Labeled calculi and finite-valued logics

Studia Logica 61 (1):7-33 (1998)
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A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number of truth values, and it is shown that this bound is tight.
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The Logics of Strict-Tolerant Logic.Barrio, Eduardo; Rosenblatt, Lucas & Tajer, Diego
Hypersequent and Display Calculi – a Unified Perspective.Ciabattoni, Agata; Ramanayake, Revantha & Wansing, Heinrich
Truth-Values as Labels: A General Recipe for Labelled Deduction.Sernadas, Cristina; Viganò, Luca; Rasga, João & Sernadas, Amílcar

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