The impact of the list constructor on two important classes of relational dependencies is investigated. Lists represent an inevitable data structure whenever order matters and data is allowed to occur repeatedly. The list constructor is therefore supported by many advanced data models such as genomic sequence, deductive and object-oriented data models including XML. The article proposes finite axiomatisations of functional, multivalued and both functional and multivalued dependencies in nested databases supporting record and list constructor. In order to capture different data models at a time, an abstract algebraic approach based on nested attributes is taken. The presence of the list constructor calls for a new inference rule which allows to infer non-trivial functional dependencies from multivalued dependencies. Further differences to the relational theory become apparent when the independence of the inference rules is investigated. The extension of the relational theory to nested databases allows to specify more real-world constraints and increases therefore the number of application domains.
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S. Abiteboul, P. Buneman and D. Suciu, Data on the web: From relations to semistructured data and XML (Morgan Kaufmann, 2000).
S. Abiteboul, R. Hull and V. Vianu, Foundations of databases (Addison-Wesley, 1995).
M. Arenas and L. Libkin, On verifying consistency of XML specifications, in: PODS 2002 (2002) pp. 259–270.
M. Arenas and L. Libkin, What's hard about XML schema constraints?, in: DEXA 2002 (2002) pp. 269–278.
M. Arenas and L. Libkin, An information-theoretic approach to normal forms for relational and XML data, in: PODS 2003 (2003) pp. 15–26.
M. Arenas and L. Libkin, A normal form for XML documents, Transactions on Database Systems 29(1) (2004) 195–232.
W.W. Armstrong, Dependency structures of database relationships, Information Processing (1974) 580–583.
W.W. Armstrong, Y. Nakamura and P. Rudnicki, Armstrong's axioms, Journal of formalized Mathematics 14 (2002).
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 (1989) pp. 40–57.
C. Batini, S. Ceri and S.B. Navathe, Conceptual Database Design: An Entity-Relationship Approach (Benjamin Cummings, 1992).
C. Beeri, On the membership problem for functional and multivalued dependencies in relational databases, Transactions on Database Systems 5(3) (1980) 241–259.
C. Beeri, A formal approach to object-oriented databases, Data and Knowledge Engineering 5(4) (1990) 353–382.
C. Beeri and P.A. Bernstein, Computational problems related to the design of normal form relational schemata, in: Transactions on Database Systems (1979) pp. 30–59.
C. Beeri, P.A. Bernstein and N. Goodman, A sophisticate's introduction to database normalization theory, in: Proc. of 4th International Conference on Very Large Databases (1978) pp. 113–124.
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 (1977) pp. 47–61.
P. Bernstein, Synthesizing third normal form relations from functional dependencies, Transactions on Database Systems 1 (1976) 277–298.
P.A. Bernstein and N. Goodman, What does Boyce–Codd normal form do?, in: VLDB (1980) pp. 245–259.
G. Birkhoff, Lattice Theory (American Mathematical Society, 1940).
J. Biskup, On the complementation rule for multivalued dependencies in database relations, Acta Informatica 10(3) (1978) 297–305.
J. Biskup, Inferences of multivalued dependencies in fixed and undetermined universes, Theoretical Computer Science 10(1) (1980) 93–106.
J. Biskup, Database schema design theory: achievements and challenges, in: International Conference on Information Systems and Management of Data (1995) pp. 14–44.
J. Biskup, Achievements of relational database schema design theory revisited, in: Semantics in Databases (1998) pp. 29–54.
T. Bray, J. Paoli, C. Sperberg-McQueen, E. Maler and F. Yergeau, Extensible Markup Language (XML) 1.0 (Third Edition) W3C Recommendation 04 February 2004 (2004). http://www.w3.org/TR/2004/REC-xml-20040204/.
F. Bry and P. Kröger, A computational biology database digest: Data, data analysis, and data management, Distributed and Parallel Databases 13(1) (2003) 7–42.
P. Buneman, S. Davidson, W. Fan, C. Hara and W. Tan, Keys for XML, Computer Networks 39(5) (2002) 473–487.
P. Buneman, S. Davidson, W. Fan, C. Hara and W. Tan, Reasoning about keys for XML, Inf. Syst. Syst. 28(8) (2003) 1037–1063.
P. Buneman, W. Fan, J. Siméon and S. Weinstein, Constraints for semi-structured data and XML, SIGMOD Record 30(1) (2001) 47–54.
