| P. Atzeni and D. S. Parker. Assumptions in Relational Database Theory. In Proc. of Conf. on PODS, pages 1--9, Los Angeles, CA, March 1982. |
....of the two paths can be uniquely represented by the single path from K1 to S in S2. This second constraint corresponds to the relationship uniqueness assumption (RUA) often asserted in relational theory, that a schema represents at most one relationship between any given set of attributes [AP82] Under this assumption, and the assumption that the keys of the object classes are identical, the map f is an information preserving mapping and S1 S2. Now consider the inverse mapping function g : I(S2) I(S1) defined on instances = 2 I(S2) ffl For all nodes X 6= K2 in S1, g( X] X] ....
P. Atzeni and D. S. Parker. Assumptions in Relational Database Theory. In Proc. of Conf. on PODS, pages 1--9, Los Angeles, CA, March 1982.
....t . R) t [ R (1) is the least (in v [ set that contains all these inferences. Note that T is the outer join of ( B (R) A) t and R and that R v T . 6 Universal Relations Without involving ourselves in a discussion of the usefulness or practicality of the Universal Relation Assumption [47, 48, 21, 6], we now investigate a general characterization of universal relations that shows how the general form of their implementation can be derived from their abstract properties. Behaviorally, a universal relation can be thought of as a simple query language, or transducer, in which the possible ....
P. Atzeni and D. S. Parker. Assumptions in relational database theory. In Proc. 1st ACM Symp on Principles of Database Systems, pages 1--9, 1982.
....comprehensible (easily understood and used by a database designer) and not based on unrealistic assumptions about the set of valid instances of a schema. These practical requirements also led us to design a model that is not subject to assumptions such as the relationship uniqueness assumption [AP82] that requires there be only one relationship expressed between any two sets. Additionally, to simplify our task, we include in the model only a minimum set of constructs and constraints necessary to model a large class of commonly occurring schemas. They also appear in some form in most common ....
....SIG. As noted above, a single relation in the relational model (or a set of relations to which the universal relation assumption is applied) can only model a single relationship between a given set of attributes. This property has been called the relationship uniqueness assumption or RUA [AP82]. Hence, the two functional dependencies expressed on the relational schema of Figure 4 are not independent. A pair of city state values (c1,s1) functionally determines a single zip code value z1. This zip code in turn functionally determines a single state value. This value, however, is ....
P. Atzeni and D. S. Parker. Assumptions in Relational Database Theory. In Proc. of the ACM Sym. on Principles of Database Systems, pages 1--9, Los Angeles, CA, March 1982.
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