Logica Universalis 13 (1):77-99 (2019)

Abstract
We present dualities for implicative and residuated lattices. In combination with our recent article on a discrete duality for lattices with unary modal operators, the present article contributes in filling in a gap in the development of Orłowska and Rewitzky’s research program of discrete dualities, which seemed to have stumbled on the case of non-distributive lattices with operators. We discuss dualities via truth, which are essential in relating the non-distributive logic of two-sorted frames with their sorted, residuated modal logic, as well as full Stone duality for residuated lattices. Our results have immediate applications to the semantics of related substructural logical calculi.
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DOI 10.1007/s11787-018-0217-4
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References found in this work BETA

Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
Stone Duality for Lattice Expansions.Chrysafis Hartonas - 2018 - Logic Journal of the IGPL 26 (5):475-504.
Generalized Kripke Frames.Mai Gehrke - 2006 - Studia Logica 84 (2):241-275.

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Citations of this work BETA

Modal Translation of Substructural Logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.

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Every Free Biresiduated Lattice is Semisimple.H. Takamura - 2003 - Reports on Mathematical Logic:125-133.

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