Erratum to "Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets" (DOI:10.1016/j.tcs.2006.01.008);Axiomatisations of functional dependencies in the presence of records, lists, sets and multisets

Theoretical Computer Science

Volumn 355, Issue 2, 2006, Pages 167-196

  Hartmann, Sven ^a   Link, Sebastian ^a   Schewe, Klaus Dieter ^a  

^a MASSEY UNIVERSITY   (New Zealand)

Author keywords

Axiomatisation; Brouwerian algebra; Data types; Functional dependency; Semantics in databases

Indexed keywords

DATABASE SYSTEMS; LINEAR ALGEBRA; MATHEMATICAL MODELS; SEMANTICS;

AXIOMATISATION; BROUWERIAN ALGEBRA; DATA TYPES; SEMANTICS IN DATABASES;

SET THEORY;

EID: 30844435442     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2006.05.001     Document Type: Erratum

References (83)

1. S. Abiteboul, P. Buneman, and D. Suciu Data on the Web: From Relations to Semistructured Data and XML 2000 Morgan Kaufmann Publishers Los Altos, CA
2. S. Abiteboul, R. Hull, and V. Vianu Foundations of Databases 1995 Addison-Wesley Reading, MA
3. I. Anderson Combinatorics of Finite Sets 1987 Oxford Science Publications, The Clarendon Press, Oxford University Press New York
4. M. Arenas, and L. Libkin An information-theoretic approach to normal forms for relational and XML data Principles of Database Systems (PODS) 2003 ACM New York, NY 15 26
5. M. Arenas, and L. Libkin A normal form for XML documents Trans. Database Systems (TODS) 29 1 2004 195 232
6. W.W. Armstrong, Dependency structures of database relationships, Inform. Process. (1974) 580-583.
7. W.W. Armstrong, Y. Nakamura, P. Rudnicki, Armstrong's axioms, J. Formalized Math. 14.
8. M. Atkinson, F. Bancilhon, D. DeWitt, K. Dittrich, D. Maier, and S. Zdonik The object-oriented database system manifesto Proc. Internat. Conf. on Deductive and Object-Oriented Databases 1989 40 57
9. J. Banatre, and D. Le Metayer Programming by multiset transformation Comm. ACM 36 1 1993 98 111
10. C. Batini, S. Ceri, and S.B. Navathe Conceptual Database Design: An Entity-Relationship Approach 1992 Benjamin Cummings Menlo Park, CA
11. C. Beeri On the membership problem for functional and multivalued dependencies in relational databases Trans. Database Systems (TODS) 5 3 1980 241 259
12. C. Beeri A formal approach to object-oriented databases Data Knowledge Eng. 5 4 1990 353 382
13. C. Beeri, P.A. Bernstein, Computational problems related to the design of normal form relational schemata, Trans. Database Systems (TODS) (1979) 30-59.
14. C. Beeri, P.A. Bernstein, and N. Goodman A sophisticate's introduction to database normalization theory Proc. Internat. Conf. on Very Large Data Bases (VLDB) 1978 113 124
15. C. Beeri, R. Fagin, and J.H. Howard A complete axiomatization for functional and multivalued dependencies in database relations Internat. Conf. on Management of Data (SIGMOD) 1977 ACM New York, NY 47 61
16. C. Beeri, A.O. Mendelzon, Y. Sagiv, and J.D. Ullman Equivalence of relational database schemes SIAM J. Comput. 10 2 1981 352 370
17. P.A. Bernstein, Normalisation and functional dependencies in the relational data base model, Technical Report CSRG-60, University of Toronto, 1975.
18. P.A. Bernstein Synthesizing third normal form relations from functional dependencies Trans. Database Systems (TODS) 1 1976 277 298
19. P.A. Bernstein, and N. Goodman What does Boyce-Codd normal form do Proc. Internat. Conf. on Very Large Data Bases (VLDB) 1980 245 259
