A formal theory of conceptual modeling universals

Conceptual Modeling is a discipline of great relevance to several areas in Computer Science. In a series of papers [1,2,3] we have been using the General Ontological Language (GOL) and its underlying upper level ontology, proposed in [4,5], to evaluate the ontological correctness of conceptual models and to develop guidelines for how the constructs of a modeling language (UML) should be used in conceptual modeling. In this paper, we focus on the modeling metaconcepts of classifiers and objects from an ontological point of view. We use a philosophically and psychologically well-founded theory of universals to propose a UML profile for Ontology Representation and Conceptual Modeling. The formal semantics of the proposed modeling elements is presented in a language of modal logics with quantification restricted to Sortal universals.