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
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Date
2021
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Massey University
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Abstract
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).
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Keywords
Topological spaces, Set theory, Spatial ability, Analysis