ABSTRACT
Multi-valued depdendencies (MVDs) are an important class of relational constraints. We axiomatise MVDs in data models that support nested list types. In order to capture different data models at a time, an abstract approach based on nested attributes is taken. The set of subattributes of some fixed nested attribute carries the structure of a co-Heyting algebra. This enables us to generalise significant features of MVDs from the relational data model to the presence of lists. It is shown that an MVD is satisfied by some instance exactly when this instance can be decomposed without loss of information. The full power of the algebraic framework allows to provide a sound and complete set of inference rules for the finite implication of MVDs in the context of lists. The presence of the list operator calls for a new inference rule which is not required in the relational data model. Further differences become apparant when the minimality of the inference rules is investigated. The extension of the relational theory of MVDs to the presence of lists allows to specify more real-world constraints and increases therefore the number of application domains.
- S. Abiteboul, P. Buneman, and D. Suciu. Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann Publishers, 2000. Google ScholarDigital Library
- S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995. Google ScholarDigital Library
- M. Arenas and L. Libkin. A normal form for XML documents. In PODS 2002. ACM, 2002. Google ScholarDigital Library
- M. Atkinson, F. Bancilhon, D. DeWitt, K. Dittrich, D. Maier, and S. Zdonik. The object-oriented database system manifesto. In Proc. of Intl. Conf. on Deductive and Object-Oriented Databases, pages 40--57, 1989.Google Scholar
- C. Batini, S. Ceri, and S. B. Navathe. Conceptual Database Design: An Entity-Relationship Approach, Benjamin Cummings, 1992. Google ScholarDigital Library
- C. Beeri. On the membership problem for functional and multivalued dependencies in relational databases. TODS, 5(3):241--259, 1980. Google ScholarDigital Library
- C. Beeri. A formal approach to object-oriented databases. Data and Knowledge Engeneering, 5(4):353--382, 1990. Google ScholarDigital Library
- C. Beeri and P. A. Bernstein. Computational problems related to the design of normal form relational schemata. In Transactions on Database Systems, pages 30--59. ACM, 1979. Google ScholarDigital Library
- C. Beeri, R. Fagin, and J. H. Howard. A complete axiomatization for functional and multivalued dependencies in database relations. In International Conference on Management of Data, pages 47--61. ACM, 1977. Google ScholarDigital Library
- J. Biskup. On the complementation rule for multivalued dependencies in database relations. Acta Informatica, 10(3):297--305, 1978.Google ScholarDigital Library
- J. Biskup,. Database schema design theory:achievements and challenges. In International Conference on Information Systems and Management of Data, number 1066 in LNCS, pages 14--44. Springer, 1995.Google Scholar
- J. Biskup. Achievements of relational database schema design theory revisited. In Semantics in databases, number 1358 in LNCS, pages 29 54. Springer, 1998. Google ScholarDigital Library
- F. Bry and P. Kröger. A computational biology database digest: data, data analysis, and data management. Distributed and Parallel Databases, 13(1):7--42, 2003. Google ScholarDigital Library
- P. Buneman, S. Davidson, W. Fan, C. Hara, and W. Tan. Keys for XML. In Tenth WWW Conference. IEEE, 2001. Google ScholarDigital Library
- P. P. Chen. The entity-relationship model: Towards a unified view of data. ACM Transactions Database Systems 1, pages 9--36, 1976. Google ScholarDigital Library
- P. P. Chen. English sentence structure and entity-relationship diagrams. Information Science 29, pages 127--149, 1983.Google ScholarCross Ref
- C. Delobel. Normalisation and hierarchical dependencies in the relational data model. ToDS, 3(3):201--222, 1978. Google ScholarDigital Library
- A. Dovier, A. Policriti, and G. Rossi. A uniform axiomatic view of lists, multisets, and sets, and the unification algorithm. Fundamenta Informaticae, 36(2/3):201--234, 1998. Google ScholarDigital Library
- R. Fagin. Multivalued dependencies and a new normal form for relational databases. Association for Computing Machinery, 2(3):262--278, 1977. Google ScholarDigital Library
- R. Fagin. A normal form for relational databases that is based on domains and keys. TODS, pages 387--415, 1981. Google ScholarDigital Library
- R. Fagin and M. Vardi. The theory of data dependencies: a survey. In Mathematics of Information Processing: Proceedings of Symposia in Applied Mathematics, pages 19--71. American Mathematical Society, 1986.Google ScholarCross Ref
- W. Fan and L. Libkin. On XML integrity constraints in the presence of DTDs. In PODS 2001. ACM, 2001. Google ScholarDigital Library
- W. Fan and J. Siméon. Integrity constraints for XML. In PODS 2000. ACM, 2000. Google ScholarDigital Library
- D. Fishman, D. Beech, H. Cate, and E. e. a. Chow. Iris:an object-oriented database management system. ToIS, 5(1), 1987.Google Scholar
- Z. Galil. An almost linear-time algorithm for computing a dependency basis in a relational database. Journal of the ACM, 29(1):96--102, 1982. Google ScholarDigital Library
- G. Gardarin, J.-P. Cheiney, G. Kiernan, D. Pastre, and H. Stora. Managing complex objects in an extensible relational DBMS. In VLDB, 1989, Amsterdam, pages 55--65. Morgan Kaufmann, 1989. Google ScholarDigital Library
