Abstract
In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same notion in a suitable finite set of finite-valued ukasiewicz logics. Finally, we define an analytic and internal sequent calculus for infinite-valued ukasiewicz logic
Keywords analytic sequent calculus  infinite-valued Łukasiewicz logic  many-valued logic  McNaughton's theorem
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Reprint years 2004
DOI 10.1023/A:1008311022292
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Mathematical Fuzzy Logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.
Linear Logic and Lukasiewicz ℵ0- Valued Logic: A Logico-Algebraic Study.Jayanta Sen & M. K. Chakraborty - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):313-329.

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