Intuitionistic Interpretation of Deductive Databases with Incomplete Information

Dong, F. and L.V.S. Lakshmanan, Intuitionistic interpretation of deductive databases with incomplete information, Theoretical Computer Science 133 (1994) 267-306. The aim of this paper is to build the relationship between deductive databases with incomplete information and hypothetical reasoning using embedded implications. We first consider the semantics of deductive databases with incomplete information in the form of null values. We motivate query answering against a deductive database with nulls as the problem of extracting the maximal information from a (deductive) database in response to queries, and formalize this in the form of conditional answers in a (syntactic) higher-order logic. We give a fixpoint semantics to deductive databases with nulls, and examine the relationship between existing recursive query processing techniques and the proof procedure for deductive databases with nulls. We then examine hypothetical reasoning using embedded implications and develop an intuitionistic model semantics for embedded implications with integrity constraints. Finally, we illustrate by example a method for transforming embedded implications into deductive databases with nulls. This result shows that the important functionality of hypothetical reasoning can be implemented within the framework of deductive databases with null values.