A Categorical Approach to Semantic Interoperability across Building Lifecycle

2026-01-23

AI Summary

This study addresses the challenges of integrating heterogeneous data across the building lifecycle—such as complex mapping and poor scalability—by introducing category theory into building information modeling for the first time. The authors formalize ontologies using first-order logic and achieve cross-ontology integration through structure-preserving categorical transformations. Leveraging the Categorical Query Language (CQL), the proposed approach enables automated mapping generation, bidirectional data migration, and cross-ontology querying, reducing time complexity to O(n). Experimental results demonstrate successful automatic integration among three major building ontologies—IFC, BRICK, and RealEstateCore—thereby validating the method’s effectiveness and scalability in enabling interoperability for building data.

Technology Category

• Knowledge Representation and Reasoning: Ontologies
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Buildings generate heterogeneous data across their lifecycle, yet integrating these data remains a critical unsolved challenge. Despite three decades of standardization efforts, over 40 metadata schemas now span the building lifecycle, with fragmentation accelerating rather than resolving. Current approaches rely on point-to-point mappings that scale quadratically with the number of schemas, or universal ontologies that become unwieldy monoliths. The fundamental gap is the absence of mathematical foundations for structure-preserving transformations across heterogeneous building data. Here we show that category theory provides these foundations, enabling systematic data integration with $O(n)$ specification complexity for $n$ ontologies. We formalize building ontologies as first-order theories and demonstrate two proof-of-concept implementations in Categorical Query Language (CQL): 1) generating BRICK models from IFC design data at commissioning, and 2) three-way integration of IFC, BRICK, and RealEstateCore where only two explicit mappings yield the third automatically through categorical composition. Our correct-by-construction approach treats property sets as first-class schema entities and provides automated bidirectional migrations, and enables cross-ontology queries. These results establish feasibility of categorical methods for building data integration and suggest a path toward an app ecosystem for buildings, where mathematical foundations enable reliable component integration analogous to smartphone platforms.

Problem

• semantic interoperability
• building lifecycle
• heterogeneous data integration
• ontology alignment
• metadata schemas

Innovation

• category theory
• semantic interoperability
• building data integration
• ontology composition
• Categorical Query Language