The presented thesis documents the investigation and development of the mathematical\ud foundations for a novel knowledge-based system for surface texture (VitualSurf\ud system). This is the first time that this type of novel knowledge-based system has been\ud tried on surface texture knowledge. It is important to realize that surface texture\ud knowledge, based on new generation Geometrical Product Specification (GPS) system,\ud are considered to be too theoretical, abstract, complex and over-elaborate. Also it is not\ud easy for industry to understand and implement them efficiently in a short time.\ud \ud \ud The VirtualSurf has been developed to link surface function, specification through\ud manufacture and verification, and provide a universal platform for engineers in\ud industry, making it easier for them to understand and use the latest surface texture\ud knowledge. The intelligent knowledge-base should be capable of incorporating\ud knowledge from multiple sources (standards, books, experts, etc), adding new\ud knowledge from these sources and still remain a coherent reliable system. In this\ud research, an object-relationship data model is developed to represent surface texture\ud knowledge. The object-relationship data model generalises the relational and object\ud orientated data models. It has both the flexibility of structures for entities and also good\ud mathematical foundations, based on category theory, that ensures the knowledge-base\ud remains a coherent and reliable system as new knowledge is added.\ud \ud \ud This prototype system leaves much potential for further work. Based on the framework\ud and data models developed in this thesis, the system will be developed into\ud implemental software, either acting as a good training tool for new and less\ud experienced engineers or further connecting with other analysis software, CAD\ud software (design), surface instrument software (measurement) etc, and finally applied\ud in production industries
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