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Sequential calculi for many-valued logics with equality determinant. (English) Zbl 1061.03028

The notion “equality determinant” (a finite set of “designated propositional formulas”) is introduced. It is shown that a propositional finitely-valued logic with equality determinant admits a sequent calculus with the cut-elimination property. Furthermore it is proven that the consequence operations of cut-free versions of such sequent calculi are not algebraizible.

MSC:

03B50 Many-valued logic
03B22 Abstract deductive systems
03F05 Cut-elimination and normal-form theorems
03G25 Other algebras related to logic
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