Studia Logica 61 (1):7-33 (1998)

Authors
Richard Zach
University of Calgary
Abstract
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.
Keywords finite-valued logic  labeled calculus  signed formula  sets-as-signs
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Reprint years 2004
DOI 10.1023/A:1005022012721
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The Logics of Strict-Tolerant Logic.Eduardo Barrio, Lucas Rosenblatt & Diego Tajer - 2015 - Journal of Philosophical Logic 44 (5):551-571.
The Power of Belnap: Sequent Systems for SIXTEEN ₃. [REVIEW]Heinrich Wansing - 2010 - Journal of Philosophical Logic 39 (4):369 - 393.
Expanding the Universe of Universal Logic.James Trafford - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.

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