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  1. Correspondence and canonicity theory of quasi-inequalities and Π2-statements in modal subordination algebras.Zhiguang Zhao - forthcoming - Logic Journal of the IGPL.
    In the present paper, we study the correspondence and canonicity theory of modal subordination algebras and their dual Stone space with two relations, generalizing correspondence results for subordination algebras in [13–15, 25]. Due to the fact that the language of modal subordination algebras involves a binary subordination relation, we will find it convenient to use the so-called quasi-inequalities and |$\varPi _{2}$|-statements. We use an algorithm to transform (restricted) inductive quasi-inequalities and (restricted) inductive |$\varPi _{2}$|-statements to equivalent first-order correspondents on the (...)
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  • Beth definability and the Stone-Weierstrass Theorem.Luca Reggio - 2021 - Annals of Pure and Applied Logic 172 (8):102990.
    The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic ⊨Δ associated with an infinitary variety Δ and show that the Stone-Weierstrass Theorem is a consequence of the Beth definability property of ⊨Δ, stating that every implicit definition can be made explicit. Further, we define an infinitary propositional logic ⊢Δ by means of a Hilbert-style calculus and prove a strong completeness result whereby the semantic notion of consequence associated (...)
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  • Contact semilattices.Paolo Lipparini - forthcoming - Logic Journal of the IGPL.
    We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.
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  • A variety of algebras closely related to subordination algebras.Sergio Celani & Ramon Jansana - 2022 - Journal of Applied Non-Classical Logics 32 (2):200-238.
    We introduce a variety of algebras in the language of Boolean algebras with an extra implication, namely the variety of pseudo-subordination algebras, which is closely related to subordination algebras. We believe it provides a minimal general algebraic framework where to place and systematise the research on classes of algebras related to several kinds of subordination algebras. We also consider the subvariety of pseudo-contact algebras, related to contact algebras, and the subvariety of the strict implication algebras introduced in Bezhanishvili et al. (...)
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  • Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras.Nick Bezhanishvili, Luca Carai, Silvio Ghilardi & Lucia Landi - 2023 - Annals of Pure and Applied Logic 174 (1):103169.
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