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.

翻译：本文关注一阶Belnap-Dunn逻辑的扩张，记为$\mathrm{BD}^{\supset,\mathsf{F}}$，以及该逻辑在关系数据库理论领域中的应用。研究从该逻辑的视角出发，考察了关系数据库的概念、适用于关系数据库的查询概念，以及针对关系数据库的查询回答的若干概念，同时考虑了数据库可能为不一致数据库或含空值数据库的情形。所选取的视角尤其使得能够在不依赖数据库修复的情况下，定义针对可能不一致数据库的查询的一致回答概念。对于所考虑的每种回答概念，判断其是否为针对所考虑类型数据库的查询回答，均为可判定的。