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.
The MUltlog system will automatically construct many-sided calculi from given truth tables.
An extended version appeared as a Technical Report:
Baaz, Matthias, Christian G. Fermüller, and Richard Zach. 1993. “Systematic Construction of Natural Deduction Systems for Many-Valued Logics. Extended Report.” TUWE–185.2–BFZ.1–93. Technische Universität Wien, Institut für Computersprachen E185.2.