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Set Operations in Object-Based Data Models
August 1992 (vol. 4 no. 4)
pp. 382-398

The semantics of set operations are not adequate for the richer data models of object-based database systems that include object-oriented and semantic data modeling concepts. The reason is that precise semantics of set operations on complex objects require a clear distinction between the dual notions of a set and a type, both of which are present in the class construct found in object-based data models. This gap is filled here by a framework for executing set theoretic operations on the class construct. The proposed set operations, including set difference, union, intersection and symmetric difference, determine both the type description of the derived class as well as its set membership. For the former, inheritance rules are developed for property characteristics such as single-valued versus multivalued and required versus optional. For the latter, the object identity concept is developed if borrowed from data modeling research. The framework allows for property inheritance among classes that are not necessarily IS-A related.

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Index Terms:
object-based data models; semantics; set operations; database systems; complex objects; set; type; set theoretic operations; set difference; union; intersection; symmetric difference; set membership; inheritance rules; property characteristics; single-valued; multivalued; property inheritance; object-oriented databases
E.A. Rundensteiner, L. Bic, "Set Operations in Object-Based Data Models," IEEE Transactions on Knowledge and Data Engineering, vol. 4, no. 4, pp. 382-398, Aug. 1992, doi:10.1109/69.149933
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