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Categories of models of R-mingle

Wesley Fussner & Nick Galatos

Annals of Pure and Applied Logic 170 (10):1188-1242 (2019)

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Poset Products as Relational Models.Wesley Fussner - 2021 - Studia Logica 110 (1):95-120.details We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semantics for Hájek’s basic logic, and Lewis-Smith, Oliva, and Robinson’s semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies in a uniform (...) Download Export citation Bookmark 1 citation
Fragments of Quasi-Nelson: The Algebraizable Core.Umberto Rivieccio - 2022 - Logic Journal of the IGPL 30 (5):807-839.details This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic \|$FL_{ew}$\| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. \|$FL_{ew}$\|-algebras) that includes both Heyting and Nelson algebras (...) Download Export citation Bookmark 4 citations
Semiconic idempotent logic I: Structure and local deduction theorems.Wesley Fussner & Nikolaos Galatos - 2024 - Annals of Pure and Applied Logic 175 (7):103443.details Download Export citation Bookmark
Two Maximality Results for the Lattice of Extensions of $$\vdash _{\mathbf {RM}}$$.Krzysztof A. Krawczyk - 2022 - Studia Logica 110 (5):1243-1253.details We use an algebraic argument to prove that there are exactly two premaximal extensions of \’s consequence. We also show that one of these extensions is the minimal structurally complete extension of the unique maximal paraconsistent extension of \. Precisely, we show that there are exactly two covers of the variety of Boolean algebras in the lattice of quasivarieties of Sugihara algebras and that there is a unique minimal paraconsistent quasivariety in that lattice. We also obtain a corollary stating that (...) Download Export citation Bookmark

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