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The Finite Model Property for Various Fragments of Intuitionistic Linear Logic

Mitsuhiro Okada and Kazushige Terui
The Journal of Symbolic Logic
Vol. 64, No. 2 (Jun., 1999), pp. 790-802
DOI: 10.2307/2586501
Stable URL: http://www.jstor.org/stable/2586501
Page Count: 13
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The Finite Model Property for Various Fragments of Intuitionistic Linear Logic
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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 GL-c of Ono [11], that will settle the open problems stated in Ono [12].

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