Abstract
Traditional database query languages are based on set theory and crisp logic. Many applications, however, need similarity or retrieval-like queries producing results with truth values from the interval [0,1]. Such truth values can be regarded as continuous membership values of tuples expressing how strongly a query is matched. Formulating queries by applying existing similarity relational algebras means to express the user’s need in a procedural manner. In order to support a declarative way of formulating queries, we generalize the classical relational domain calculus by incorporating fuzzy operations and user weights. Besides defining syntax and semantics we show how to map any calculus expression onto a corresponding similarity algebra expression. In this way, we present a theoretical foundation for a declarative query language combining retrieval functionality and traditional relational databases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zadeh, L.A.: Fuzzy Logic. IEEE Computer 21, 83–93 (1988)
Codd, E.F.: A Relational Model of Data for Large Shared Data Banks. Communications of the ACM 13, 377–387 (1970)
Codd, E.F.: A Database Sublanguage Founded on the Relational Calculus. In: ACM SIGFIDET Workshop on Data Description, Access and Control, pp. 35–61 (1971)
Codd, E.F.: Relational Completeness of Data Base Sublanguages. In: Rustin, R. (ed.) Data Base Systems, vol. 6, pp. 65–98. Prentice Hall, Englewood Cliffs (1972)
Codd, E.F.: Relational Database: A Practical Foundation for Productivity. Communications of the ACM 25, 109–117 (1982)
Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)
Ullman, J.D.: Principles of Database Systems. Computer Science Press, Rockville (1982)
Biskup, J.: Grundlagen von Informationssystemen. Vieweg, Braunschweig (1995)
Schmitt, I., Schulz, N.: Safe Reduction of Similarity Calculus to Similarity Algebra. Preprint, Fakultät für Informatik, Universität Magdeburg (to appear)
Fagin, R., Wimmers, E.L.: A Formula for Incorporating Weights into Scoring Rules. Special Issue of Theoretical Computer Science (2000)
Schulz, N., Schmitt, I.: Relevanzwichtung in komplexen Ähnlichkeitsanfragen. In: Weikum, G., Schöning, H., Rahm, E. (eds.) Datenbanksysteme in Business, Technologie und Web, BTW’03, 10. GI-Fachtagung, Leipzig, Bonn, Gesellschaft für Informatik, Februar 2003. Lecture Notes in Informatics (LNI), vol. P-26, pp. 187–196 (2003)
Kießling, W.: Foundations of preferences in database systems. In: Proceedings of the 28th International Conference on Very Large Databases (VLDB), Hong Kong, China, pp. 311–322 (2002)
Bolloju, N.: A Calculus for Fuzzy Queries on Fuzzy Entity-Relationship Model. Technical Report 94/26, Department of Information Systems at the City Polytechnic of Hong Kong (1994)
Galindo, J., Medina, J.M., Pons, O., Cubero, J.C.: A Server for Fuzzy SQL Queries. In: Andreasen, T., Christiansen, H., Larsen, H.L. (eds.) FQAS 1998. LNCS (LNAI), vol. 1495, pp. 164–174. Springer, Heidelberg (1998)
Takahashi, Y.: Fuzzy Database Query Languages and Their Relational Completeness Theorem. IEEE Transaction on Knowledge and Data Engineering 5, 122–125 (1993)
Adali, S., Bonatti, B., Sapino, M.L., Subrahmanian, V.S.: A Multi-Similarity Algebra. In: ACM SIGMOD Int. Conf. on Management of Data, Seattle, Washington, USA, pp. 402–413 (1998)
Ciaccia, P., Montesi, D., Penzo, W., Trombetta, A.: Imprecision and user preferences in multimedia queries: A generic algebraic approach. In: Schewe, K.-D., Thalheim, B. (eds.) FoIKS 2000. LNCS, vol. 1762, pp. 50–71. Springer, Heidelberg (2000)
Fuhr, N., Rölleke, T.: A Probabilistic Relational Algebra for the Integration of Information Retrieval and Databases Systems. ACM Transactions on Information Systems (TOIS) 15, 32–66 (1997)
Sung, S.Y.: A Linear Transform Scheme for Combining Weights into Scores. Technical report, Rice University (1998)
Schulz, N., Schmitt, I.: A Survey of Weighted Scoring Rules in Multimedia Database Systems. Preprint 7, Fakultät für Informatik, Universität Magdeburg (2002)
Carson, C., Belongie, S., Greenspan, H., Malik, J.: Region-based image querying. In: Proc. of the IEEE Workshop CVPR 1997 Workshop on Content-Based Access of Image and Video Libraries, Puerto Rico, pp. 42–49 (1997)
Ortega, M., Rui, Y., Chakrabarti, K., Porkaew, K., Mehrotra, S., Huang, T.S.: Supporting Ranked Boolean Similarity Queries in MARS. Tkde 10, 905–925 (1998)
Gelder, A.V., Topor, R.W.: Safety and Translation of Relational Calculus Queries. ACM Transactions on Database Systems 16, 235–278 (1991)
Atnafu, S., Brunie, L., Kosch, H.: Similarity-Based Operators and Query Optimization for Multimedia Database Systems. In: Adiba, M.E., Collet, C., Desai, B.C. (eds.) Proceedings of International Database Engineering & Applications Symposium, IDEAS 2001, Grenoble, France, July 16-18, pp. 346–355. IEEE Computer Society, Los Alamitos (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmitt, I., Schulz, N. (2004). Similarity Relational Calculus and Its Reduction to a Similarity Algebra. In: Seipel, D., Turull-Torres, J.M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2004. Lecture Notes in Computer Science, vol 2942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24627-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-24627-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20965-2
Online ISBN: 978-3-540-24627-5
eBook Packages: Springer Book Archive