A Sahlqvist theorem for substructural logic

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

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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Citations of this work

On Sahlqvist Formulas in Relevant Logic.Guillermo Badia - 2018 - Journal of Philosophical Logic 47 (4):673-691.
Modal translation of substructural logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.
The Distributivity on Bi-Approximation Semantics.Tomoyuki Suzuki - 2016 - Notre Dame Journal of Formal Logic 57 (3):411-430.

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References found in this work

A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Semantic analysis of orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
Modal Logic.Marcus Kracht - 2002 - Bulletin of Symbolic Logic 8 (2):299-301.
A Sahlqvist theorem for distributive modal logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1-3):65-102.

View all 19 references / Add more references