Subset Dependencies and a Completeness Result for a Subclass of Embedded Multivalued Dependencies

It tS shown that embedded multwalued dependencies do not have a complete axlomatizatlon A new type of dependenoes, called subset dependencies, is introduced. Subset dependencies are a generahzauon of embedded multtvalued dependencies It is shown that a subclass of subset dependenoes (that does not include all the embedded multwalued dependenoes) has a complete axlomatlzation consisting of reflexivity and translt~vity rules As a result, ~t ~s shown how to test implications of embedded muluvalued dependencies under some restricted conditions

[1]  Journal of the Association for Computing Machinery , 1961, Nature.

[2]  E. F. CODD,et al.  A relational model of data for large shared data banks , 1970, CACM.

[3]  Hans Hermes,et al.  Introduction to mathematical logic , 1973, Universitext.

[4]  Carlo Zaniolo,et al.  Analysis and design of relational schemata for database systems. , 1976 .

[5]  Ronald Fagin,et al.  Multivalued dependencies and a new normal form for relational databases , 1977, TODS.

[6]  Akifumi Makinouchi,et al.  A Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data Model , 1977, VLDB.

[7]  Ronald Fagin,et al.  Functional Dependencies in a Relational Data Base and Propositional Logic , 1977, IBM J. Res. Dev..

[8]  Catriel Beeri,et al.  A complete axiomatization for functional and multivalued dependencies in database relations , 1977, SIGMOD '77.

[9]  Alfred V. Aho,et al.  The theory of joins in relational data bases , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[10]  Jean-Marie Nicolas.  First order logic formalization for functional, multivalued and mutual dependencies , 1978, SIGMOD '78.

[11]  Claude Delobel,et al.  Normalization and hierarchical dependencies in the relational data model , 1978, TODS.

[12]  Alberto O. Mendelzon.  On Axiomatizing Multivalued Dependencies in Relational Databases , 1979, JACM.

[13]  Elliott Mendelson,et al.  Introduction to Mathematical Logic , 1979 .

[14]  Tadao Kasami,et al.  Decision Problems for Multivalued Dependencies in Relational Databases , 1979, SIAM J. Comput..

[15]  Catriel Beeri,et al.  On the Properties of Join Dependencies , 1979, Advances in Data Base Theory.

[16]  Philip A. Bernstein,et al.  Computational problems related to the design of normal form relational schemas , 1979, TODS.

[17]  Claude Delobel,et al.  Decompositions and functional dependencies in relations , 1980, TODS.

[18]  Horn clauses and database dependencies (Extended Abstract) , 1980, STOC '80.

[19]  Kamran Parsaye-Ghomi,et al.  Inferences involving embedded multivalued dependencies and transitive dependencies , 1980, SIGMOD '80.

[20]  Catriel Beeri,et al.  On the menbership problem for functional and multivalued dependencies in relational databases , 1980, TODS.

[21]  Joachim Biskup.  Inferences of Multivalued Dependencies in Fixed and Undetermined Universes , 1980, Theor. Comput. Sci..

[22]  Yehoshua Sagiv.  An Algorithm for Inferring Multivalued Dependencies with an Application to Propositional Logic , 1980, JACM.

[23]  Jeffrey D. Ullman,et al.  A complete axiomatization for a large class of dependencies in relational datatbases , 1980, STOC '80.

[24]  Jan Paredaens.  The Interaction of Integrity Constraints in an Information System , 1980, J. Comput. Syst. Sci..

[25]  Mihalis Yannakakis,et al.  Algebraic dependencies , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[26]  Mihalis Yannakakis,et al.  Algebraic dependencies , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[27]  Ronald Fagin,et al.  An Equivalence Between Relational Database Dependencies and a Fragment of Propositional Logic , 1981, JACM.

[28]  Edward Sciore,et al.  A Complete Axiomatization of Full Join Dependencies , 1982, JACM.

[29]  Ronald Fagin,et al.  Horn clauses and database dependencies , 1982, JACM.

[30]  Zvi Galil,et al.  An Almost Linear-Time Algorithm for Computing a Dependency Basis in a Relational Database , 1982, JACM.