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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DOI | 10.2307/2586501 |
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References found in this work BETA
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.
The Finite Model Property for BCI and Related Systems.Wojciech Buszkowski - 1996 - Studia Logica 57 (2-3):303 - 323.
The Finite Model Property for BCK and BCIW.Robert K. Meyer & Hiroakira Ono - 1994 - Studia Logica 53 (1):107 - 118.
Citations of this work BETA
Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Studia Logica 83 (1-3):279-308.
Algebraic Proof Theory for Substructural Logics: Cut-Elimination and Completions.Agata Ciabattoni, Nikolaos Galatos & Kazushige Terui - 2012 - Annals of Pure and Applied Logic 163 (3):266-290.
Structural Completeness in Substructural Logics.J. S. Olson, J. G. Raftery & C. J. Van Alten - 2008 - Logic Journal of the IGPL 16 (5):453-495.
The Logic of Resources and Capabilities.Marta Bílková, Giuseppe Greco, Alessandra Palmigiano, Apostolos Tzimoulis & Nachoem Wijnberg - 2018 - Review of Symbolic Logic 11 (2):371-410.
Cut Elimination and Strong Separation for Substructural Logics: An Algebraic Approach.Nikolaos Galatos & Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (9):1097-1133.
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