P. Buneman, W. Fan and S. Weinstein, Path constraints in semistructured databases, Journal of Computer and System Sciences 61(2) (2000) 146–193.
P.P. Chen, The entity-relationship model: Towards a unified view of data, ACM Transactions Database Systems 1 (1976) 9–36.
P.P. Chen, English sentence structure and entity-relationship diagrams, Information Science 29 (1983) 127–149.
E.F. Codd, Further normalization of the database relational model, in: Courant Computer Science Symposia 6: Data Base Systems (1972) pp. 33–64.
C. Delobel, Normalisation and hierarchical dependencies in the relational data model, Transactions on Database Systems 3(3) (1978) 201–222.
C. Delobel and M. Adiba, Relational Database Systems (North Holland, 1985).
J. Diederich and J. Milton, New methods and fast algorithms for database normalization, Transactions on Database Systems 13(3) (1988) 339–365.
R. Fagin, Functional dependencies in a relational data base and propositional logic, IBM Journal of Research and Development 21(6) (1977) 543–544.
R. Fagin, Multivalued dependencies and a new normal form for relational databases, Association for Computing Machinery 2(3) (1977) 262–278.
R. Fagin, A normal form for relational databases that is based on domains and keys, Transactions on Database Systems (1981) pp. 387–415.
R. Fagin and M. Vardi, The theory of data dependencies: A survey, in: Mathematics of Information Processing: Proceedings of Symposia in Applied Mathematics (1986) pp. 19–71.
W. Fan and L. Libkin, On XML integrity constraints in the presence of DTDs, Journal of the ACM 49(3) (2002) 368–406.
W. Fan and J. Siméon, Integrity constraints for XML, Journal of Computer and System Sciences 66(1) (2003) 254–291.
P. Fischer, L. Saxton, S. Thomas and D. van Gucht, Interactions between dependencies and nested relational structures, Journal of Computer and System Sciences 31(3) (1985) 105–129.
D. Fishman, D. Beech, H. Cate and E.E.A. Chow, IRIS: An object-oriented database management system, ToIS 5(1) (1987).
Z. Galil, An almost linear-time algorithm for computing a dependency basis in a relational database, Journal of the ACM 29(1) (1982) 96–102.
G. Gardarin, J.-P. Cheiney, G. Kiernan, D. Pastre and H. Stora, Managing complex objects in an extensible relational DBMS, in: VLDB (Amsterdam, 1989) pp. 55–65.
G. Gottlob, Computing covers for embedded functional dependencies, in: PoDS (1987) pp. 58–69.
G. Grahne and K. Räihä, Database decomposition into 4NF, in: 9th VLDB (1983) pp. 186–196.
K. Hagihara, M. Ito, K. Taniguchi and T. Kasami, Decision problems for multivalued dependencies in relational databases, SIAM Journal of Computation 8(2) (1979) 247–264.
C. Hara and S. Davidson, Reasoning about nested functional dependencies, in: PODS 1999 (1999) pp. 91–100.
S. Hartmann, Decomposing relationship types by pivoting and schema equivalence, Data & Knowledge Engineering 39 (2001) 75–99.
S. Hartmann, On the implication problem for cardinality constraints and functional dependencies, Annals of Mathematics and Artificial Intelligence 33 (2001) 253–307.
S. Hartmann and S. Link, More functional dependencies for XML, in: Advances in Databases and Information Systems, 7th East European Conference, ADBIS 2003, Dresden, Germany, September 3–6, Vol. 2798 of Lecture Notes in Computer Science (2003) pp. 355–369.
S. Hartmann and S. Link, On functional dependencies in advanced data models, Electronic Notes in Theoretical Computer Science 84 (2003).
S. Hartmann and S. Link, A membership algorithm for functional and multi-valued dependencies in the presence of lists, ENTCS 91 (2004).
S. Hartmann and S. Link, Multi-valued dependencies in the presence of lists, in: 23rd Symposium on Principles of Database Systems (PoDS) (2004) pp. 134–154.
S. Hartmann and S. Link, Normalisation in the presence of lists, in: 15th Australasian Database Conference (ADC), Vol. 27 of Conferences in Research and Practice in Information Technology (2004) pp. 53–64.
S. Hartmann, S. Link and M. Kirchberg, A subgraph-based approach towards functional dependencies for XML, in: Proceedings of the 7th World-Multiconference on Systemics, Cybernetics and Informatics (SCI), Volume IX, Computer Science and Engineering II (Orlando, Florida, USA, July 27–30 2003) pp. 200–205.
