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    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
    (Massey University, 2021) Izadi, Azadeh
    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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    The relationship between spatial ability and mathematical ability : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Psychology at Massey University
    (Massey University, 1996) Flynn, Peter M
    The purpose of this study was to examine the relationship between spatial ability and general mathematical ability. Many researchers have assumed that a positive correlational relationship exists between mathematics and spatial ability. However, a review of the literature shows that the relationship is not as simple as thought, partly because there is disagreement among researchers on a definition of spatial ability. In the present study general mathematical ability was indexed by the Progressive Achievement Test: Mathematics. A group of 50 high ability and a group of 50 low ability children completed five tests relating to spatial ability from the Kit of factor Related Cognitive Tests. Results from a discriminant function analysis supported the hypothesis that a positive correlational relationship exists between spatial ability and general mathematical ability. This result is important because it provides new evidence to support the argument that there is a relationship between spatial ability and general mathematical ability. The potential for spatial ability tasks to aid in the understanding of mathematics is discussed. However, it is argued that there is a need for greater refinement of the spatial ability construct before more research using it as a factor is conducted.