The Problem of Transitivity of Part-Whole Relations in Conceptual Modeling Revisited

Abstract. Parthood is a relation of fundamental importance in a number of dis-ciplines including cognitive science, linguistics and conceptual modeling. How-ever, one classical problem for conceptual modeling theories of parthood is de-ciding on the transitivity of these relations. This issue is of great importance since transitivity plays a fundamental role both conceptually (e.g., to afford in-ferences in problem-solving) and computationally (e.g., to afford propagations of properties and events in a transitive chain). In this article we address this problem by presenting a solution to the case of part-whole relations between functional complexes, which are the most common types of entities represented in conceptual models. This solution comes in two parts. Firstly, we present a formal theory founded on results from formal ontology and linguistics. Second-ly, we use this theory to provide a number of visual patterns that can be used to isolate scopes of transitivity in part-whole relations represented in diagrams.