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  1. Duality Results for (Co)Residuated Lattices.Chrysafis Hartonas - 2019 - Logica Universalis 13 (1):77-99.
    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 (...)
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  • Discrete Duality for Nelson Algebras with Tense Operators.Aldo V. Figallo, Gustavo Pelaitay & Jonathan Sarmiento - 2023 - Studia Logica 111 (1):1-19.
    In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson D-algebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given in Sendlewski (...)
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  • Discrete Dualities for Double Stone Algebras.Ivo Düntsch & Ewa Orłowska - 2011 - Studia Logica 99 (1-3):127-142.
    We present two discrete dualities for double Stone algebras. Each of these dualities involves a different class of frames and a different definition of a complex algebra. We discuss relationships between these classes of frames and show that one of them is a weakening of the other. We propose a logic based on double Stone algebras.
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  • A discrete duality between apartness algebras and apartness frames.Ivo Düntsch & Ewa Orlowska - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):213-227.
    Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of (Bridges et al., 2003), and we prove a discrete duality for them.
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  • Algorithmic correspondence and canonicity for non-distributive logics.Willem Conradie & Alessandra Palmigiano - 2019 - Annals of Pure and Applied Logic 170 (9):923-974.
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