The exploration of a category theory-based virtual geometrical product specification system for design and manufacturing

ions such as inheritance are more naturally represented by graphs than as sets (Levene and Poulovassilis, 1991 [33]; Poulovassilis and Levene, 1994 [34]). (4) Data modellings in object-relational DBMSs still have weaknesses in semantic supports. For example, because the functional data model is the “lowest common denominator” of data models (refer to Section 2.2.3.1), there is lack of semantic foundations for knowledge-based applications. Compared to E-R model, the functional data model cannot clearly represent the stratification of entities, attributes, and relationships. 2.2.4 Object-oriented DBMS To solve the problems presented by the aforementioned object-relational DBMSs, especially for these scientific and engineering applications, the next generation of database paradigm —object-oriented DBMSs are emerging. Several standards were proposed to develop object-oriented DBMSs, which include three manifestos, and standards from Object Data Management Group (ODMG93, ODMG2.0, ODMG3.0) as well as Object Management Group (OMG). 2.2.4.1 Object-oriented DBMS Standards There are three manifestos for specifying the object-oriented DBMSs. The first manifesto provided 13 features that an object-oriented DBMS must include, should include and may include (Atkinson, 1990 [35]). However, there are no details and largely ignored the important part of object-oriented DBMSs − the data model. So it is just a vision not a formal standard (Committee for Advanced DBMS Function, 1990 [36]). The second manifesto detailed the first manifesto and proposed three tenets for