Bounded contraction and Gentzen-style formulation of łukasiewicz logics

Studia Logica 57 (2-3):437 - 456 (1996)
In this paper, we consider multiplicative-additive fragments of affine propositional classical linear logic extended with n-contraction. To be specific, n-contraction (n 2) is a version of the contraction rule where (n+ 1) occurrences of a formula may be contracted to n occurrences. We show that expansions of the linear models for (n + 1)- valued ukasiewicz logic are models for the multiplicative-additive classical linear logic, its affine version and their extensions with n-contraction. We prove the finite axiomatizability for the classes of finite models, as well as for the class of infinite linear models based on the set of rational numbers in the interval [0, 1]. The axiomatizations obtained in a Gentzen-style formulation are equivalent to finite and infinite-valued ukasiewicz logics.
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DOI 10.1007/BF00370844
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References found in this work BETA
Natural 3-Valued Logics--Characterization and Proof Theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
Axiom Schemes for M-Valued Propositional Calculi.J. B. Rosser & A. R. Turquette - 1945 - Journal of Symbolic Logic 10 (3):61-82.

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Citations of this work BETA
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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