and entity comparison in knowledge graphs. In this paper, we investigate the existence of a separating formula for data in the presence of an ontology. Both for the ontology language and the separation language, we concentrate on first-order logic and the following important fragments thereof: the description logic ALCI, the guarded fragment, the two-variable fragment, and the guarded negation fragment. For separation, we also consider (unions of) conjunctive queries. We consider several forms of separability that differ in the treatment of negative examples and in whether or not they admit the use of additional helper symbols to achieve separation. Our main results are model-theoretic characterizations of (all variants of) separability, the comparison of the separating power of different languages, and the investigation of the computational complexity of deciding separability.