This paper concerns the paraconsistent logic LPQ$^{\supset,\mathsf{F}}$ and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent answer to a query with respect to a possibly inconsistent relational database are considered from the perspective of this logic. This perspective enables among other things the definition of a consistent answer to a query with respect to a possibly inconsistent database without resort to database repairs. In a previous paper, LPQ$^{\supset,\mathsf{F}}$ is presented with a sequent-style natural deduction proof system. In this paper, a sequent calculus proof system is presented because it is common to use a sequent calculus proof system as the basis of proof search procedures and such procedures may form the core of algorithms for computing consistent answers to queries.

翻译：本文关注次协调逻辑LPQ$^{\supset,\mathsf{F}}$及其在关系数据库理论领域的应用。从该逻辑的视角出发，对关系数据库、适用于关系数据库的查询、以及针对可能不一致的关系数据库的查询一致性回答等概念进行了考察。这一视角使得在不借助数据库修复的情况下定义针对可能不一致数据库的查询一致性回答成为可能。在先前的一篇论文中，LPQ$^{\supset,\mathsf{F}}$已配备了一个基于矢列式的自然演绎证明系统。本文则进一步给出一个矢列演算证明系统，这是因为矢列演算证明系统常被用作证明搜索程序的基础，而此类程序可构成计算查询一致性回答算法的核心。