- G. Grahne and K. Räihä. Database decomposition into 4NF. In 9th VLDB, pages 186--196, 1983. Google ScholarDigital Library
- K. Hagihara, M. Ito, K. Taniguchi, and T. Kasami. Decision problems for multivalued dependencies in relational databases. SIAM Journal of Computation, 8(2):247--264, 1979.Google ScholarDigital Library
- S. Hartmann. Decomposing relationship types by pivoting and schema equivalence. Data & Knowledge Engineering, 39:75--99, 2001. Google ScholarDigital Library
- S. Hartmann and S. Link, More functional dependencies for XML. In Advances in Databases and Information Systems, volume 2798 of Lecture Notes in Computer Science, pages 355--369, 2003.Google ScholarCross Ref
- S. Hartmann, S. Link, and K.-D. Schewe. A new normal form for conceptual databases. In Information Modelling and Knowledge Bases XV, Frontiers in Artificial Intelligence and Applications, pages 88--105. IOS Press, 2003.Google Scholar
- S. Hartmann, S. Link, and K.-D. Schewe. Functional dependencies in the presence of records, lists, sets and multisets. Technical Report 1/2004, Information Science Research Centre, Massey University, Department of Information Systems, Palmerston North, New Zealand, 2004.Google Scholar
- S. Hartmann, S. Link, and K.-D. Schewe. Reasoning about functional and multi-valued dependencies in the presence of lists. In Foundations of Information and Knowledge Systems, volume 2942 of Lecture Notes in Computer Science, pages 134--154, 2004.Google ScholarCross Ref
- R. Hull and R. King. Semantic database modeling: Survey, applications and research issues. ACM Computing Surveys, 19(3), 1987. Google ScholarDigital Library
- M. Levene. The Nested Universal Relation Database Model. Springer, 1992.Google ScholarCross Ref
- J. McKinsey and A. Tarski. On closed elements in closure algebras. Annals of Mathematics, 47:122--146, 1946.Google ScholarCross Ref
- A. Mendelzon. On axiomatising multivalued dependencies in relational databases. Journal of the ACM, 26(1):37--44, 1979. Google ScholarDigital Library
- W. Y. Mok, Y. K. Ng, and D. W. Embley. A normal form for precisely charachterizing redundancy in nested relations. Transactions on Database Systems, 21:77--106, 1996. Google ScholarDigital Library
- S. Naqvi and S. Tsur. A logical language for data and knowledge bases. Computer Science Press, 1989. Google ScholarDigital Library
- Z. M. özsoyoglu and L. Y. Yuan. A new normal form for nested relations. Transactions on Database Systems, 12:111--136, 1987. Google ScholarDigital Library
- Z. M. özsoyoglu and L. Y. Yuan. Reduced mvds and minimal covers. Transactions on Database Systems, 12(3):377--394, 1987. Google ScholarDigital Library
- J. Paredaens, P. De Bra, M. Gyssens, and D. Van Gucht. The Structure of the Relational Database Model. Springer-Verlag, 1989. Google ScholarCross Ref
- J. Richardson. Supporting lists in a datamodel. In Proceeding of VLDB, pages 127--192, 1992. Google ScholarDigital Library
- Y. Sagiv. An algorithm for inferring multivalued dependencies with an application to propositional logic. Journal of the ACM, 27(2):250--262, 1980. Google ScholarDigital Library
- K.-D. Schewe and B. Thalheim. Fundamental concepts of object oriented databases. Acta Cybernetica, 11(4):49--85, 1993.Google Scholar
- M. Scholl and H.-J. Schek. A relational object model. In Proceedings of International Conference on Database Theory (ICDT), pages 89--105. Springer Lecture Notes Series, 1990. Google ScholarDigital Library
- P. Seshadri, M. Livny, and R. Ramakrishnan. The design and implementation of sequence database system. In VLDB, Mumbai, India, 1996. Google ScholarDigital Library
- Z. Tari, J. Stokes, and S. Spaccapietra. Object normal forms and dependency constraints for object-oriented schemata. ACM ToDS, 22:513--569, 1997. Google ScholarDigital Library
- B. Thalheim. Dependencies in Relational Databases. Teubner-Verlag, 1991.Google ScholarCross Ref
- B. Thalheim. Entity-Relationship Modeling: Foundations of Database Technology. Springer-Verlag, 2000. Google ScholarCross Ref
- A. M. Tjoa and L. Berger. Transformation of requirement specifications expressed in natural language into an eer model. In Entity-Relationship Approach, volume 823 of Lecture Notes in Computer Science. Springer, 1993. Google ScholarDigital Library
- M. Y. Vardi. Fundamentals of dependency theory. In E. Börger, editor, Trends in Theoretical Computer Science, pages 171--224. Computer Science Press, 1987.Google Scholar
- M. Vincent and J. Liu. Multivalued dependencies in XML. In BNCOD, volume 2712 of Lecture Notes in Computer Science, pages 4--18. Springer, 2003. Google ScholarDigital Library
- M. Vincent, J. Liu, and C. Liu. A redundancy free 4NF for XML. In XML Database Symposium, 2003.Google ScholarCross Ref
- M. Vincent and B. Srinivasan. Redundancy and the justification of fourth normal form in relational databases. International Journal of Foundations of Computer Science, 4(4):355--365, 1993.Google ScholarCross Ref
- M. Vincent and B. Srinivasan. Update anomalies and the justification of fourth normal form in relational databases. Information Sciences, 81:87--102, 1994. Google ScholarDigital Library
- G. Vossen. A new characterization of fd implication with an application to update anomalies. Information Processing Letters, 29:131--135, 1988. Google ScholarDigital Library
- W3C. Xml schema part 2: Datatypes. http://www.w3.org/TR/xmlschema-2/#datatype, 2001.Google Scholar
- C. Zaniolo. Analysis and Design of Relational Schemata for Database Systems. PhD thesis, UCLA, Technical Report UCLA-ENG-7769, 1976. Google Scholar
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