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arXiv · 1710.04256

Categories of Models of R-Mingle

Wesley Fussner·Nick Galatos
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Abstract

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 to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics.

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BibTeXRIS

Wesley Fussner, Nick Galatos. 2017-10-11. Categories of Models of R-Mingle. https://doi.org/10.1016/j.apal.2019.05.003

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