Cone Semantics for Logics with Negation
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
Main track. Pages 1820-1826. https://doi.org/10.24963/ijcai.2020/252
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.
Knowledge Representation and Reasoning: Other
Machine Learning: Knowledge-based Learning
Knowledge Representation and Reasoning: Description Logics and Ontologies
Knowledge Representation and Reasoning: Qualitative, Geometric, Spatial, Temporal Reasoning