Equivalence of consequence relations: an order-theoretic and categorical perspective

DOI10.2178/jsl/1245158085zbMath1181.03063OpenAlexW2125805198MaRDI QIDQ3399178

Constantine Tsinakis, Nikolaos Galatos

Publication date: 29 September 2009

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1245158085

zbMATH Keywords

closure operatorconsequence relationalgebraizable logicmoduleprojectiveresiduated lattice

Mathematics Subject Classification ID

Categorical logic, topoi (03G30) Ordered semigroups and monoids (06F05) Abstract deductive systems (03B22) Galois correspondences, closure operators (in relation to ordered sets) (06A15) Abstract algebraic logic (03G27)

Related Items (15)

Universal extensions of specialization semilattices ⋮ Modules over quantaloids: applications to the isomorphism problem in algebraic logic and \(\pi\)-institutions ⋮ The semantic isomorphism theorem in abstract algebraic logic ⋮ Coproduct and amalgamation of deductive systems by means of ordered algebras ⋮ Universal specialization semilattices ⋮ Abstract algebraic logic. An introductory chapter ⋮ Representations of structural closure operators ⋮ A SUBSTRUCTURAL GENTZEN CALCULUS FOR ORTHOMODULAR QUANTUM LOGIC ⋮ Recognizability in residuated lattices ⋮ Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL ⋮ Cut elimination and strong separation for substructural logics: an algebraic approach ⋮ AN ABSTRACT APPROACH TO CONSEQUENCE RELATIONS ⋮ Disjunctive and conjunctive multiple-conclusion consequence relations ⋮ \(M\)-sets and the representation problem ⋮ Categorical abstract algebraic logic: truth-equational \(\pi\)-institutions

Cites Work

• Residuated lattices. An algebraic glimpse at substructural logics
• Definitional equivalence and algebraizability of generalized logical systems
• Lattices and ordered algebraic structures
• Equivalence of consequence operations
• Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL
• Minimal varieties of residuated lattices
• THE STRUCTURE OF RESIDUATED LATTICES

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