20. G. Berry, and G. Boudol The chemical abstract machine Theoret. Comput. Sci. 96 1992 217 248
21. J. Biskup, Database schema design theory: achievements and challenges, in: Information Systems and Data Management, Lecture Notes in Computer Science, vol. 1066, Springer, Berlin, 1995, pp. 14-44.
22. J. Biskup, Achievements of relational database schema design theory revisited, in: Semantics in Databases, Lecture Notes in Computer Science, vol. 1358, Springer, Berlin, 1998, pp. 29-54.
23. M.F. Bommel, and G.E. Weddell Reasoning about equations and functional dependencies on complex objects Trans. Knowledge Data Eng. 6 3 1994 455 469
24. T. Bray, J. Paoli, C.M. Sperberg-McQueen, E. Maler, F. Yergeau, Extensible markup language (XML) 1.0, third ed., W3C Recommendation 04 February 2004. 〈 http://www.w3.org/TR/2004/REC-xml-20040204/ 〉 (2004).
25. F. Bry, and P. Kröger A computational biology database digest: data, data analysis, and data management Distributed Parallel Databases 13 1 2003 7 42
26. P. Buneman, W. Fan, J. Siméon, and S. Weinstein Constraints for semi-structured data and XML SIGMOD Record 30 1 2001 47 54
27. C. Calude, G. Paun, G. Rozenberg, A. Salomaa (Eds.), Multiset processing, mathematical, computer science, and molecular computing points of view, in: Workshop on Multiset Processing, WMP 2000, Curtea de Arges, Romania, August 21-25, 2000, Lecture Notes in Computer Science, vol. 2235, Springer, Berlin, 2001.
28. P.P. Chen The entity-relationship model: towards a unified view of data Trans. Database Systems (TODS) 1 1976 9 36
29. P.P. Chen English sentence structure and entity-relationship diagrams Inform. Sci. 29 1983 127 149
30. E.F. Codd, Further normalization of the database relational model, in: Courant Computer Science Symposia, vol. 6: Data Base Systems, Prentice-Hall, Englewood Cliffs, NJ, 1972, pp. 33-64.
31. E.F. Codd Recent investigations in relational database system Proc. IFIP Conf. 1974 1017 1021
32. B. Courcelle Fundamental properties of infinite trees Theoret. Comput. Sci. 25 1983 95 169
33. A. Dovier, A. Policriti, and G. Rossi A uniform axiomatic view of lists, multisets, and sets, and the unification algorithm Fund. Inform. 36 2/3 1998 201 234
34. K. Engel Sperner Theory 1997 Cambridge University Press Cambridge
35. R. Fagin Multivalued dependencies and a new normal form for relational databases Trans. Database Systems (TODS) 2 3 1977 262 278
36. R. Fagin A normal form for relational databases that is based on domains and keys Trans. Database Systems (TODS) 6 3 1981 387 415
37. R. Fagin, and M.Y. Vardi The theory of data dependencies: a survey Mathematics of Information Processing: Proc. Symp. in Applied Mathematics 1986 American Mathematical Society Providence, RI 19 71
38. W. Fan, and L. Libkin On XML integrity constraints in the presence of DTDs J. ACM 49 3 2002 368 406
39. W. Fan, and J. Siméon Integrity constraints for XML J. Comput. System Sci. 66 1 2003 254 291
40. D.H. Fishman, D. Beech, H.P. Cate, E.F. Chow, T. Connors, J.W. Davis, N. Derret, C.G. Hoch, W. Kent, P. Lyngbæk, B. Mahbod, M.-A. Neimat, T.A. Ryan, and M.-C. Shan IRIS: an object-oriented database management system Trans. Office Inform. Systems 5 1 1987 48 69
41. G. Gardarin, J.-P. Cheiney, G. Kiernan, D. Pastre, and H. Stora Managing complex objects in an extensible relational DBMS Proc. Internat. Conf. on Very Large Data Bases 1989 Morgan Kaufmann Los Altos, CA 55 65
