A CATEGORY-THEORY APPROACH FOR CONSTRUCTION ONTOLOGIES IN SUBSURFACE MASS TRANSIT

Abstract. The construction and expansion of subway systems represents an important step towards better livability conditions in a rapidly urbanizing world. However, underground construction has not benefited from well-established ontologies of semantic and geometric representation, such as Building Information Modelling (which is used for standalone structures) and City Geography Markup Language (which is designed for continuous urban elements). To bridge that gap, this paper proposes a novel and highly flexible means to underpin a relevant ontology. The approach uses the ontology log, or olog, a model of knowledge representation based on Category Theory. In an olog, dependencies between objects are restricted to functional relationships (for every object there is a unique correspondence). This robust mathematical formulation allows for a more flexible, yet also informative and user-readable model of the studied entities. In this paper, the olog’s usability is demonstrated through the ontological representation of common items in the fare-control areas of two New York City metro stations. Ologs are shown to capture similar underlying structures both across different stations and within the same station. Importantly, the olog allows for further generalization to incorporate pre-existing data, as well as being a transferable framework for conceptualizations of other metro systems.