Paraconsistent logic and query answering in inconsistent databases

ABSTRACT

This paper concerns the paraconsistent logic LPQ^⊃,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 an earlier paper, LPQ^{⊃ ,F} is presented with a sequent-style natural deduction proof system. In this paper, a sequent calculus proof system is presented instead because such proof systems are generally considered more suitable as the basis of proof search procedures than natural deduction proof systems and proof search procedures can serve as the core of algorithms for computing consistent answers to queries.

KEYWORDS:

• Relational database
• inconsistent database
• consistent query answering
• paraconsistent logic
• sequent calculus

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 If we replace the inference rule ¬-R by the inference rule ¬-L in the sequent calculus proof system of ${\mathrm{LPQ}}^{\supset ,\mathsf{F}}(\mathrm{\Sigma })$, then we obtain a sound and complete proof system of the paracomplete analogue of LPQ^⊃,F. The propositional part of that logic (K3^⊃,F) is studied in e.g. Middelburg (2021).