Syntactic decision procedures in information systems

There are a number of algebraic models of information systems. They have been proposed by Codd (1972), Salton (1968), Scott (1970) and others. We deal here with a model which is the basis of a rough set investigations (Orlowska, 1984; Pawlak, 1982; Pawlak, 1984). This model was proved in (Marek, 1985) to be equivalent with the Codd's model of relational database with one schema. We focus here on purely syntactical problems within this model. In particular we point out problems which can be solved using the automatic syntactic methods. We do it by first constructing, for a given system S its description language ℒ_S. Then we define a set of a Gentzen-like (Gentzen, 1934) transformation rules for its terms and describe an easy programmable procedure which generates the answers for queries submitted to the system. We show how to extend this procedure to a procedure for generating the equivalent normal form of a given term. This leads to a method of constructing not only definable sets within a given system, but also all its elementary components.