Connection Relations in Mereotopology

A model-theoretic framework forigating and comparing a variety of mereotopological theories with respect to the intended interpretation of their primitives and the composition of their intended do- mains is provided.

Abstract

. We provide a model-theoretic framework for investigating and comparing a variety of mereotopological theories with respect to (i) the intended interpretation of their connection primitives, and (ii) the composition of their intended domains (e.g., whether or not they allow for boundary elements). 1. INTRODUCTION In recent years there has been an outgrowth of theories for representing space and time in a qualitative way based on a primitive notion of topological connection [32]. Most of these theories have been influenced by the work of Clarke [10, 11], which in turn was inspired by Whitehead [35]. However, various other theories have been developed on independent grounds [29], and it is interesting to see how topology has itself become a point of connection among previously unrelated research areas. Unfortunately, this variety of outlooks corresponds to a variety of theories that are not always in agreement on the basic terms. In some cases there is genuine philosophical dissension...