The Distributed Ontology Language (DOL): Ontology Integration and Interoperability Applied to Mathematical Formalization

TL;DR

The paper presents the Distributed Ontology Language (DOL), a standardized framework for integrating and interoperating heterogeneous ontologies, demonstrated through its application in formalizing mathematical concepts and validating their relationships.

Contribution

It introduces DOL's application in mathematical formalization, showcasing its ability to validate relationships between ontological formalizations in COLORE.

Findings

Successful validation of relationships between mathematical ontologies

Demonstration of DOL's utility in formalizing real-world concepts

Enhanced interoperability of heterogeneous ontologies

Abstract

The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper focuses on an application of DOL's meta-theoretical features in mathematical formalization: validating relationships between ontological formalizations of mathematical concepts in COLORE (Common Logic Repository), which provide the foundation for formalizing real-world notions such as spatial and temporal relations.