A construction principle for natural deduction systems for arbitrary finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically 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.
Baaz, Matthias, Christian G. Fermüller, and Richard Zach. 1993. “Systematic Construction of Natural Deduction Systems for Many-Valued Logics.” In 23rd International Symposium on Multiple-Valued Logic. Proceedings, 208–13. Los Alamitos: IEEE Press. https://doi.org/10.1109/ISMVL.1993.289558.