Logical separability of labeled data examples under ontologies



Jung, Jean Christoph, Lutz, Carsten, Pulcini, Hadrien and Wolter, Frank
(2022) Logical separability of labeled data examples under ontologies. Artificial Intelligence, 313. p. 103785.

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: Logical separability, Decidable fragments of first -order logic, Description logic, Learning from examples, Complexity, Ontologies
Depositing User: Symplectic Admin
Date Deposited: 04 Oct 2022 07:36
Last Modified: 18 Jan 2023 20:41
DOI: 10.1016/j.artint.2022.103785
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3165038