S. Hartmann, S. Link and K.-D. Schewe, A new normal form for conceptual databases, in: Information Modelling and Knowledge Bases XV, 13th European–Japanese Conference on Information Modelling and Knowledge Bases (EJC 2003), Kitakyushu, Japan, June 3–6, 2003, Vol. 105 of Frontiers in Artificial Intelligence and Applications, eds. Y. Kiyoki, E. Kawaguchi, H. Jaakkola and H. Kangassalo (2004) pp. 93–110.
S. Hartmann, S. Link and K.-D. Schewe, Reasoning about functional and multi-valued dependencies in the presence of lists, in: 3rd International Symposium on Foundations of Information and Knowledge Systems (FoIKS), Vol. 2942 of Lecture Notes in Computer Science (2004) pp. 134–154.
S. Hartmann, S. Link and K.-D. Schewe, Axiomatisations of Functional Dependencies in the Presence of Records, Lists, Sets and Multisets. (2006) accepted for Theoretical Computer Science (TCS).
R. Hull and R. King, Semantic database modeling: Survey, applications and research issues, ACM Computing Surveys 19(3) (1987).
M. Ito, M. Iwasaki, K. Taniguchi and K. Kasami, Membership problems for data dependencies in relational expressions, Theoretical Computer Science 34 (1984) 315–335.
J. Kivinen and H. Mannila, Approximate inference of functional dependencies from relations, Theoretical Computer Science 149(1) (1995) 129–149.
V. Lakshmanan and C. VeniMadhavan, An algebraic theory of functional and multivalued dependencies in relational databases, Theoretical Computer Science 54 (1987) 103–128.
M. Levene, The Nested Universal Relation Database Model (Springer, 1992).
M. Levene, A lattice view of functional dependencies in incomplete relations, Acta Cybernetica 12(2) (1995) 181–208.
M. Levene and G. Loizou, Semantics for null extended nested relations, Transactions on Database Systems 18(3) (1993) 414–459.
M. Levene and G. Loizou, Database design for incomplete relations, Transactions on Database Systems 24(1) (1999) 80–125.
J. Li, S. Ng and L. Wong, Bioinformatics adventures in database research, in: Database Theory – ICDT 2003, Vol. 2572 of Lecture Notes in Computer Science (2002) pp. 31–46.
T. Ling and L. Yan, NF–NR: A practical normal form for nested relations, Journal of Systems Integration 4 (1994) 309–340.
S. Lopes, J.-M. Petit and L. Lakhal, Efficient discovery of functional dependencies and armstrong relations, in: Proceedings of the 7th International Conference on Extending Database Technology: Advances in Database Technology, Vol. 1777 of Lecture Notes In Computer Science (2000) pp. 350–364.
D. Maier, Minimum covers in relational database model, Journal of the ACM 27(4) (1980) 664–674.
H. Mannila and K. Räihä, On the complexity of inferring functional dependencies, Discrete Applied Mathematics 40(2) (1992) 237–243.
H. Mannila and K. Räihä, Algorithms for inferring functional dependencies from relations, Data & Knowledge Engineering 12(1) (1994) 83–99.
J. McKinsey and A. Tarski, On closed elements in closure algebras, Annals of Mathematics 47 (1946) 122–146.
A. Mendelzon, On axiomatising multivalued dependencies in relational databases, Journal of the ACM 26(1) (1979) 37–44.
W.Y. Mok, A comparative study of various nested normal forms, IEEE Transactions on Knowledge & Data Engineering 14(2) (2002) 369–385.
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 (1996) 77–106.
S. Naqvi and S. Tsur, A Logical Language for Data and Knowledge Bases (Computer Science, 1989).
Z.M. Özsoyoglu and L.Y. Yuan, A new normal form for nested relations, Transactions on Database Systems 12 (1987) 111–136.
Z.M. Özsoyoglu and L.Y. Yuan, On the normalisation in nested relational databases, in: Nested Relations and Complex Objects in Databases, Vol. 361 of Lecture Notes in Computer Science (1989) pp. 243–271.
J. Paredaens, P. De Bra, M. Gyssens and D. Van Gucht, The Structure of the Relational Database Model (Springer, 1989).
D. Parker and C. Delobel, Algorithmic applications for a new result on multivalued dependencies, in: Proc. of the 5th International Conference on Very Large Databases (1979) pp. 67–74.
