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The finite model property for various fragments of intuitionistic linear logic

  • Mitsuhiro Okada (a1) and Kazushige Terui (a2)

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].

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[1] V. Michele Abrusci , Non-commutative intuitionistic linear propositional logic, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 36 (1990), pp. 297318.

[2] W. Buszkowski , The finite model property for BCI and related systems, Studia Logica, vol. 57 (1996), pp. 303323.

[3] Jean-Yves Girard , Linear logic, Theoretical Computer Science, vol. 50 (1987), pp. 1102.

[5] Alexei P. Kopylov , Decidability of linear affine logic, Tenth Annual IEEE Symposium on Logic in Computer Science (San Diego, California) ( D. Kozen , editor), 061995, pp. 496504.

[8] Robert K. Meyer and H. Ono , The finite model property for BCK and BCIW, Studia Logica, vol. 53 (1994), pp. 107118.

[9] Mitsuhiro Okada , Phase semantics for higher order completeness, cut-elimination and normalization proofs, Theoretical Computer Science, to appear, 111999.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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