Null Values in Definite Programs

Abstract : Null values are a special kind of incomplete information that appear in relational database applications. There are several kinds of null values. The one modeled in this paper are those that represent entitles that are known to exist but whose exact values are only known to be in a finite subset of constants in a given domain. For example, if we know that Paul is the fraternal grandfather of John, then we know that there is someone who is the father of John and a child of Paul. If we futher assume that there are only finitely many individuals, then this someone can be represented by the kind of null value mentioned here. In this paper we incorporate these null values into definite programs by using a new kind of symbols called S-constants. We present model theoretic, proof theoretic and fixpoint semantics for such programs. In the above example, given the additional knowledge that Mike is the father of Joe, these semantics allow us to answer the question are John and Joe brothers? by yes, if the (unknown) father of John is Mike. The proposed semantics reduce to the usual semantics for definite programs when there are no null values present.