Categories of models of R-mingle

Annals of Pure and Applied Logic 170 (10):1188-1242 (2019)
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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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References found in this work

The semantics of entailment II.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (1):53 - 73.
The semantics of entailment — III.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (2):192 - 208.
Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
On extensions of intermediate logics by strong negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
On the representation of n4-lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.

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