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

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.