Incomplete relational model for formal treatmentof partial information

Abstract

Currently in many applications, database systems inevitably contain null values because of a lack of complete information about the world of interest. Naturally, it is necessary to have some way of handling incompleteness in such environment. Incomplete information can be represented by the notion of partial information to represent incomplete information, in the sense that the value of an attribute can be a subset of its domain. For exploring the formal treatment of partial information, this thesis represents partial information as the entry for an attribute of a tuple in relational framework, and name it as the incomplete relational model. The incomplete relational model represents not only known information, but also partial information about uncertain facts. By this model, two types of results to a given query Q can be expected. One is the set of tuples which truely satisfy the query Q. The other is the set of tuples which may implicitly satisfy Q, that is, all tuples except the tuples which are not definitely satisfying Q. These types of response can support more wide range of queries against incomplete relations. To establish theoretical basis for those responses, an extended relational algebra is defined, whose semantics is restricted to this model. Based on the notion of weak satisfiability of the constraints, maybe functional dependency is formalized. Also, the procedures for handling the evolution of partial information using maybe functional dependency are described. Since the truth-functionality is not pertinent during the evaluation of gueries against incomplete relations, that is, the predicate expression against incomplete relation does not have the same interpretation as the logical composition of all its atomic predicates, the nontruth-functionality is formally studied. In addition, an abstract procedure for query processing is also discussed.