A formal analysis of Identity and Sortality in the Unified Foundational Ontology (UFO)

Abstract

The Unified Foundational Ontology (UFO) is a conceptual framework grounded on principles derived from Ontology discipline of Philosophy, with applications in the field of Software Engineering, specially in Conceptual Modeling, as the semantic reference for the OntoUML modeling language. Among the concepts described in the UFO fragment of endurants (UFO-A), the concept of sortality plays a central role in the classification of UFO substantial universals. However, this concept, and the related concepts of identity and individuality currently lack a systematic formal characterization, hindering their application in the analysis of substantial universals. This research enriches the Unified Foundational Ontology (UFO) literature with a formal specification for a fragment of UFO-A that allows the characterization of these concepts. This specification is presented in Isabelle/HOL, a logical formalism that allows a machine-assisted verification. We construct a formal framework, based on this specification and on categoric-theoretic concepts through which we propose formal definitions for the concepts of individuality and identity, and, from these definitions, we propose a formal characterization of the concept of sortality. Illustrations and the application of the proposed definitions on the domain of conceptual modeling are also presented.