The finite model property for various fragments of intuitionistic linear logic

Journal of Symbolic Logic 64 (2):790-802 (1999)
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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 FL c and GL - c of Ono [11], that will settle the open problems stated in Ono [12]

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References found in this work

Non-commutative intuitionistic linear logic.V. Michele Abrusci - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (4):297-318.
Non‐commutative intuitionistic linear logic.V. Michele Abrusci - 1990 - Mathematical Logic Quarterly 36 (4):297-318.

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