Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets

We investigate functional dependencies in databases that support complex values such as records, lists, sets anu multisets. Therefore, an abstract algebraic framework is proposed that classifies data models according to the underlying types they support. This allows to emphasise the impact of the data types rather than the specifics of a particular data model.The main results are finite, minimal, sound and complete sets of inference rules for the implication of functional dependencies in the presence of records and all combinations of lists, sets and multisets. The inference rules are similar to Armstrong's original axioms for the relational data model, thanks to the algebraic framework. The completeness result, however, requires a deep analysis in the case of sets and, in particular, multisets.

[1]  Joachim Biskup,et al.  Achievements of Relational Database Schema Design Theory Revisited , 1995, Semantics in Databases.

[2]  Tok Wang Ling,et al.  Designing Functional Dependencies for XML , 2002, EDBT.

[3]  Agostino Dovier,et al.  A Uniform Axiomatic View of Lists, Multisets, and Sets, and the Relevant Unification Algorithms , 1998, Fundam. Informaticae.

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

[5]  Jixue Liu,et al.  Multivalued Dependencies in XML , 2003, BNCOD.

[6]  Peter P. Chen.  English Sentence Structure and Entity-Relationship Diagrams , 1983, Inf. Sci..

[7]  Zahir Tari,et al.  Object normal forms and dependency constraints for object-oriented schemata , 1997, TODS.

[8]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[9]  Marcelo Arenas,et al.  An information-theoretic approach to normal forms for relational and XML data , 2003, PODS.

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

[11]  Sven Hartmann,et al.  More Functional Dependencies for XML , 2003, ADBIS.

[12]  Millist Walter Vincent,et al.  THE SEMANTIC JUSTIFICATION FOR NORMAL FORMS IN RELATIONAL DATABASE DESIGN , 1994 .

[13]  Nicolás Marín,et al.  Review of Data on the Web: from relational to semistructured data and XML by Serge Abiteboul, Peter Buneman, and Dan Suciu. Morgan Kaufmann 1999. , 2003, SGMD.

[14]  Hazel Perfect.  COMBINATORICS OF FINITE SETS (Oxford Science Publications) , 1988 .

[15]  Bernhard Thalheim,et al.  Fundamental Concepts of Object Oriented Databases , 1993, Acta Cybern..

[16]  Shamim A. Naqvi,et al.  A Logical Language for Data and Knowledge Bases , 1989 .

[17]  Catriel Beeri,et al.  A Sophisticate's Introduction to Database Normalization Theory , 1978, VLDB.

[18]  Yatsuka Nakamura,et al.  Armstrong's Axioms , 2007 .

[19]  Hans-Jörg Schek,et al.  A Relational Object Model , 1990, ICDT.

[20]  Klaus-Dieter Schewe,et al.  Reasoning about Functional and Multi-valued Dependencies in the Presence of Lists , 2004, FoIKS.

[21]  Jeffrey D. Ullman,et al.  Principles of Database Systems , 1980 .

[22]  Roger King,et al.  Semantic database modeling: survey, applications, and research issues , 1987, CSUR.

[23]  Joel E. Richardson,et al.  Supporting Lists in a Data Model (A Timely Approach) , 1992, VLDB.

[24]  Wenfei Fan,et al.  On XML integrity constraints in the presence of DTDs , 2001, JACM.

[25]  Wenfei Fan,et al.  Constraints for semistructured data and XML , 2001, SGMD.

[26]  Gottfried Vossen.  A New Characterization of FD Implication with an Application to Update Anomalies , 1988, Inf. Process. Lett..

[27]  Jinyan Li,et al.  Bioinformatics Adventures in Database Research , 2003, ICDT.

[28]  Catriel Beeri,et al.  A Formal Approach to Object-Oriented Databases , 1990, Data Knowl. Eng..

[29]  David Maier.  Minimum Covers in Relational Database Model , 1980, JACM.

[30]  Mark Levene,et al.  Semantics for null extended nested relations , 1993, TODS.

[31]  Joachim Biskup,et al.  Database Schema Design Theory : Achievements and Challenges , 1995, CISMOD.

[32]  David W. Embley,et al.  A normal form for precisely characterizing redundancy in nested relations , 1996, TODS.

[33]  Gianfranco Lamperti,et al.  On Multisets in Database Systems , 2000, WMP.

[34]  Victor Vianu,et al.  A Web Odyssey: from Codd to XML , 2001, PODS.

[35]  Sven Hartmann,et al.  Normalisation in the Presence of Lists , 2004, ADC.

[36]  Ronald Fagin,et al.  The theory of data dependencies - a survey , 1984 .

[37]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[38]  Bernhard Thalheim,et al.  Dependencies in relational databases , 1991, Teubner-Texte zur Mathematik.

[39]  Ming-Chien Shan,et al.  Iris: An Object-Oriented Database Management System , 1989, ACM Trans. Inf. Syst..

[40]  Philip A. Bernstein,et al.  Synthesizing third normal form relations from functional dependencies , 1976, TODS.

[41]  Grant E. Weddell,et al.  Reasoning About Equations and Functional Dependencies on Complex Objects , 1994, IEEE Trans. Knowl. Data Eng..

