Dual box embeddings for the description logic EL++

OWL ontologies, whose formal semantics are rooted in Description Logic (DL), have been widely used for knowledge representation. Similar to Knowledge Graphs (KGs), ontologies are often incomplete, and maintaining and constructing them has proved challenging. While classical deductive reasoning algorithms use the precise formal semantics of an ontology to predict missing facts, recent years have witnessed growing interest in inductive reasoning techniques that can derive probable facts from an ontology. Similar to KGs, a promising approach is to learn ontology embeddings in a latent vector space, while additionally ensuring they adhere to the semantics of the underlying DL. While a variety of approaches have been proposed, current ontology embedding methods suffer from several shortcomings, especially that they all fail to faithfully model one-to-many, many-to-one, and many-to-many relations and role inclusion axioms. To address this problem and improve ontology completion performance, we propose a novel ontology embedding method named Box2EL for the DL EL++, which represents both concepts and roles as boxes (i.e., axis-aligned hyperrectangles), and models inter-concept relationships using a bumping mechanism. We theoretically prove the soundness of Box2EL and conduct an extensive experimental evaluation, achieving state-of-the-art results across a variety of datasets on the tasks of subsumption prediction, role assertion prediction, and approximating deductive reasoning

Box2^2EL: Concept and Role Box Embeddings for the Description Logic EL++

Description logic (DL) ontologies extend knowledge graphs (KGs) with conceptual information and logical background knowledge. In recent years, there has been growing interest in inductive reasoning techniques for such ontologies, which promise to complement classical deductive reasoning algorithms. Similar to KG completion, several existing approaches learn ontology embeddings in a latent space, while additionally ensuring that they faithfully capture the logical semantics of the underlying DL. However, they suffer from several shortcomings, mainly due to a limiting role representation. We propose Box$^2$EL, which represents both concepts and roles as boxes (i.e., axis-aligned hyperrectangles) and demonstrate how it overcomes the limitations of previous methods. We theoretically prove the soundness of our model and conduct an extensive experimental evaluation, achieving state-of-the-art results across a variety of datasets. As part of our evaluation, we introduce a novel benchmark for subsumption prediction involving both atomic and complex concepts

dtControl: Decision Tree Learning Algorithms for Controller Representation

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are smaller and more explainable. We present dtControl, an easily extensible tool for representing memoryless controllers as decision trees. We give a comprehensive evaluation of various decision tree learning algorithms applied to 10 case studies arising out of correct-by-construction controller synthesis. These algorithms include two new techniques, one for using arbitrary linear binary classifiers in the decision tree learning, and one novel approach for determinizing controllers during the decision tree construction. In particular the latter turns out to be extremely efficient, yielding decision trees with a single-digit number of decision nodes on 5 of the case studies

Dual Box Embeddings for the Description Logic EL⁺⁺

OWL ontologies, whose formal semantics are rooted in Description Logic (DL), have been widely used for knowledge representation. Similar to Knowledge Graphs (KGs), ontologies are often incomplete, and maintaining and constructing them has proved challenging. While classical deductive reasoning algorithms use the precise formal semantics of an ontology to predict missing facts, recent years have witnessed growing interest in inductive reasoning techniques that can derive probable facts from an ontology. Similar to KGs, a promising approach is to learn ontology embeddings in a latent vector space, while additionally ensuring they adhere to the semantics of the underlying DL. While a variety of approaches havebeen proposed, current ontology embedding methods suffer from several shortcomings, especially that they all fail to faithfully model one-to-many, many-to-one, and many-to-many relations and role inclusion axioms. To address this problem and improve ontology completion performance, we propose a novel ontology embedding method named Box2EL for the DL EL++, which represents both concepts and roles as boxes (i.e., axis-aligned hyperrectangles), andmodels inter-concept relationships using a bumping mechanism. We theoretically prove the soundness of Box2EL and conduct an extensive experimental evaluation, achieving state-of-the-art results across a variety of datasets on the tasks of subsumption prediction, role assertion prediction, and approximating deductive reasoning.1<br/