Finiteness in infinite-valued łukasiewicz logic

Journal of Logic, Language and Information 9 (1):5-29 (2000)
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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

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References found in this work

Algebraic foundations of many-valued reasoning.Roberto Cignoli - 1999 - Boston: Kluwer Academic Publishers. Edited by Itala M. L. D'Ottaviano & Daniele Mundici.
A theorem about infinite-valued sentential logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
Elimination of Cuts in First-order Finite-valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
A Theorem About Infinite-Valued Sentential Logic.Robert Mcnaughton - 1951 - Journal of Symbolic Logic 16 (3):227-228.

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