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  1. Categories of Models of R-Mingle.Wesley Fussner & Nick Galatos - 2019 - Annals of Pure and Applied Logic 170 (10):1188-1242.
    We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle (...)
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  • A Categorical Equivalence Motivated by Kalman’s Construction.Hernán San Martín & Marta Sagastume - 2016 - Studia Logica 104 (2):185-208.
    An equivalence between the category of MV-algebras and the category $${{\rm MV^{\bullet}}}$$ MV ∙ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations $${a = \neg \neg a, \vee = 1}$$ a = ¬ ¬ a, ∨ = 1 and $${a \odot = a \wedge b}$$ a ⊙ = a ∧ b. An object of $${{\rm MV^{\bullet}}}$$ MV ∙ is a residuated lattice which in (...)
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  • A Categorical Equivalence Motivated by Kalman’s Construction.Marta S. Sagastume & Hernán J. San Martín - 2016 - Studia Logica 104 (2):185-208.
    An equivalence between the category of MV-algebras and the category \ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations \ \vee = 1}\) and \ = a \wedge b}\). An object of \ is a residuated lattice which in particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where (...)
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  • Logic for Abstract Hoop Twist-Structures.Shokoofeh Ghorbani - 2018 - Annals of Pure and Applied Logic 169 (10):981-996.
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