Synthesizing third normal form relations from functional dependencies
ACM Transactions on Database Systems (TODS)
Multivalued dependencies and a new normal form for relational databases
ACM Transactions on Database Systems (TODS)
Independent components of relations
ACM Transactions on Database Systems (TODS)
Unit Refutations and Horn Sets
Journal of the ACM (JACM)
A complete axiomatization for functional and multivalued dependencies in database relations
SIGMOD '77 Proceedings of the 1977 ACM SIGMOD international conference on Management of data
The decomposition versus synthetic approach to relational database design
VLDB '77 Proceedings of the third international conference on Very large data bases - Volume 3
SLFD Logic: Elimination of Data Redundancy in Knowledge Representation
IBERAMIA 2002 Proceedings of the 8th Ibero-American Conference on AI: Advances in Artificial Intelligence
Artificial Intelligence
A Complete Logic for Fuzzy Functional Dependencies over Domains with Similarity Relations
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Spoilt for Choice: Full First-Order Hierarchical Decompositions
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Comment on "decomposition of a data base and the theory of boolean switching fynctions"
IBM Journal of Research and Development
An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
An Equivalence between Dependencies in Nested Databases and a Fragment of Propositional Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Fundamental study: The multiple facets of the canonical direct unit implicational basis
Theoretical Computer Science
When data dependencies over SQL tables meet the logics of paradox and S-3
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Armstrong axioms and Boyce-Codd-Heath Normal Form under bag semantics
Information Processing Letters
Solving the implication problem for XML functional dependencies with properties
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Normalization of relations and ontologies
AIKED'11 Proceedings of the 10th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases
Codd table representations under weak possible world semantics
DEXA'11 Proceedings of the 22nd international conference on Database and expert systems applications - Volume Part I
Characterisations of multivalued dependency implication over undetermined universes
Journal of Computer and System Sciences
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
ACM Transactions on Database Systems (TODS)
On Inferences of Full First-Order Hierarchical Decompositions
Fundamenta Informaticae - Logic, Language, Information and Computation
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An equivalence is shown between functional dependency statements of a relational database, where "→" has the meaning of "determines," and implicational statements of propositional logic, where"⇒" has the meaning of "implies." Specifically, it is shown that a dependency statement is a consequence of a set of dependency statements if the corresponding implicational statement is a consequence of the corresponding set of implicational statements. The database designer can take advantage of this equivalence to reduce problems of interest to him to simpler problems in propositional logic. A detailed algorithm is presented for such an application. Two proofs of the equivalence are presented: a "syntactic" proof and a "semantic" proof. The syntactic proof proceeds in several steps. It is shown that 1) Armstrong's Dependency Axioms are complete for dependency statements in the usual logical sense that they are strong enough to prove every consequence, and that 2) Armstrong's Axioms are also complete for implicational statements in propositional logic. The equivalence then follows from 1) and 2). The other proof proceeds by considering appropriate semantic interpretations for the propositional variables. The Delobel-Casey Relational Database Decomposition Theorems, which heretofore have seemed somewhat fortuitous, are immediate and natural corollaries of the equivalence. Furthermore, a counterexample is demonstrated, which shows that what seems to be a mild extension of the equivalence fails.