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 with probability from the interval <a,[3> c <0,1>. In the particular case where <a,[3>=<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 <a,[3>=<1,1> or <a,{3>=<0,0> 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/or equivalent transformations of queries is presented ( only for terms). Syntactical and semantic equivalences for terms are defined and completeness properties are shown.