Cone Semantics for Logics with Negation
Abstract
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.
Cite
Text
Özçep et al. "Cone Semantics for Logics with Negation." International Joint Conference on Artificial Intelligence, 2020. doi:10.24963/IJCAI.2020/252Markdown
[Özçep et al. "Cone Semantics for Logics with Negation." International Joint Conference on Artificial Intelligence, 2020.](https://mlanthology.org/ijcai/2020/ozcep2020ijcai-cone/) doi:10.24963/IJCAI.2020/252BibTeX
@inproceedings{ozcep2020ijcai-cone,
title = {{Cone Semantics for Logics with Negation}},
author = {Özçep, Özgür Lütfü and Leemhuis, Mena and Wolter, Diedrich},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2020},
pages = {1820-1826},
doi = {10.24963/IJCAI.2020/252},
url = {https://mlanthology.org/ijcai/2020/ozcep2020ijcai-cone/}
}