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Systematic Construction of Natural Deduction Systems for Many-valued Logics: Extended Report

Matthias Baaz, Christian G. Fermüller, Richard Zach

Abstract

We exhibit a construction principle for natural deduction systems for arbitrary finitely-many-valued first order logics. These systems are systematically obtained from sequent calculi, which in turn can be extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness and normal form theorems for the natural deduction systems.

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Key concepts: Soundness, Sequent, Natural deduction, Sequent calculus, Completeness (order theory), Mathematics, Calculus (dental), Cut-elimination theorem