Congratulations to Azadeh Izadi for passing her PhD without emendations.
Azadeh’s thesis was on Modelling of Topological Relations in Multidimensional Space.
My research examines spatial knowledge representation and reasoning with applications in multi-dimensional Geographic Information System (GIS). The development and widespread application of GIS have increased demand for a more accurate analysis and querying method considering multi-dimensional (0D, 1D, 2D and 3D) geographic data as an input. Several studies have investigated the multi-dimensional environment, however, none have proposed a solution that is based on mereotopology, which describes the space by using “part of” and “connection” relations. We are trying to develop a framework that can describe spatial objects with various dimensions based on mereotopology. This framework will improve the expressive power and accuracy of 3D queries in GIS.
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 commonsense of space. Among the various types of qualitative representation of spatial objects, describing their comparative properties, 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. How- ever, sometimes spatial entities of different dimensions must be considered (e.g., in map reading) in order to gain a proper understanding. The inability of the current theories to interact with entities of different dimensions has formed 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 (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. Furthermore, we verified the cognitive adequacy of the proposed set of relations using human subjects experiments, applying clustering and thematic analyses to the empirical data.
In addition, we demonstrate our multidimensional theory by applying it to a real-world scenario (i.e., a flood event). The results showed an improvement in the query answering procedure relative to current methods implemented in spatial information systems such as the Geographic Information Systems (GIS).