Optimal finite-valued covers of Hilbert calculi are computable, and a calculus has an effective sequential finite-valued approximation exactly when its theorem set is decidable.
Studia Logica 61 (1998) 7–33
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Effective Finite-Valued Approximations of General Propositional Logics
Optimal finite-valued covers of Hilbert calculi are computable, and a calculus has an effective sequential finite-valued approximation exactly when its theorem set is decidable.