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Studia Logica

, Volume 61, Issue 1, pp 7–33

# Labeled Calculi and Finite-Valued Logics

• Matthias Baaz
• Christian G. Fermüller
• Gernot Salzer
• Richard Zach
Article

## 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 (sets-as-signs). 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.

finite-valued logic labeled calculus signed formula sets-as-signs

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## Copyright information

© Kluwer Academic Publishers 1998

## Authors and Affiliations

• Matthias Baaz
• 1
• Christian G. Fermüller
• 1
• Gernot Salzer
• 1
• Richard Zach
• 1
1. 1.Institut für Algebra und Diskrete MathematikTechnische Universität WienViennaAustria

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