Idempotent residuated structures: Some category equivalences and their applications

DOI10.1090/S0002-9947-2014-06072-8zbMath1402.06005MaRDI QIDQ5246960

Nikolaos Galatos, James G. Raftery

Publication date: 22 April 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

interpolationidempotentnucleusamalgamationcategory equivalencerepresentableepimorphismsemilinearresiduationSugihara monoidR-minglebeth definabilityrelative stone algebra

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Ordered semigroups and monoids (06F05) Quasivarieties (08C15) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Categories of algebras (08C05) Abstract algebraic logic (03G27)

Related Items (17)

Structural completeness in relevance logics ⋮ Representation of De Morgan and (semi-)Kleene lattices ⋮ Group representation for even and odd involutive commutative residuated chains ⋮ Twist structures and Nelson conuclei ⋮ Epimorphisms in varieties of residuated structures ⋮ Structure theorems for idempotent residuated lattices ⋮ A category equivalence for odd Sugihara monoids and its applications ⋮ VARIETIES OF DE MORGAN MONOIDS: COVERS OF ATOMS ⋮ Semilinear De Morgan monoids and epimorphisms ⋮ Epimorphism surjectivity in varieties of Heyting algebras ⋮ Complemented MacNeille completions and algebras of fractions ⋮ Epimorphisms in varieties of subidempotent residuated structures ⋮ Varieties of De Morgan monoids: minimality and irreducible algebras ⋮ Sugihara algebras and Sugihara monoids: Multisorted dualities ⋮ The Hahn embedding theorem for a class of residuated semigroups ⋮ Categories of models of \(\mathbf{R}\)-mingle ⋮ On semiconic idempotent commutative residuated lattices

Cites Work

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• Linear logic
• *-autonomous categories. With an appendix by Po-Hsiang Chu
• Residuated lattices. An algebraic glimpse at substructural logics
• Congruence distributive quasivarieties whose finitely subdirectly irreducible members form a universal class
• Positive Sugihara monoids
• On categories of algebras equivalent to a variety
• On categories of algebras equivalent to a quasivariety
• Cylindric algebras. Part II
• On an implication connective of RM
• Local deductions theorems
• The semantics and proof theory of linear logic
• A Kripke-style semantics for R-mingle using a binary accessibility relation
• Structural completeness of Gödel's and Dummett's propositional calculi
• Algebraic characterizations of various Beth definability properties
• A category equivalence for odd Sugihara monoids and its applications
• The Beth property in algebraic logic
• Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL
• Subdirectly irreducible residuated semilattices and positive universal classes
• Minimal varieties of involutive residuated lattices
• Interpolation and Beth's property in propositional many-valued logics: a semantic investigation
• The intersection property of amalgamations
• On the structural completeness of some pure implicational propositional calculi
• Minimal varieties of residuated lattices
• Craig interpolation for semilinear substructural logics
• Correspondences between gentzen and hilbert systems
• Representable idempotent commutative residuated lattices
• Structural Completeness in Substructural Logics
• Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics
• Residuated Lattices as an Algebraic Semantics for Paraconsistent Nelson's Logic
• Algebraizable logics
• Model-Theoretic Logics
• THE STRUCTURE OF COMMUTATIVE RESIDUATED LATTICES
• Substructural fuzzy logics
• Algebras Whose Congruence Lattices are Distributive.
• Lattices With Involution
• Algebraic completeness results for R-mingle and its extensions
• Protoalgebraic logics

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