KR2020Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 12-18, 2020.

Edited by

ISSN: 2334-1033
ISBN: 978-0-9992411-7-2

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Published by

Copyright © 2020 International Joint Conferences on Artificial Intelligence Organization

Logical Separability of Incomplete Data under Ontologies

  1. Jean Christoph Jung(University of Bremen)
  2. Carsten Lutz(University of Bremen)
  3. Hadrien Pulcini(University of Liverpool)
  4. Frank Wolter(University of Liverpool)


  1. Computational aspects of knowledge representation-General
  2. Description logics-General
  3. Ontology formalisms and models-General
  4. KR and machine learning, inductive logic programming, knowledge acquisition-


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, and generating referring expressions. In this paper, we investigate the existence of a separating formula for incomplete data in the presence of an ontology. Both for the ontology language and the separation language, we concentrate on first-order logic and three important fragments thereof: the description logic ALCI, the guarded fragment, and the two-variable fragment. 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. We characterize separability in a model-theoretic way, compare the separating power of the different languages, and determine the computational complexity of separability as a decision problem.