On semantic issues connected with incomplete information databases

Abstract

Various approaches to interpreting queries in a database with incomplete information are discussed. A simple model of a database is described, based on attributes which can take values in specified attribute domains. Information incompleteness means that instead of having a single value of an attribute, we have a subset of the attribute domain, which represents our knowledge that the actual value, though unknown, is one of the values in this subset. This extends the idea of Codd's null value, corresponding to the case when this subset is the whole attribute domain. A simple query language to communicate with such a system is described and its various semantics are precisely defined. We emphasize the distinction between two different interpretations of the query language—the external one, which refers the queries directly to the real world modeled in an incomplete way by the system, and the internal one, under which the queries refer to the system's information about this world, rather than to the world itself. Both external and internal interpretations are provided with the corresponding sets of axioms which serve as a basis for equivalent transformations of queries. The technique of equivalent transformations of queries is then extensively exploited for evaluating the interpretation of (i.e. the response to) a query.