Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Integrated modelling for 3D GIS

A three dimensional (3D) model facilitates the study of the real world objects it represents. A geoinformation system (GIS) should exploit the 3D model in a digital form as a basis for answering questions pertaining to aspects of the real world. With respect to the earth sciences, different kinds of objects of reality can be realized. These objects are components of the reality under study. At the present state-of-the-art different realizations are usually situated in separate systems or subsystems. This separation results in redundancy and uncertainty when different components sharing some common aspects are combined. Relationships between different kinds of objects, or between components of an object, cannot be represented adequately. This thesis aims at the integration of those components sharing some common aspects in one 3D model. This integration brings related components together, minimizes redundancy and uncertainty. Since the model should permit not only the representation of known aspects of reality, but also the derivation of information from the existing representation, the design of the model is constrained so as to afford these capabilities. The tessellation of space by the network of simplest geometry, the simplicial network, is proposed as a solution. The known aspects of the reality can be embedded in the simplicial network without degrading their quality. The model provides finite spatial units useful for the representation of objects. Relationships between objects can also be expressed through components of these spatial units which at the same time facilitate various computations and the derivation of information implicitly available in the model. Since the simplicial network is based on concepts in geoinformation science and in mathematics, its design can be generalized for n-dimensions. The networks of different dimension are said to be compatible, which enables the incorporation of a simplicial network of a lower dimension into another simplicial network of a higher dimension.The complexity of the 3D model fulfilling the requirements listed calls for a suitable construction method. The thesis presents a simple way to construct the model. The raster technique is used for the formation of the simplicial network embedding the representation of the known aspects of reality as constraints. The prototype implementation in a software package, ISNAP, demonstrates the simplicial network's construction and use. The simplicial network can facilitate spatial and non spatial queries, computations, and 2D and 3D visualizations. The experimental tests using different kinds of data sets show that the simplicial network can be used to represent real world objects in different dimensionalities. Operations traditionally requiring different systems and spatial models can be carried out in one system using one model as a basis. This possibility makes the GIS more powerful and easy to use