In this paper, we present Ontolearn-a framework for learning OWL class expressions over large knowledge graphs. Ontolearn contains efficient implementations of recent stateof-the-art symbolic and neuro-symbolic class expression learners including EvoLearner and DRILL. A learned OWL class expression can be used to classify instances in the knowledge graph. Furthermore, Ontolearn integrates a verbalization module based on an LLM to translate complex OWL class expressions into natural language sentences. By mapping OWL class expressions into respective SPARQL queries, Ontolearn can be easily used to operate over a remote triplestore. The source code of Ontolearn is available at https://github.com/dice-group/Ontolearn.

In the field of knowledge management and computer science, ontologies provide a structured framework for modeling domain-specific knowledge by defining concepts and their relationships. However, the lack of tools that provide effective visualization is still a significant challenge. While numerous ontology editors and viewers exist, most of them fail to graphically represent ontology structures in a meaningful and non-overwhelming way, limiting users' ability to comprehend dependencies and properties within large ontological frameworks. In this paper, we present OntView, an ontology viewer that is designed to provide users with an intuitive visual representation of ontology concepts and their formal definitions through a user-friendly interface. Building on the use of a DL reasoner, OntView follows a "What you see is what you meant" paradigm, showing the actual inferred knowledge. One key aspect for this is its ability to visualize General Concept Inclusions (GCI), a feature absent in existing visualization tools. Moreover, to avoid a possible information overload, Ontview also offers different ways to show a simplified view of the ontology by: 1) creating ontology summaries by assessing the importance of the concepts (according to different available algorithms), 2) focusing the visualization on the existing TBox elements between two given classes and 3) allowing to hide/show different branches in a dynamic way without losing the semantics. OntView has been released with an open-source license for the whole community.

Graph Neural Networks (GNNs) are effective for node classification in graph-structured data, but they lack explainability, especially at the global level. Current research mainly utilizes subgraphs of the input as local explanations or generates new graphs as global explanations. However, these graph-based methods are limited in their ability to explain classes with multiple sufficient explanations. To provide more expressive explanations, we propose utilizing class expressions (CEs) from the field of description logic (DL). Our approach explains heterogeneous graphs with different types of nodes using CEs in the EL description logic. To identify the best explanation among multiple candidate explanations, we employ and compare two different scoring functions: (1) For a given CE, we construct multiple graphs, have the GNN make a prediction for each graph, and aggregate the predicted scores. (2) We score the CE in terms of fidelity, i.e., we compare the predictions of the GNN to the predictions by the CE on a separate validation set. Instead of subgraph-based explanations, we offer CE-based explanations.

In this paper, we introduce the problem of rewriting finite formal languages using syntactic macros such that the rewriting is minimal in size. We present polynomial-time algorithms to solve variants of this problem and show their correctness. To demonstrate the practical relevance of the proposed problems and the feasibility and effectiveness of our algorithms in practice, we apply these to biomedical ontologies authored in OWL. We find that such rewritings can significantly reduce the size of ontologies by capturing repeated expressions with macros. In addition to offering valuable assistance in enhancing ontology quality and comprehension, the presented approach introduces a systematic way of analysing and evaluating features of rewriting systems (including syntactic macros, templates, or other forms of rewriting rules) in terms of their influence on computational problems.

We aim at development white-box machine learning algorithms. We focus here on algorithms for learning axioms in description logic. We extend the Class Expression Learning for Ontology Engineering (CELOE) algorithm contained in the DL-Learner tool. The approach uses multiple search trees and a shared pool of refinements in order to split the search space in smaller subspaces. We introduce the conjunction operation of best class expressions from each tree, keeping the results which give the most information. The aim is to foster exploration from a diverse set of starting classes and to streamline the process of finding class expressions in ontologies. The current implementation and settings indicated that the Forest Mixing approach did not outperform the traditional CELOE. Despite these results, the conceptual proposal brought forward by this approach may stimulate future improvements in class expression finding in ontologies.