[42]  Daniel Le Métayer,et al.  Programming by multiset transformation , 1993, CACM.

[43]  Gérard Berry,et al.  The chemical abstract machine , 1989, POPL '90.

[44]  Sven Hartmann,et al.  On the implication problem for cardinality constraints and functional dependencies , 2001, Annals of Mathematics and Artificial Intelligence.

[45]  Chengfei Liu,et al.  A Redundancy Free 4NF for XML , 2003, Xsym.

[46]  Peter P. Chen.  The Entity-Relationship Model: Towards a unified view of Data , 1976 .

[47]  Sven Hartmann,et al.  Multi-valued dependencies in the presence of lists , 2004, PODS '04.

[48]  Cristian S. Calude,et al.  Proceedings of the Workshop on Multiset Processing: Multiset Processing, Mathematical, Computer Science, and Molecular Computing Points of View , 2000 .

[49]  M. Levene.  A universal relation model for a nested database , 1992 .

[50]  Peter P. Chen.  The entity-relationship model: toward a unified view of data , 1975, VLDB '75.

[51]  Peer Kröger,et al.  A Computational Biology Database Digest: Data, Data Analysis, and Data Management , 2004, Distributed and Parallel Databases.

[52]  Carmem S. Hara,et al.  Reasoning about nested functional dependencies , 1999, PODS '99.

[53]  I. Anderson.  Combinatorics of Finite Sets , 1987 .

[54]  A. Tarski,et al.  On Closed Elements in Closure Algebras , 1946 .

[55]  Grant E. Weddell,et al.  Reasoning about functional dependencies generalized for semantic data models , 1992, TODS.

[56]  Shamkant B. Navathe,et al.  Conceptual Database Design: An Entity-Relationship Approach , 1991 .

[57]  Egon Börger,et al.  Trends in theoretical computer science , 1988 .

[58]  Z. Meral Özsoyoglu,et al.  A new normal form for nested relations , 1987, TODS.

[59]  Ronald Fagin,et al.  A normal form for relational databases that is based on domains and keys , 1981, TODS.

[60]  Catriel Beeri,et al.  Equivalence of Relational Database Schemes , 1981, SIAM J. Comput..

[61]  Dan Suciu,et al.  On database theory and XML , 2001, SGMD.

[62]  Sven Hartmann,et al.  A Membership Algorithm for Functional and Multi-valued Dependencies in the Presence of Lists , 2004, Electron. Notes Theor. Comput. Sci..

[63]  A Min Tjoa,et al.  Transformation of Requirement Specifications Expressed in Natural Language into an EER Model , 1993, ER.

[64]  David J. DeWitt,et al.  The Object-Oriented Database System Manifesto , 1994, Building an Object-Oriented Database System, The Story of O2.

[65]  Bernhard Thalheim,et al.  Entity-relationship modeling - foundations of database technology , 2010 .

[66]  Klaus-Dieter Schewe,et al.  A New Normal Form for Conceptual Database , 2003, EJC.

[67]  Dan Suciu,et al.  Data on the Web: From Relations to Semistructured Data and XML , 1999 .

[68]  Marc Gyssens,et al.  The Structure of the Relational Database Model , 1989, EATCS Monographs on Theoretical Computer Science.

[69]  Jixue Liu,et al.  Functional Dependencies for XML , 2003, APWeb.

[70]  M. W. VINCENT,et al.  Update Anomalies and the Justification for 4NF in Relational Databases , 1994, Inf. Sci..

[71]  Marcelo Arenas,et al.  A normal form for XML documents , 2002, PODS '02.

[72]  Mark Levene,et al.  The Nested Universal Relation Database Model , 1992, Lecture Notes in Computer Science.

[73]  Philip Alan Bernstein,et al.  Normalization and functional dependencies in the relational data base model. , 1975 .

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

[75]  Sven Hartmann.  Decomposing relationship types by pivoting and schema equivalence , 2001, Data Knowl. Eng..

[76]  E. F. Codd,et al.  Recent Investigations in Relational Data Base Systems , 1974, ACM Pacific.

[77]  MILLIST W. VINCENT,et al.  Redundancy and the Justification for Fourth Normal Form in Relational Databases , 1993, Int. J. Found. Comput. Sci..

[78]  Sven Hartmann,et al.  On Functional Dependencies in Advanced Data Models , 2003, Electron. Notes Theor. Comput. Sci..

[79]  K. Engel.  Sperner Theory , 1996 .

[80]  Miron Livny,et al.  The Design and Implementation of a Sequence Database System , 1996, VLDB.

[81]  Philip A. Bernstein,et al.  What does Boyce-Codd Normal Form Do? , 1980, VLDB.

[82]  Dominique Pastre,et al.  Managing Complex Objects in an Extensible Relational DBMS , 1989, VLDB.

[83]  C. M. Sperberg-McQueen,et al.  Extensible markup language , 1997 .

[84]  Wenfei Fan,et al.  Integrity constraints for XML , 2000, PODS.

[85]  A BernsteinPhilip,et al.  Computational problems related to the design of normal form relational schemas , 1979 .

[86]  Bruno Courcelle,et al.  Fundamental Properties of Infinite Trees , 1983, Theor. Comput. Sci..