Elimination of cuts in first-order finite-valued logics

Baaz, Matthias, Christian G. Fermüller, and Richard Zach. 1993. “Elimination of Cuts in First-Order Finite-Valued Logics.” Journal of Information Processing and Cybernetics EIK 29 (6): 333–55. https://doi.org/10.11575/PRISM/38801.

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.

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