The increasing importance of resource-efficient production entails that manufacturing companies have to create a more dynamic production environment, with flexible manufacturing machines and processes. To fully utilize this potential of dynamic manufacturing through automatic production planning, formal skill descriptions of the machines are essential. However, generating those skill descriptions in a manual fashion is labor-intensive and requires extensive domain-knowledge. In this contribution an ontology-based semi-automatic skill description system that utilizes production logs and industrial ontologies through inductive logic programming is introduced and benefits and drawbacks of the proposed solution are evaluated.

Class expression learning is a branch of explainable supervised machine learning of increasing importance. Most existing approaches for class expression learning in description logics are search algorithms or hard-rule-based. In particular, approaches based on refinement operators suffer from scalability issues as they rely on heuristic functions to explore a large search space for each learning problem. We propose a new family of approaches, which we dub synthesis approaches. Instances of this family compute class expressions directly from the examples provided. Consequently, they are not subject to the runtime limitations of search-based approaches nor the lack of flexibility of hard-rule-based approaches. We study three instances of this novel family of approaches that use lightweight neural network architectures to synthesize class expressions from sets of positive examples. The results of their evaluation on four benchmark datasets suggest that they can effectively synthesize high-quality class expressions with respect to the input examples in under a second on average. Moreover, a comparison with the state-of-the-art approaches CELOE and ELTL suggests that we achieve significantly better F-measures on large ontologies. For reproducibility purposes, we provide our implementation as well as pre-trained models in the public GitHub repository at https://github.com/ConceptLengthLearner/NCES

Classifying nodes in knowledge graphs is an important task, e.g., predicting missing types of entities, predicting which molecules cause cancer, or predicting which drugs are promising treatment candidates. While black-box models often achieve high predictive performance, they are only post-hoc and locally explainable and do not allow the learned model to be easily enriched with domain knowledge. Towards this end, learning description logic concepts from positive and negative examples has been proposed. However, learning such concepts often takes a long time and state-of-the-art approaches provide limited support for literal data values, although they are crucial for many applications. In this paper, we propose EvoLearner - an evolutionary approach to learn ALCQ(D), which is the attributive language with complement (ALC) paired with qualified cardinality restrictions (Q) and data properties (D). We contribute a novel initialization method for the initial population: starting from positive examples (nodes in the knowledge graph), we perform biased random walks and translate them to description logic concepts. Moreover, we improve support for data properties by maximizing information gain when deciding where to split the data. We show that our approach significantly outperforms the state of the art on the benchmarking framework SML-Bench for structured machine learning. Our ablation study confirms that this is due to our novel initialization method and support for data properties.

Competency Questions (CQs) are used in many ontology engineering methodologies to collect requirements and track the completeness and correctness of an ontology being constructed. Although they are frequently suggested by ontology engineering methodologies, the publicly available datasets of CQs and their formalizations in ontology query languages are very scarce. Since first efforts to automate processes utilizing CQs are being made, it is of high importance to provide large and diverse datasets to fuel these solutions. In this paper, we present BigCQ, the biggest dataset of CQ templates with their formalizations into SPARQL-OWL query templates. BigCQ is created automatically from a dataset of frequently used axiom shapes. These pairs of CQ templates and query templates can be then materialized as actual CQs and SPARQL-OWL queries if filled with resource labels and IRIs from a given ontology. We describe the dataset in detail, provide a description of the process leading to the creation of the dataset and analyze how well the dataset covers real-world examples. We also publish the dataset as well as scripts transforming axiom shapes into pairs of CQ patterns and SPARQL-OWL templates, to make engineers able to adapt the process to their particular needs.

AlphaZero learns to play go, chess and shogi at a superhuman level through self play given only the rules of the game. This raises the question of whether a similar thing could be done for mathematics -- a MathZero. MathZero would require a formal foundation and an objective. We propose the foundation of set-theoretic dependent type theory and an objective defined in terms of the classification problem -- the problem of classifying concept instances up to isomorphism. The natural numbers arise as the solution to the classification problem for finite sets. Here we generalize classical Bourbaki set-theoretic isomorphism to set-theoretic dependent type theory. To our knowledge we give the first isomorphism inference rules for set-theoretic dependent type theory with propositional set-theoretic equality. The presentation is intended to be accessible to mathematicians with no prior exposure to type theory.