42. C.S. Hara, and S.B. Davidson Reasoning about nested functional dependencies Principles of Database Systems (PODS) 1999 ACM New York 91 100
43. S. Hartmann On the implication problem for cardinality constraints and functional dependencies Ann. Math. Artificial Intelligence 33 2001 253 307
44. S. Hartmann Decomposing relationship types by pivoting and schema equivalence Data Knowledge Eng. 39 2001 75 99
45. S. Hartmann, S. Link, More functional dependencies for XML, in: Advances in Databases and Information Systems, Seventh East European Conf. ADBIS 2003, Dresden, Germany, September 3-6, Lecture Notes in Computer Science, vol. 2798, Springer, Berlin, 2003, pp. 355-369.
46. S. Hartmann, S. Link, Normalisation in the presence of lists, in: 15th Australasian Database Conf. (ADC), Conf. in Research and Practice in Information Technology, vol. 27, Australian Computer Society, 2004, pp. 53-64.
47. S. Hartmann, and S. Link Multi-valued dependencies in the presence of lists Proc. 23rd Internat. Conf. on Principles of Database Systems (PODS) 2004 ACM New York, NY 330 341
48. S. Hartmann, and S. Link A membership algorithm for functional and multi-valued dependencies in the presence of lists Electron. Notes Theoret. Comput. Sci. (ENTCS) 91 2004 171 194
49. S. Hartmann, S. Link, On functional dependencies in advanced data models, Electron. Notes Theoret. Comput. Sci. (ENTCS) 84.
50. S. Hartmann, S. Link, M. Kirchberg, A subgraph-based approach towards functional dependencies for XML, in: Proc. Seventh World-Multiconf. on Systemics, Cybernetics and Informatics (SCI), Computer Science and Engineering II, vol. IX, Orlando, Florida, USA, July 27-30, 2003, pp. 200-205.
51. S. Hartmann, S. Link, K.-D. Schewe, A new normal form for conceptual databases, in: Y. Kiyoki, E. Kawaguchi, H. Jaakkola, H. Kangassalo (Eds.), Information Modelling and Knowledge Bases XV, 13th European-Japanese Conf. on Information Modelling and Knowledge Bases (EJC 2003), Kitakyushu, Japan, June 3-6, 2003, Frontiers in Artificial Intelligence and Applications, vol. 105, IOS Press, 2004, pp. 93-110.
52. S. Hartmann, S. Link, K.-D. Schewe, Reasoning about functional and multi-valued dependencies in the presence of lists, in: Third Internat. Symp. on Foundations of Information and Knowledge Systems (FoIKS), Lecture Notes in Computer Science, vol. 2942, Springer, Berlin, 2004, pp. 134-154.
53. R. Hull, R. King, Semantic database modeling: survey, applications and research issues, ACM Comput. Surveys 19(3).
54. G. Lamperti, M. Melchiori, M. Zanella, On multisets in database systems, in: Workshop on Multiset Processing (WMP), Lecture Notes in Computer Science, vol. 2235, Springer, Berlin, 2000, pp. 147-216.
55. M. Lee, T. Ling, W. Low, Designing functional dependencies for XML, in: Advances in Database Technology - EDBT 2002, Eighth Internat. Conf. on Extending Database Technology, Prague, Czech Republic, March 25-27, Lecture Notes in Computer Science, vol. 2287, Springer, Berlin, 2002, pp. 124-141.
56. M. Levene The Nested Universal Relation Database Model 1992 Springer Berlin
57. M. Levene, and G. Loizou Semantics for null extended nested relations Trans. Database Systems (TODS) 18 3 1993 414 459
58. J. Li, S. Ng, L. Wong, Bioinformatics adventures in database research, in: Proc. Internat. Conf. on Database Theory (ICDT), Lecture Notes in Computer Science, vol. 2572, Springer, Berlin, 2002, pp. 31-46.
59. D. Maier Minimum covers in relational database model J. ACM 27 4 1980 664 674
