Modelling of mereotopological relationships in multidimensional space : a thesis submitted for the degree of Doctor of Philosophy, School of Natural and Computational Sciences, Massey University

Thumbnail Image
Open Access Location
Journal Title
Journal ISSN
Volume Title
Massey University
The Author
Inferences based on spatial knowledge play an important role in human lives. Humans are easily able to deal with spatial knowledge without any need to refer to numerical computation. The field of Qualitative Spatial Representation and Reasoning (QSRR) aims to model human common sense of space. Among the various types of qualitative relationship between spatial objects, connectivity (or topology) and parthood (or mereology) serve as the most basic underlying aspects. Most current mereotopological theories are restricted to objects with the same dimension. However, sometimes spatial entities of different dimensions must be considered for many practical applications (e.g. map reading, spatial analysis). The inability of current theories to interact with entities of different dimensions has motivated the foundation of multidimensional spatial theories. However, these theories are less efficient in terms of reasoning power. Moreover, their set of introduced mereotopological relations has not been cognitively validated. This research presents a multidimensional mereotopological theory using part of and boundary part as primitive concepts. We introduce a set of nine spatial relations with the jointly exhaustive and pairwise disjoint property based on these primitives. This property allows us to develop an efficient reasoning strategy (i.e. constraint-based reasoning) which makes our approach more practical than previous works. We used automated theorem provers and finite model finders to aid the formal verification of the theory, proving its properties and generating the composition table for reasoning purposes. This work is the first multidimensional mereotopological theory that not only has properties that are verified by traditional logical deduction techniques (like the other multidimensional mereotopological theories), but that also it supports an efficient reasoning strategy that was not being available before. Furthermore, we verified the cognitive adequacy of our proposed set of relations using human subjects experiments, applying clustering and thematic analyses to empirical data. Our study is the first to pro- vide evidence for the cognitive plausibility of a multidimensional mereotopological theory (going beyond previous studies that have only shown cognitive adequacy for equidimensional mereotopological theories) supporting its closeness to human cognition. In addition, we demonstrate our multidimensional theory by applying it to a real-world scenario (i.e. a flood event).
Topological spaces, Set theory, Spatial ability, Analysis