Relational Theories with Null Values and Non-Herbrand Stable Models
This work addresses the challenge of handling incomplete data in databases for researchers and practitioners in knowledge representation and logic programming, though it appears incremental as it builds on existing theories and methods.
The paper tackles the problem of representing incomplete information in relational databases by showing that any generalized relational theory with null values can be converted into an equivalent logic program, enabling model generation using answer set programming methods.
Generalized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption.