A Sahlqvist theorem for substructural logic

Review of Symbolic Logic 6 (2):229-253 (2013)

In this paper, we establish the first-order definability of sequents with consistent variable occurrence on bi-approximation semantics by means of the Sahlqvist–van Benthem algorithm. Then together with the canonicity results in Suzuki (2011), this allows us to establish a Sahlqvist theorem for substructural logic. Our result is not limited to substructural logic but is also easily applicable to other lattice-based logics
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DOI 10.1017/s1755020313000026
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.
A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
A Sahlqvist Theorem for Distributive Modal Logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1):65-102.

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Citations of this work BETA

On Sahlqvist Formulas in Relevant Logic.Guillermo Badia - 2018 - Journal of Philosophical Logic 47 (4):673-691.
Game-Theoretic Semantics for Non-Distributive Logics.Chrysafis Hartonas - 2019 - Logic Journal of the IGPL 27 (5):718-742.
On Polarity Frames: Applications to Substructural and Lattice-Based Logics.Tomoyuki Suzuki - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 533-552.

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