Making Mathematical Knowledge Explainable, Accessible and Interoperable Through Large Language Model Integration (arxiv.org)
arXiv:2607.24512v1 Announce Type: new
Abstract: Mathematical models are central to formalizing research problems, yet their documentation often falls short of FAIR principles. Knowledge bases such as the Mathematical Model Database (MathModDB) address this gap by providing curated, semantically rich representations of mathematical models. Built on Wikibase, the same open-source infrastructure underlying Wikidata, MathModDB utilizes Semantic Web technologies to support Linked Open Data, collaborative editing, and the storage of semantically enriched metadata, making it a domain-specific knowledge graph within the broader Wikidata ecosystem. However, access to MathModDB currently requires either navigating a complex web interface or proficiency in SPARQL and Wikibase APIs, posing significant barriers for potential users. In addition, the combination of such curated knowledge bases with actual research data stored, e.g., in Dataverse repository instances, remains a challenge. To overcome these limitations, we propose integrating Large Language Models (LLMs) with MathModDB via a Model Context Protocol (MCP) server that exposes a vector-indexed schema retrieval and Steiner-tree-based join planner, combining dialogue-based natural language interaction with curated, epistemically grounded knowledge. Although instantiated on MathModDB, the architecture can be applied to other Wikibase-based systems. We demonstrate that this approach enables epistemically grounded LLM usage, improves model explainability and accessibility beyond what the standard Wikibase interface offers, and simplifies interoperability with external databases and tools, such as Dataverse data repositories. We illustrate the benefits of combining the accessibility of an LLM with the epistemic safety of a curated knowledge base through the adaptability of the MCP protocol by two use cases involving mathematical models in the fields of continuum mechanics and enzyme kinetics.
Abstract: Mathematical models are central to formalizing research problems, yet their documentation often falls short of FAIR principles. Knowledge bases such as the Mathematical Model Database (MathModDB) address this gap by providing curated, semantically rich representations of mathematical models. Built on Wikibase, the same open-source infrastructure underlying Wikidata, MathModDB utilizes Semantic Web technologies to support Linked Open Data, collaborative editing, and the storage of semantically enriched metadata, making it a domain-specific knowledge graph within the broader Wikidata ecosystem. However, access to MathModDB currently requires either navigating a complex web interface or proficiency in SPARQL and Wikibase APIs, posing significant barriers for potential users. In addition, the combination of such curated knowledge bases with actual research data stored, e.g., in Dataverse repository instances, remains a challenge. To overcome these limitations, we propose integrating Large Language Models (LLMs) with MathModDB via a Model Context Protocol (MCP) server that exposes a vector-indexed schema retrieval and Steiner-tree-based join planner, combining dialogue-based natural language interaction with curated, epistemically grounded knowledge. Although instantiated on MathModDB, the architecture can be applied to other Wikibase-based systems. We demonstrate that this approach enables epistemically grounded LLM usage, improves model explainability and accessibility beyond what the standard Wikibase interface offers, and simplifies interoperability with external databases and tools, such as Dataverse data repositories. We illustrate the benefits of combining the accessibility of an LLM with the epistemic safety of a curated knowledge base through the adaptability of the MCP protocol by two use cases involving mathematical models in the fields of continuum mechanics and enzyme kinetics.
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