Abstract.
The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.
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Avron, A., Ben-Naim, J. & Konikowska, B. Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics. Log. univers. 1, 41–70 (2007). https://doi.org/10.1007/s11787-006-0003-6
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DOI: https://doi.org/10.1007/s11787-006-0003-6