MMLKG: Knowledge Graph for Mathematical Definitions, Statements and Proofs

Abstract

Nowadays, Knowledge Graphs (KGs) are important and developing in different areas. However, there is a lack of genuinely interoperable datasets representing mathematics that allow for information exchange between datasets in the Web ecosystem. In this paper, we address this matter based on the Mizar Mathematical Library (MML), a collection of articles written in the Mizar language. MML includes definitions and theorems with proofs to which authors can easily refer from newly written Mizar articles. However, extracting information directly from Mizar scripts by external projects is not very straightforward. Therefore, we propose a new data storage and retrieval approach based on the Knowledge Organization System (KOS) model and the KG concept that provides a way to organize and access knowledge. We present Mizar Mathematical Library Knowledge Graph (MMLKG), a thesaurus for describing mathematical objects. MMLKG supports semantic interoperability and allows linking data from different sources, e.g., Wikidata. Moreover, it satisfies the FAIR data principles. The data is publicly available via a Cypher endpoint.