Categories of Models of R-Mingle
Logic
2021-06-09 v2
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.
Keywords
Cite
@article{arxiv.1710.04256,
title = {Categories of Models of R-Mingle},
author = {Wesley Fussner and Nick Galatos},
journal= {arXiv preprint arXiv:1710.04256},
year = {2021}
}