Abstract
In this paper, we explore the precise connection between dependencies in relational databases and variants of cylindric algebras, and apply recent algebraic results to problems of axiomatizing dependencies. First, we will consider project-join dependencies and the corresponding class of (representable) cylindric semilattices. Since representable cylindric semilattices have a non-finitely axiomatizable quasi-equational theory, there is no finite axiomatization for n-dimensional unrestricted project-join dependencies. Then we will look at Cosmadakis (in: A.K. Chandra (Ed.), Proc. 28th Annual Symp. on Foundations of Computer Science, IEEE Computer Society Press, Los Angeles, CA, 1987, pp. 411–420) who introduces cylindric dependencies, and makes several claims regarding the structural properties of these dependencies. Using the above-mentioned precise connection, we show that recent algebraic investigations of cylindric lattices provide counterexamples to Cosmadaki's claim that cylindric dependencies are finitely (schema) axiomatizable.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.