Faithiful Embeddings for EL++ Knowledge Bases

Recently, increasing efforts are put into learning continual representations for symbolic knowledge bases (KBs). However, these approaches either only embed the data-level knowledge (ABox) or suffer from inherent limitations when dealing with concept-level knowledge (TBox), i.e., they cannot faithfully model the logical structure present in the KBs. We present BoxEL, a geometric KB embedding approach that allows for better capturing the logical structure (i.e., ABox and TBox axioms) in the description logic EL++. BoxEL models concepts in a KB as axis-parallel boxes that are suitable for modeling concept intersection, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the learned model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on (plausible) subsumption reasonings and a real-world application for protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.Comment: Published in ISWC'2

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

Quantum Mathematics in Artificial Intelligence

In the decade since 2010, successes in artificial intelligence have been at the forefront of computer science and technology, and vector space models have solidified a position at the forefront of artificial intelligence. At the same time, quantum computers have become much more powerful, and announcements of major advances are frequently in the news. The mathematical techniques underlying both these areas have more in common than is sometimes realized. Vector spaces took a position at the axiomatic heart of quantum mechanics in the 1930s, and this adoption was a key motivation for the derivation of logic and probability from the linear geometry of vector spaces. Quantum interactions between particles are modelled using the tensor product, which is also used to express objects and operations in artificial neural networks. This paper describes some of these common mathematical areas, including examples of how they are used in artificial intelligence (AI), particularly in automated reasoning and natural language processing (NLP). Techniques discussed include vector spaces, scalar products, subspaces and implication, orthogonal projection and negation, dual vectors, density matrices, positive operators, and tensor products. Application areas include information retrieval, categorization and implication, modelling word-senses and disambiguation, inference in knowledge bases, and semantic composition. Some of these approaches can potentially be implemented on quantum hardware. Many of the practical steps in this implementation are in early stages, and some are already realized. Explaining some of the common mathematical tools can help researchers in both AI and quantum computing further exploit these overlaps, recognizing and exploring new directions along the way.Comment: Adding journal reference, recommended by JAIR editors upon publicatio

Testing Ontology Embedding Visualization

This dissertation presents an experiment conducted with human participants on human-information interaction with visualizations of ontologies. The research question is whether embedding visualizations or graph based visualizations lead to better task performance for human-information interaction. A literature review of word embeddings, information retrieval applications, cartesian and radial visualizations, and knowledge graph visualizations is conducted. This literature review is grounded in a facet analysis of the intersecting topics of the central research question. The context of embeddings as used for information retrieval in the 20th century, as opposed to more recent 21st century inventions such as Google's word2vec is explored. A training ontology, the African Wildlife Ontology (AWO) was selected. It was extended using public lexical resources taken from the internet to include classes of common African plants and animals. This ontology was then visualised both as vectorspace embeddings and as a classical graph visualization. Participants were presented with one of four different knowledge graph visualizations: WebVOWL, OntoGraf, SquareVis and CircleVis and had to perform a specific information retrieval task. This task was to record as many African animals as they could find on the chart. The results are analyzed in terms of precision, recall, spam and average time. Although ultimately the results do not reject the null hypothesis, there is an opportunity for further research in the visualization of embeddings of knowledge graphs, especially for information retrieval