On syntax and semantics related to incomplete information databases

Abstract

We propose a mathematical model of a database with incomplete information, which we call the N-system. Basically speaking, such a system stores information concerning properties of some objects. The information may be incomplete in that it may be known that the object has a property, from the interval <o, �> C <0 , 1>. In the particular case where <u, �> =<0 , 1 > , means that it may be not known whether an object has a property , the N-system is equivalent to Lipski "s system [3] . In another particular case, when <o, �> =< 1 , 1 >. , the N-system presented corresponds to Codd's relational model of databases.

The first level, the level of terms of a query language to communicate with the N-system, is described and its semantics and syntax are defined . A system of axioms , which serves as a basis for equivalent transformations of queries is presented (only for terms). Syntactical and semantic equivalences for terms are defined and completeness properties are shown.