Elimination of Cuts in First-order Finite-valued Logics

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Abstract
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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Archival date: 2017-10-10
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Expanding the Universe of Universal Logic.James Trafford - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.

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