60. J.C.C. McKinsey, and A. Tarski On closed elements in closure algebras Ann. Math. 47 1946 122 146
61. W.Y. Mok, Y.K. Ng, and D.W. Embley A normal form for precisely charachterizing redundancy in nested relations Trans. Database Systems TODS 21 1996 77 106
62. S. Naqvi, and S. Tsur A Logical Language for Data and Knowledge Bases 1989 Computer Science Press Rockville, MD
63. Z.M. Özsoyoglu, and L.Y. Yuan A new normal form for nested relations Trans. Database Systems TODS 12 1987 111 136
64. J. Paredaens, P. De Bra, M. Gyssens, and D. Van Gucht The Structure of the Relational Database Model 1989 Springer Berlin
65. J. Richardson Supporting lists in a datamodel Proc. Internat. Conf. on Very Large Data Bases (VLDB) 1992 127 192
66. K.-D. Schewe, and B. Thalheim Fundamental concepts of object oriented databases Acta Cybernet. 11 4 1993 49 85
67. M.H. Scholl, H.-J. Schek, A relational object model, in: Proc. of Internat. Conf. on Database Theory (ICDT), Lecture Notes Series, Springer, Berlin, 1990, pp. 89-105.
68. P. Seshadri, M. Livny, and R. Ramakrishnan The design and implementation of sequence database system Proc. Internat. Conf. on Very Large Data Bases (VLDB) 1996 99 110
69. D. Suciu On database theory and XML SIGMOD Record 30 3 2001 39 45
70. Z. Tari, J. Stokes, and S. Spaccapietra Object normal forms and dependency constraints for object-oriented schemata Trans. Database Systems (TODS) 22 1997 513 569
71. B. Thalheim Dependencies in Relational Databases 1991 Teubner Stuttgart
72. B. Thalheim Entity-Relationship Modeling: Foundations of Database Technology 2000 Springer New York, NY
73. A.M. Tjoa, L. Berger, Transformation of requirement specifications expressed in natural language into an EER model, in: Entity-Relationship Approach, Lecture Notes in Computer Science, vol. 823, Springer, Berlin, 1993, pp. 206-217.
74. M.Y. Vardi Fundamentals of dependency theory E. Börger Trends in Theoretical Computer Science 1987 Computer Science Press Rockville, MD 171 224
75. V. Vianu A web odyssey: from Codd to XML PODS 2001 ACM New York, NY 1 15
76. M. Vincent, The semantic justification for normal forms in relational database design, Ph.D. Thesis, Monash University, Melbourne, Australia, 1994.
77. M. Vincent, J. Liu, Multivalued dependencies in XML, in: British National Conf. on Databases, Lecture Notes in Computer Science, vol. 2712, Springer, Berlin, 2003, pp. 4-18.
78. M. Vincent, J. Liu, Functional dependencies for XML, in: M.O.X. Zhou, Y. Zhang (Eds.), Web Technologies and Applications: Fifth Asia-Pacific Web Conf. APWeb 2003, Xian, China, April 23-25, 2003. Proc., Lecture Notes in Computer Science, vol. 2642, Springer, Berlin, 2003, pp. 22-34.
79. M. Vincent, J. Liu, C. Liu, A redundancy free 4NF for XML, in: Proc. XML Database Symp., Lecture Notes in Computer Science, vol. 2824, Springer, Berlin, 2003, pp. 254-266.
80. M. Vincent, and B. Srinivasan Redundancy and the justification of fourth normal form in relational databases Internat. J. Found. Comput. Sci. 4 4 1993 355 365
81. M. Vincent, and B. Srinivasan Update anomalies and the justification of fourth normal form in relational databases Inform. Sci. 81 1994 87 102
82. G. Vossen A new characterization of FD implication with an application to update anomalies Inform. Process. Lett. 29 1988 131 135
83. G.E. Weddell Reasoning about functional dependencies generalized for semantic data models Trans. Database Systems (TODS) 17 1 1992 32 64