Journal of Logic, Language and Information 9 (1):5-29 (2000)
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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Keywords | analytic sequent calculus infinite-valued Łukasiewicz logic many-valued logic McNaughton's theorem |
Categories | (categorize this paper) |
Reprint years | 2004 |
DOI | 10.1023/A:1008311022292 |
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References found in this work BETA
A Theorem About Infinite-Valued Sentential Logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
A Theorem About Infinite-Valued Sentential Logic.Robert Mcnaughton - 1951 - Journal of Symbolic Logic 16 (3):227-228.
Bounded Contraction and Gentzen-Style Formulation of Łukasiewicz Logics.Andreja Prijatelj - 1996 - Studia Logica 57 (2-3):437 - 456.
Many-Valued Logics of Extended Gentzen Style II.Moto-O. Takahashi - 1970 - Journal of Symbolic Logic 35 (4):493-528.
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Citations of this work BETA
Giles’s Game and the Proof Theory of Łukasiewicz Logic.Christian G. Fermüller & George Metcalfe - 2009 - Studia Logica 92 (1):27 - 61.
Proving Properties of Binary Classification Neural Networks Via Łukasiewicz Logic.Sandro Preto & Marcelo Finger - forthcoming - Logic Journal of the IGPL.
Logic, Language, Information and Computation: 15th International Workshop, Wollic 2008 Edinburgh, Uk, July 1-4, 2008, Proceedings. [REVIEW]Wilfrid Hodges & Ruy de Queiroz (eds.) - 2008 - Berlin and New York: Springer.
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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