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Stone-Type Representations and Dualities for Varieties of Bisemilattices

Antonio Ledda

Studia Logica 106 (2):417-448 (2018)

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The Categorical Equivalence Between Domains and Interpolative Generalized Closure Spaces.Longchun Wang & Qingguo Li - 2023 - Studia Logica 111 (2):187-215.details Closure space has been proven to be a useful tool to restructure lattices and various order structures. This paper aims to provide an approach to characterizing domains by means of closure spaces. The notion of an interpolative generalized closure space is presented and shown to generate exactly domains, and the notion of an approximable mapping between interpolative generalized closure spaces is identified to represent Scott continuous functions between domains. These produce a category equivalent to that of domains with Scott continuous (...) Download Export citation Bookmark
Revisiting Constructive Mingle: Algebraic and Operational Semantics.Yale Weiss - 2022 - In Katalin Bimbó (ed.), Relevance Logics and other Tools for Reasoning: Essays in Honor of J. Michael Dunn. London: College Publications. pp. 435-455.details Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) Download Export citation Bookmark
A Duality for Involutive Bisemilattices.Stefano Bonzio, Andrea Loi & Luisa Peruzzi - 2019 - Studia Logica 107 (2):423-444.details We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation. Download Export citation Bookmark 10 citations
Logics of left variable inclusion and Płonka sums of matrices.S. Bonzio, T. Moraschini & M. Pra Baldi - 2020 - Archive for Mathematical Logic (1):49-76.details The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic $$\vdash $$. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic $$\vdash $$ is related to the construction of Płonka sums of the matrix models of $$\vdash $$. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, (...) Download Export citation Bookmark 14 citations

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