We present the zbMATH Open Knowledge Graph, a large-scale RDF knowledge graph (KG) covering more than 250 years of mathematical scholarship. Unlike existing scholarly knowledge graphs that primarily capture bibliographic metadata and citation structures, the zbMATH Open KG integrates expert-curated semantic content, including reviews, keywords, subject classifications, software references, and disambiguated authorship. This combination of domain-specific representation of mathematical knowledge and extensive temporal coverage supports analyses that require fine-grained exploration of mathematical concepts, research fields, and scholarly relationships over time. The resulting graph comprises 34 million entities and 168 million RDF triples represented using established Semantic Web vocabularies, supporting interoperability and FAIR data principles. We further demonstrate its capabilities through query-driven historically grounded scholarly exploration use cases, illustrating how the knowledge graph can surface relationships and patterns that may be difficult to identify from bibliographic and citation information alone. The zbMATH Open KG provides an open semantic infrastructure for studying the development of mathematical knowledge and tracing scholarly connections across centuries of scholarship.
Applying machine learning to web pages is challenging due to the need to interpret HTML together with associated resources and perform rendering to obtain a meaningful visual and layout-aware representation. As a result, machine learning over web content remains comparatively underexplored. In this paper, we present a platform for visual-aware representation and machine learning over web pages based on the open-source rendering tool FitLayout. The platform provides a server capable of rendering web pages, explicitly capturing their visual and structural properties in an RDF-based representation, and persisting the rendered documents in an integrated storage. The processing pipeline is controlled via a REST API, while SPARQL queries are used to retrieve structured data suitable as input for machine learning algorithms. By explicitly modeling rendered web pages, including fine-grained layout details, the platform enables dataset sharing and supports the reproducibility of experimental results. The architecture supports the complete dataset preparation workflow, from web page collection and rendering through preprocessing and annotation of content elements to downstream learning tasks. We further provide a Python client library that integrates the platform with standard machine learning workflows. As a demonstration, we show how rendered web pages can be transformed into graph-based representations and used to train graph neural networks for recognizing key content elements, illustrating both the applicability of the approach and the reproducibility of the results.
Yuyang Li, Lukas Kubelka, Julia Butte +1cs.AI cs.FL cs.LO
Knowledge graphs modeled in RDF are powerful for describing static knowledge, but they cannot capture or reason about the dynamic behavior of physical systems, e.g., systems described by differential equations, which is a critical gap for AI-driven cyber-physical systems. To solve this, we propose RDFdL, a framework that integrates RDF with Differential Dynamic Logic (dL) to represent and reason about both static knowledge and the continuous dynamics of physical systems. For the dynamic part, we syntactically represent differential equations and ranges in the state space in RDF and SHACL and provide semantics using a translation to dL. Linking RDF and dL through their shared foundation in first-order logic achieves a unique integration: verification results for safety and reachability properties in the dynamic logic domain become available as entailment to SPARQL queries over RDF data. We implement the pipeline using Apache Jena for ontology-driven RDF reasoning and KeYmaera X, the theorem prover for dL, and sketch its applicability in manufacturing.