Bounded contraction and Gentzen-style formulation of Łukasiewicz logics
✍ Scribed by Andreja Prijatelj
- Publisher
- Springer Netherlands
- Year
- 1996
- Tongue
- English
- Weight
- 834 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0039-3215
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✦ Synopsis
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 Lukasiewicz 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 Lukasiewicz logics.