J. Richardson, Supporting lists in a datamodel, in: Proceeding of VLDB (1992) pp. 127–192.
M. Roth and H. Korth, The design of \({\neg}\)1nf relational databases into nested normal form, in: Proc. of 1987 ACM–SIGMOD Conference (1987) pp. 143–159.
M. Roth, H. Korth and A. Silberschatz, Theory of non-first-normal form relational databases, Technical Report TR-84-36, University of Texas, Austin, Texas, USA, (1986).
M.A. Roth, H.F. Korth and A. Silberschatz, Extended algebra and calculus for nested relational databases, Transactions on Database Systems (TODS) 13(4) (1988) 389–417.
Y. Sagiv, An algorithm for inferring multivalued dependencies with an application to propositional logic, Journal of the ACM 27(2) (1980) 250–262.
I. Savnik and P. Flach, Discovery of multivalued dependencies from relations, Intelligent Data Analysis 4(3–4) (2000) 195–211.
K.-D. Schewe and B. Thalheim, Fundamental concepts of object oriented databases, Acta Cybernetica 11(4) (1993) 49–85.
M. Scholl and H.-J. Schek, A relational object model, in: Proc of International Conference on Database Theory (ICDT) (1990) pp. 89–105.
P. Seshadri, M. Livny and R. Ramakrishnan, The design and implementation of sequence database system, in: VLDB, Mumbai, India (1996).
Z. Tari, J. Stokes and S. Spaccapietra, Object normal forms and dependency constraints for object-oriented schemata, ACM Transactions on Database Systems 22 (1997) 513–569.
B. Thalheim, Dependencies in Relational Databases (Teubner-Verlag, 1991).
B. Thalheim, Entity-Relationship Modeling: Foundations of Database Technology (Springer, 2000).
B. Thalheim, Conceptual treatment of multivalued dependencies, in: 22nd International Conference on Conceptual Modeling, Vol. 2813 of Lecture Notes in Computer Science (2003) pp. 363–375.
A.M. Tjoa and L. Berger, Transformation of requirement specifications expressed in natural language into an EER model, in: Entity-Relationship Approach, Vol. 823 of Lecture Notes in Computer Science (1993).
D.-M. Tsou and P. Fischer, Decomposition of a relation scheme into Boyce–Codd normal form, SIGACT News 14(3) (1982) 23–29.
M. Vardi, Inferring multivalued dependencies from functional and join dependencies, Acta Informatica 19(2) (1983) 305–324.
M.Y. Vardi, Fundamentals of dependency theory, in: Trends in Theoretical Computer Science, ed. E. Börger (1987) pp. 171–224.
M. Vincent, Modification anomalies and Boyce–Codd normal form, Research and Practical Issues in Databases (1992) pp. 251–264.
M. Vincent, Insertion anomalies and the justification for 4NF in relational databases, Australian Computer Science Communications 17(1) (1995) 540–545.
M. Vincent, Semantic foundation of 4NF in relational database design, Acta Informatica 36 (1999) 1–41.
M. Vincent and J. Liu, Multivalued dependencies in XML, in: British National Conference on Databases, Vol. 2712 of Lecture Notes in Computer Science (2003) pp. 4–18.
M. Vincent, J. Liu and C. Liu, A redundancy free 4NF for XML, in: XML Database Symposium (2003).
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) (1993) 355–365.
M. Vincent and B. Srinivasan, Update anomalies and the justification of fourth normal form in relational databases, Information Sciences 81 (1994) 87–102.
G. Vossen, A new characterization of FD implication with an application to update anomalies, Information Processing Letters 29 (1988) 131–135.
M. Yan and A.-C. Fu, Algorithm for discovering multivalued dependencies, in: Proc. of the ACM CIKM International Conference on Information and Knowledge Management (2001) pp. 556–558.
C. Zaniolo, Analysis and design of relational schemata for database systems, PhD thesis, UCLA, Technical Report UCLA-ENG-7769 (1976).
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** Sebastian Link was supported by Marsden Funding, Royal Society of New Zealand.
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Hartmann, S., Link, S. & Schewe, KD. Functional and multivalued dependencies in nested databases generated by record and list constructor. Ann Math Artif Intell 46, 114–164 (2006). https://doi.org/10.1007/s10472-005-9015-9
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DOI: https://doi.org/10.1007/s10472-005-9015-9