Relational Theories with Null Values and Non-Herbrand Stable Models

TL;DR

This paper demonstrates how generalized relational theories with null values can be transformed into logic programs, enabling the use of answer set programming to compute models for databases with incomplete information.

Contribution

It introduces a method to convert relational theories with nulls into logic programs, facilitating computational reasoning with incomplete data.

Findings

Equivalent logic programs can represent relational theories with nulls.

Stable models can be computed without assuming unique names.

The approach bridges relational theories and answer set programming.

Abstract

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.