Database Abstractions: Aggregation and Generalization

Database Abstractions: Aggregation and Generalization

June 1977 | JOHN MILES SMITH and DIANE C.P. SMITH
This paper introduces two fundamental abstractions in database design: aggregation and generalization. Aggregation transforms relationships between objects into higher-level objects, while generalization transforms a class of objects into a generic object. The authors propose a new data type called "generic" to uniformly represent all objects (individual, aggregate, generic) in models of the real world. Models are structured as sets of aggregation and generalization hierarchies, with abstract objects at their intersections. This structure provides a disciplined approach to organizing relational databases, enabling the integration and maintenance of views, stability under evolutionary changes, easier understanding of complex models, systematic design, and more optimization at lower levels. The paper discusses the formalization of the generic data type through invariant properties that must be satisfied by all relations in a database to preserve abstractions. A triggering mechanism is proposed to automatically maintain these invariants during update operations. The authors also present a mapping of aggregation/generalization hierarchies onto owner-coupled set structures. The paper emphasizes the importance of both aggregation and generalization in database design, noting that while aggregation has been the focus of much database research, generalization has been largely ignored. The authors argue that combining aggregation and generalization into a single structuring discipline can benefit both database and artificial intelligence research. The paper develops a philosophy for representing generalization abstractions in Codd's relational schema, leading to a powerful generic structure for defining relational models. This structure is described in detail, including how it can be used to handle various modeling situations. The paper also examines five invariant properties of relational models that must remain unchanged during update operations, forming a partial axiomatic definition of the generic structure. Rules for maintaining these invariants are developed based on semantic considerations. The paper concludes with a discussion of the implications of the generic structure for database design methods, implementation techniques, and access languages. The authors argue that the generic structure provides a more systematic and efficient approach to database design and implementation.This paper introduces two fundamental abstractions in database design: aggregation and generalization. Aggregation transforms relationships between objects into higher-level objects, while generalization transforms a class of objects into a generic object. The authors propose a new data type called "generic" to uniformly represent all objects (individual, aggregate, generic) in models of the real world. Models are structured as sets of aggregation and generalization hierarchies, with abstract objects at their intersections. This structure provides a disciplined approach to organizing relational databases, enabling the integration and maintenance of views, stability under evolutionary changes, easier understanding of complex models, systematic design, and more optimization at lower levels. The paper discusses the formalization of the generic data type through invariant properties that must be satisfied by all relations in a database to preserve abstractions. A triggering mechanism is proposed to automatically maintain these invariants during update operations. The authors also present a mapping of aggregation/generalization hierarchies onto owner-coupled set structures. The paper emphasizes the importance of both aggregation and generalization in database design, noting that while aggregation has been the focus of much database research, generalization has been largely ignored. The authors argue that combining aggregation and generalization into a single structuring discipline can benefit both database and artificial intelligence research. The paper develops a philosophy for representing generalization abstractions in Codd's relational schema, leading to a powerful generic structure for defining relational models. This structure is described in detail, including how it can be used to handle various modeling situations. The paper also examines five invariant properties of relational models that must remain unchanged during update operations, forming a partial axiomatic definition of the generic structure. Rules for maintaining these invariants are developed based on semantic considerations. The paper concludes with a discussion of the implications of the generic structure for database design methods, implementation techniques, and access languages. The authors argue that the generic structure provides a more systematic and efficient approach to database design and implementation.
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