DELE: Deductive $mathcal{EL}^{++} hinspace $ Embeddings for Knowledge Base Completion

2024-11-03

AI Summary

Existing $mathcal{EL}^{++}$ embedding methods fail to distinguish between *unprovable* and *falsifiable* statements and neglect axioms derivable—but not explicitly asserted—within the deductive closure, leading to biased negative sampling and reduced inference fidelity. To address this, we propose the first deductive-closure-aware negative sampling loss function, which explicitly models unprovability and generates semantically grounded negative examples from the closure. We further design a vector-space embedding framework adhering to $mathcal{EL}^{++}$ semantic constraints, enabling joint representation of classes, roles, and individuals. Additionally, we introduce a customized evaluation protocol tailored to ontological reasoning. Experiments demonstrate that our approach significantly outperforms state-of-the-art ontology embedding baselines on knowledge base completion, while improving both logical consistency and completion accuracy.

Technology Category

• Knowledge Representation and Reasoning: Ontologies
• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Ontology embeddings map classes, relations, and individuals in ontologies into $mathbb{R}^n$, and within $mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $mathcal{EL}^{++}$, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $mathcal{EL}^{++}$ ontologies, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives and formulated evaluation methods for knowledge base completion. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.

Problem

• Distinguish unprovable vs provably false statements in ontology embeddings
• Utilize deductive closure to identify inferred but unasserted statements
• Improve knowledge base completion via enhanced negative loss methods

Innovation

• Uses deductive closure for ontology embeddings
• Introduces novel negative loss functions
• Improves knowledge base completion accuracy