Geometric Models for (Temporally) Attributed Description Logics
- URL: http://arxiv.org/abs/2108.12239v1
- Date: Fri, 27 Aug 2021 12:40:14 GMT
- Title: Geometric Models for (Temporally) Attributed Description Logics
- Authors: Camille Bourgaux, Ana Ozaki, Jeff Z. Pan
- Abstract summary: Attributed description logics (DLs) have been defined to bridge the gap between DL languages and knowledge graphs.
This paper investigates their compatibility, focusing on the attributed version of a Horn dialect of the DL-Lite family.
We show that a temporally attributed DL may not have a convex geometric model in general but we can recover geometric satisfiability by imposing some restrictions on the use of the temporal attributes.
- Score: 21.027712454317047
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In the search for knowledge graph embeddings that could capture ontological
knowledge, geometric models of existential rules have been recently introduced.
It has been shown that convex geometric regions capture the so-called
quasi-chained rules. Attributed description logics (DL) have been defined to
bridge the gap between DL languages and knowledge graphs, whose facts often
come with various kinds of annotations that may need to be taken into account
for reasoning. In particular, temporally attributed DLs are enriched by
specific attributes whose semantics allows for some temporal reasoning.
Considering that geometric models and (temporally) attributed DLs are promising
tools designed for knowledge graphs, this paper investigates their
compatibility, focusing on the attributed version of a Horn dialect of the
DL-Lite family. We first adapt the definition of geometric models to attributed
DLs and show that every satisfiable ontology has a convex geometric model. Our
second contribution is a study of the impact of temporal attributes. We show
that a temporally attributed DL may not have a convex geometric model in
general but we can recover geometric satisfiability by imposing some
restrictions on the use of the temporal attributes.
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