Algebraic logic in database state description

The Halmos (polyadic) algebra is a notion introduced by Halmos as a tool in the algebraization of the first order predicate calculus. This paper shows how Halmos's theory is used for the definition of algebraic model of a relational database. The model allows, in particular, to develop a formal algebraic approach to the definition of a database state description. The description is based on the notion of filters in Halmos algebras, closely related to the problem of derivability in Halmos algebras and first order language. In this paper, connections between these notions are studied. Using some results on categoricity and D-categoricity of a set of formulas, several examples of database state descriptions are built.