Testing implications of data dependencies
ACM Transactions on Database Systems (TODS)
Multivalued dependencies and a new normal form for relational databases
ACM Transactions on Database Systems (TODS)
Decompositions and functional dependencies in relations
ACM Transactions on Database Systems (TODS)
An Equivalence Between Relational Database Dependencies and a Fragment of Propositional Logic
Journal of the ACM (JACM)
First order logic formalization for functional, multivalued and mutual dependencies
SIGMOD '78 Proceedings of the 1978 ACM SIGMOD international conference on management of data
A complete axiomatization for a large class of dependencies in relational datatbases
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Safety and correct translation of relational calculus formulas
PODS '87 Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Towards an efficient evaluation of general queries: quantifier and disjunction processing revisited
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Logic programming as constructivism: a formalization and its application to databases
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Reactive consistency control in deductive databases
ACM Transactions on Database Systems (TODS)
Abstraction in query processing
Journal of the ACM (JACM)
Syntactical characterization of a subset of domain-independent formulas
Journal of the ACM (JACM)
A normal form for relational databases that is based on domains and keys
ACM Transactions on Database Systems (TODS)
Subset Dependencies and a Completeness Result for a Subclass of Embedded Multivalued Dependencies
Journal of the ACM (JACM)
Horn clauses and database dependencies
Journal of the ACM (JACM)
Degrees of acyclicity for hypergraphs and relational database schemes
Journal of the ACM (JACM)
On the Structure of Armstrong Relations for Functional Dependencies
Journal of the ACM (JACM)
Logic and Databases: A Deductive Approach
ACM Computing Surveys (CSUR)
Relational database: a practical foundation for productivity
Communications of the ACM
Inferences involving embedded multivalued dependencies and transitive dependencies
SIGMOD '80 Proceedings of the 1980 ACM SIGMOD international conference on Management of data
Applying approximate order dependency to reduce indexing space
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
PODS '84 Proceedings of the 3rd ACM SIGACT-SIGMOD symposium on Principles of database systems
Inference rules for functional and inclusion dependencies
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
Inverting relational expressions: a uniform and natural technique for various database problems
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
Dynamic constraints and database evolution
PODS '83 Proceedings of the 2nd 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
Notions of dependency satisfaction
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
A theory of data dependencies over relational expressions
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
The inference problem for template dependencies
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
The implication and finite implication problems for typed template dependencies
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
Embedded implicational dependencies and their inference problem
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
A complete axiomatization for a large class of dependencies in relational datatbases
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Unary inclusion dependencies have polynomial time inference problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
TARK '88 Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge
Relational database: a practical foundation for productivity
ACM Turing award lectures
Impacts of logic and databases (invited paper)
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
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In the last year or so, a number of generalizations of these dependencies have appeared: Nicolas's mutual dependencies [Ni], which say that a relation is the join of three of its projections; Rissanen's and Aho, Beeri, and Ullman's join dependencies ([Ri], [ABU]), which generalize further to an arbitrary number of projections; Paradaens' transitive dependencies [Pa], which generalize both FDs and MVDs; Sagiv and Walecka's subset dependencies [SW] which generalize embedded MVDs; and Sadri and Ullman's template dependencies [SU], which generalize embedded join dependencies. The purpose of this paper is to help bring order to the chaos by presenting certain mathematical properties shared by all of these dependencies. In Section 2, we introduce the concept of “faithfulness” (with respect to direct product), and show that IDs and EIDs are faithful, whereas slight variations are not necessarily faithful. In Section 3, we discuss “Armstrong relations”, which were known to exist in certain special cases (such as when the only sentences of interest were functional, multivalued, and join dependencies).In Section 4, we discuss finite Armstrong relations.In Section 5, we present some more counterexamples about the existence of Armstrong relations. In Section 6, we discuss projections of classes of relations. Although Zaiddan [Za] showed that projections of FD classes are not necessarily FD classes, it turns out that projections of FD classes (and, even more, of ID classes) are ID classes. In Section 7, we discuss certain extensions of our results.