This paper presents an embedding of ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. Our main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC.

Original languageEnglish
Pages1820 - 1826
Number of pages7
Publication statusPublished - 08.07.2020
Event29th International Joint Conference on Artificial Intelligence - Yokohama, Japan
Duration: 01.01.202101.01.2021
Conference number: 165342


Conference29th International Joint Conference on Artificial Intelligence
Abbreviated titleIJCAI 2020

Research Areas and Centers

  • Centers: Center for Artificial Intelligence Luebeck (ZKIL)
  • Research Area: Intelligent Systems


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