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

Parthood is a relation of fundamental importance in a number of disciplines including cognitive science, linguistics and conceptual modeling. However, one classical problem for conceptual modeling theories of parthood is deciding on the transitivity of these relations. This issue is of great importance since transitivity plays a fundamental role both conceptually (e.g., to afford inferences 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. Secondly, 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.