Representing part–whole relations in conceptual spaces

In this paper, we propose a cognitive semantic approach to represent part–whole relations. We base our proposal on the theory of conceptual spaces, focusing on prototypical structures in part–whole relations. Prototypical structures are not accounted for in traditional mereological formalisms. In our account, parts and wholes are represented in distinct conceptual spaces; parts are joined to form wholes in a structure space. The structure space allows systematic similarity judgments between wholes, taking into consideration shared parts and their configurations. A point in the structure space denotes a particular part structure; regions in the space represent different general types of part structures. We argue that the structural space can represent prototype effects: structural types are formed around typical arrangements of parts. We also show how structure space captures the variations in part structure of a given concept across different domains. In addition, we discuss how some taxonomies of part–whole relations can be understood within our framework.