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  1. The Poset of All Logics I: Interpretations and Lattice Structure.R. Jansana & T. Moraschini - 2021 - Journal of Symbolic Logic 86 (3):935-964.
    A notion of interpretation between arbitrary logics is introduced, and the poset$\mathsf {Log}$of all logics ordered under interpretability is studied. It is shown that in$\mathsf {Log}$infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between$\mathsf {Log}$and the lattice of interpretability types of varieties are investigated.
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  • Countably Many Weakenings of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - 2020 - Studia Logica 108 (2):163-198.
    Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...)
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  • Dualities for Bounded Prelinear Hilbert Algebras.Hernán J. San Martín & Valeria A. Sígal - 2022 - Logic Journal of the IGPL 30 (3):409-421.
    This paper deals about dualities for bounded prelinear Hilbert algebras. In particular, we give an Esakia-style duality between the algebraic category of bounded prelinear Hilbert algebras and a category of H-spaces whose morphisms are certain continuous p-morphisms.
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