Cylindric algebras and relational databases
نویسنده
چکیده
An interpretation of the relational data model and various dependencies is given within the framework of cylindric algebras. It turns out that there is a natural translation of relational databases into cylindric set lattices, and that Codd’s relational operators have a simple interpretation in these structures. Consequently, various database constraints can be expressed in the equational language, and recent results in equational logic have been able to shed some light on the expressiveness and axiomatizability of these constraints.
منابع مشابه
Cylindric structures and dependencies in relational databases
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. We will consider project-join dependencies and the corresponding class of cylindric semilattices. We will also look at Cosmadakis (1987) who introduces cylindric dependencies, and makes seve...
متن کاملAn Application of Relation Algebra to Lexical Databases
This paper presents an application of relation algebra to lexical databases. The semantics of knowledge representation formalisms and query languages can be provided either via a set-theoretic semantics or via an algebraic structure. With respect to formalisms based on n-ary relations (such as relational databases or power context families), a variety of algebras is applicable. In standard rela...
متن کاملConnections between cylindric algebras and relation algebras
We investigate the class SRaCAn for 4 n < ! and survey some recent results. We see that RAn | the subalgebras of relation algebras with relational bases | is too weak, and that the class of relation algebras whose canonical extension has an n-dimensional cylindric basis is too strong to deene the class. We introduce the notion of an n-dimensional hyperbasis and show that for any relation algebr...
متن کاملUniversal (and Existential) Nulls
Incomplete Information research is quite mature when it comes to so called existential nulls, where an existential null is a value stored in the database, representing an unknown object. For some reason universal nulls, that is, values representing all possible objects, have received almost no attention. We remedy the situation in this paper, by showing that a suitable finite representation mec...
متن کاملAtom canonicity, and omitting types in temporal and topological cylindric algebras
We study what we call topological cylindric algebras and tense cylindric algebras defined for every ordinal α. The former are cylindric algebras of dimension α expanded with S4 modalities indexed by α. The semantics of representable topological algebras is induced by the interior operation relative to a topology defined on their bases. Tense cylindric algebras are cylindric algebras expanded by...
متن کامل