Elimination of cuts in first-order finite-valued logics

Journal of Information Processing and Cybernetics 29 (1993) 333–355
(with Matthias Baaz and Christian G. Fermüller)

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

Note Errata section at very end for corrected inference rules for the Dunn-Belnap (FDE) system used as an example in the paper.