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The finite model property for various fragments of intuitionistic linear logic

Published online by Cambridge University Press:  12 March 2014

Mitsuhiro Okada  and
Kazushige Terui
Mitsuhiro Okada
Affiliation:
Department of Philosophy, Keio University, 2–15–45 Mita, Minatoku, Tokyo 108, Japan E-mail: [email protected]
Kazushige Terui
Affiliation:
Department of Philosophy, Keio University, 2–15–45 Mita, Minatoku, Tokyo 108, Japan E-mail: [email protected]
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Abstract

Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction. and for its intuitionistic version (ILLC). The finite model property for related substructural logics also follow by our method. In particular, we shall show that the property holds for all of FL and GL−-systems except FLc and of Ono [11], that will settle the open problems stated in Ono [12].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 790 - 802
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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