I am what I have and I have what I am, what am I?: Homeomerosity in formal concept analysis

Abstract

The term homeomerosity refers to when a whole and its parts are the same kind of thing. For instance, a computer and its processor can both be classified as machines. Homeomerosity is a prerequisite for meaningful addition and subtraction. For example, adding the area sizes of two independent regions gives another area size, but adding an area size and a number of hours yields a number with a peculiar unit. In earlier work, homeomerosity has been formalized with respect to mereological parthood, but not in concurrence with a notion of class subsumption. Both are essential to homeomerosity, as a part can only be observed to be of the same kind as the whole if they are observed to be of some kinds in the first place. In this work, we use formal concept analysis to organize conceptual representations of parts and wholes in a shared contextual model. In our doing so, we show wholes and parts can be represented by sub-concepts of a concept with respect to which they are homeomerous.