Consequences of assuming a universal relation
ACM Transactions on Database Systems (TODS)
On interpretations of relational languages and solutions to the implied constraint problem
ACM Transactions on Database Systems (TODS)
The theory of joins in relational databases
ACM Transactions on Database Systems (TODS)
Testing implications of data dependencies
ACM Transactions on Database Systems (TODS)
Database abstractions: aggregation and generalization
ACM Transactions on Database Systems (TODS)
Independent components of relations
ACM Transactions on Database Systems (TODS)
Equality and Domain Closure in First-Order Databases
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A Complete Axiomatization of Full Join Dependencies
Journal of the ACM (JACM)
Horn clauses and database dependencies
Journal of the ACM (JACM)
On the family of generalized dependency constraints
Journal of the ACM (JACM)
Database relations with null values
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
Inclusion dependencies and their interaction with functional dependencies
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
Properties and update semantics of consistent views
ACM Transactions on Database Systems (TODS)
Unique complements and decompositions of database schemata
Journal of Computer and System Sciences
Decomposition of relational schemata into components defined by both projection and restriction
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Canonical view update support through boolean algebras of components
PODS '84 Proceedings of the 3rd ACM SIGACT-SIGMOD symposium on Principles of database systems
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An algebraic framework for investigating the problem of decomposing a relational database schema into components is developed. It is argued that the views of a relational schema which are to be the components of a decomposition should form a finite atomic Boolean algebra. The unit of the algebra is the identity view, and the zero is the null view. The join operation in this algebra is to be a generalization of the usual concept of join; the resulting view should contain precisely the representation contained in the two component views as a unit. The meet operation in this algebra is to measure the interdependence of the components, and is to be zero if and only if they are independent. A decomposition of the schema is then to be a decomposition of the identity component, with the ultimate decomposition the one consisting entirely of atoms.The thrust of the results is in two directions. First, the general properties of relational schemata particular to this problem are developed, within the framework of first-order logic. The key formulations are those of abstract meet and join of schemata. Using these formulations, it is shown that a completely general decomposition theory is impossible. The second part of the work islolates a relatively large class of schemata which do admit reasonable decompositions. These schemata include all of the usual decomposition problems, including project-join decompositions and horizontal decompositions of schemata constrained by universal Horn sentences.