# Lattice-preserving ALC ontology embeddings with saturation

arXiv: https://arxiv.org/abs/2305.07163 · HTML: https://mlsanity.com/paper/2305.07163/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 77 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Order-Embeddings of Images and Language](https://mlsanity.com/paper/1511.06361/) (2015)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [PyKEEN 1.0: A Python Library for Training and Evaluating Knowledge Graph Embeddings](https://mlsanity.com/paper/2007.14175/) (2020)
- [OWL2Vec*: Embedding of OWL Ontologies](https://mlsanity.com/paper/2009.14654/) (2020)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Knowledge-aware Zero-Shot Learning: Survey and Perspective](https://mlsanity.com/paper/2103.00070/) (2021)
- [Universal Representation Learning of Knowledge Bases by Jointly Embedding Instances and Ontological Concepts](https://mlsanity.com/paper/2103.08115/) (2021)
- [Contextual Semantic Embeddings for Ontology Subsumption Prediction](https://mlsanity.com/paper/2202.09791/) (2022)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling](https://mlsanity.com/paper/1911.06904/) (2019)
- [Onto2Vec: joint vector-based representation of biological entities and their ontology-based annotations](https://mlsanity.com/paper/1802.00864/) (2018)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [A survey on knowledge-enhanced multimodal learning](https://mlsanity.com/paper/2211.12328/) (2022)
- [Category-theoretical Semantics of the Description Logic ALC (extended version)](https://mlsanity.com/paper/2110.08837/) (2021)
- [Reasoning in the Description Logic ALC under Category Semantics](https://mlsanity.com/paper/2205.04911/) (2022)
- [From axioms over graphs to vectors, and back again: evaluating the properties of graph-based ontology embeddings](https://mlsanity.com/paper/2303.16519/) (2023)

## Abstract (arXiv)

Generating vector representations (embeddings) of OWL ontologies is a growing task due to its applications in predicting missing facts and knowledge-enhanced learning in fields such as bioinformatics. The underlying semantics of OWL ontologies are expressed using Description Logics (DLs). Initial approaches to generate embeddings relied on constructing a graph out of ontologies, neglecting the semantics of the logic therein. Recent semantic-preserving embedding methods often target lightweight DL languages like EL++, ignoring more expressive information in ontologies. Although some approaches aim to embed more descriptive DLs like ALC, those methods require the existence of individuals, while many real-world ontologies are devoid of them. We propose an ontology embedding method for the ALC DL language that considers the lattice structure of concept descriptions. We use connections between DL and Category Theory to materialize the lattice structure and embed it using an order-preserving embedding method. We show that our method outperforms state-of-the-art methods in several knowledge base completion tasks. Furthermore, we incoporate saturation procedures that increase the information within the constructed lattices. We make our code and data available at urlhttps://github.com/bio-ontology-research-group/catE.