Categories of Residuated Lattices

<p>We present dual variants of two algebraic constructions of certain classes of residuated lattices: The Galatos-Raftery construction of Sugihara monoids and their bounded expansions, and the Aguzzoli-Flaminio-Ugolini quadruples construction of srDL-algebras. Our dual presentation of these constructions is facilitated by both new algebraic results, and new duality-theoretic tools. On the algebraic front, we provide a complete description of implications among nontrivial distribution properties in the context of lattice-ordered structures equipped with a residuated binary operation. We also offer some new results about forbidden configurations in lattices endowed with an order-reversing involution. On the duality-theoretic front, we present new results on extended Priestley duality in which the ternary relation dualizing a residuated multiplication may be viewed as the graph of a partial function. We also present a new Esakia-like duality for Sugihara monoids in the spirit of Dunn's binary Kripke-style semantics for the relevance logic R-mingle.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Year dc:date.available

2018

Author dc:creator

• Fussner, Daniel Wesley

Contributors dc:contributor

• Nikolaos Galatos, Ph.D.
• Michael Kinyon
• Andrew Linshaw
• Kimon Valavanis

• Algebraic logic
• Categorical equivalences
• Duality theory
• Residuated lattices
• Substructural logic
• Topological dualities
• Algebra
• Logic and Foundations
• Mathematics

Statement dc:rights

• <p>Copyright is held by the author. User is responsible for all copyright compliance.</p>

Language dc:language

en

Repository record dc:identifier

https://digitalcommons.du.edu/etd/1527

OAI identifier oai:identifier

oai:digitalcommons.du.edu:etd-2527