Abstract
Since the introduction of the relational database model, a lot of efforts have been spent to describe conditions under which data decompositions can be achieved. In the past, these conditions were expressed in terms of dependencies. Here, we encapsulate more recent approaches based on partitioning in a categorical framework in order to obtain a very general context to study views and decomposition that is also applicable to complex-object models. Thereto, we use the categorical notion of presheaf. We argue that our model provides a more fundamental perspective on the concept of object-orientedness which compared to relational theory has developed in a rather adhoc manner. In particular, we show that the notion of sheaf yields a characterization for the presence of object-identity.
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References
Alagić S. and Alagić M., Joins as Pullbacks, Proceedings of Third Workshop on Foundations of Models and Languages for Data and Objects, Aigen, 1991, pp. 197–207
Abiteboul S. and Kanellakis P.C., Object Identity as a Query Language Primitive, Proceedings of the 1989 ACM SIGMOD International Conference on the Management of Data, ACM, 1989, pp. 159–173
Arbib M.A. and Manes E.G., Arrows, Structures and Functors, Academic Press, New-York, 1975
Atkinson M. et al., The Object-Oriented Database System Manifesto, Proceedings of the First International Conference on Deductive and Object-Oriented Databases, Kyoto, 1989, pp. 40–57
Barr M. and Wells C., Category Theory for Computing Science, Prentice Hall, 1990
Barr M. and Wells C., Toposes, Triples and Theories, Springer-Verlag, New-York, 1985
Bell J.L., Categories, Toposes and Sets, D. Reidel Publishing Company, Dordrecht, 1982
Beeri C., Fagin R., Maier D., Mendelzon A.O., Ullman J.D., Yannakakis M., Properties of Acyclic Database Schemes, Proceedings of the 13th Ann. ACM Symp. on the Theory of Computing, 1981, pp. 355–362
Cardelli L., A Semantics of Multiple Inheritance, Semantics of Data Types, Lecture Notes of Computer Science 173, Springer-Verlag, 1984
Cosmadakis S.S., Kanellakis P.C., Spyratos N., Partition Semantics for Relations, Proceedings of the 4 th Symposium on Principles of Database Systems, ACM, 1985, pp. 261–275
Codd E.F., A Relational Model of Data for Large Shared Data Banks, Communications of ACM, 13:6, 1970, pp. 377–387
De Bra P., Paredaens J., Conditional Dependencies for Horizontal Decompositions, Proceedings of the 10 th ICALP, Lecture Notes in Computer Science, Volume 154, Springer-Verlag, 1983, pp. 67–82
Fagin R., Yardi M.Y., The Theory of Data Dependencies—An Overview, Proceedings of the 11 th ICALP, Lecture Notes in Computer Science, Volume 172, Springer-Verlag, 1984, pp. 1–22
Gyssens M. and Paredaens J., A Graph-Oriented Object Model for Database End-User Interfaces, Proceedings of the ACM SIGMOD International Conference on Management of Data, Atlantic City, 1990
Hegner S.J., Pairwise-Definable Subdirect Decompositions of General Database Schemata, Proceedings of the Symposium on Mathematical Fundamentals of Database Systems, Rostock, 1991
Lee T.T., An Algebraic Theory of Relational Databases, The Bell System Technical Journal, Vol. 63, nr. 10, 1983
Özsoyoğlu Z.M., Yuan L.-Y., On the Normalization in Nested Relational Databases, in Nested Relations and Complex Objects in Databases, Abiteboul S., Fischer P.C., Schek H.-J., Eds., Lecture Notes in Computer Science, Volume 361, Springer-Verlag, 1989, pp. 243–271
Paredaens J., De Bra P., Gyssens M. and Van Gucht, D., The Structure of the Relational Database Model, EATCS Monographs on Theoretical Computer Science, Volume 17, Springer-Verlag, 1989
Schek H.-J., Scholl M.H., The Relational Model with Relation-Valued Attributes, Information Systems, 11(2), 1986, pp. 137–147
Scholl M.H., Laasch C. and Tresch M., Updatable Views in Object-Oriented Databases, Proceedings of the Second International Conference on Deductive and Object-Oriented Databases, Munich, 1991, pp. 189–207
Thomas S.J., Fischer P.C., Nested Relational Structures, The Theory of Databases, Advances in Computer Research III, P.C. Kanellakis, ed., JAI PRESS, Greenwich, CT, 1986, pp. 269–307
Tuijn C., Gyssens M. and Paredaens J., A Categorical Approach to Object-Oriented Data Modeling, Proceedings of Third Workshop on Foundations of Models and Languages for Data and Objects, Aigen, 1991, pp. 187–196
Weddel G.E., Coburn N., Path Constraints for Graph-Based Data Models: Towards a Unified Theory of Typing Constraints, Equations and Functional Dependencies, Proceedings of the Second International Conference on Deductive and Object-Oriented Databases, Munich, 1991, pp. 312–331
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Tuijn, C., Gyssens, M. (1992). Views and decompositions of databases from a categorical perspective. In: Biskup, J., Hull, R. (eds) Database Theory — ICDT '92. ICDT 1992. Lecture Notes in Computer Science, vol 646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56039-4_35
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DOI: https://doi.org/10.1007/3-540-56039-4_35
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