Belnap-Dunn logic and query answering in inconsistent databases with null values

TL;DR

This paper introduces an expanded Belnap-Dunn logic for relational databases, enabling consistent query answering in the presence of inconsistencies and null values without repairs, with all notions being decidable.

Contribution

It extends Belnap-Dunn logic to handle inconsistent and null-valued databases, providing a logical framework for consistent query answering without repairs.

Findings

Defined a notion of consistent query answer without database repairs

Extended Belnap-Dunn logic for database applications

All query answering notions are decidable

Abstract

This paper concerns an expansion of first-order Belnap-Dunn logic, named $\mathrm{BD}^{\supset,\mathsf{F}}$, and an application of this logic in the area of relational database theory. The notion of a relational database, the notion of a query applicable to a relational database, and several notions of an answer to a query with respect to a relational database are considered from the perspective of this logic, taking into account that a database may be an inconsistent database or a database with null values. The chosen perspective enables among other things the definition of a notion of a consistent answer to a query with respect to a possibly inconsistent database without resort to database repairs. For each of the notions of an answer considered, being an answer to a query with respect to a database of the kind considered is decidable.