Cut-free ordinary sequent calculi for logics having generalized finite-valued semantics

Logica Universalis 1 (1):41-70 (2007)
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.
Keywords Finite-valued logic   n-sequent systems  ordinary system calculi  soundness  completeness  non-deterministic matrices  cut elimination
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