Glivenko theorems for substructural logics over FL

DOI10.2178/jsl/1164060460zbMath1109.03016OpenAlexW2135641508MaRDI QIDQ3416119

Hiroakira Ono, Nikolaos Galatos

Publication date: 19 January 2007

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

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.4368

zbMATH Keywords

substructural logicGlivenko's theoremfull Lambek calculusKolmogorov translationpointed residuated latticebasic-logic algebradouble negation interpretationGlivenko translation

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10) Ordered semigroups and monoids (06F05) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47)

Related Items (18)

Integrally closed residuated lattices ⋮ \(L\)-algebras and three main non-classical logics ⋮ Postponement of $\mathsf {raa}$ and Glivenko's theorem, revisited ⋮ The Jacobson radical for an inconsistency predicate ⋮ THE JACOBSON RADICAL OF A PROPOSITIONAL THEORY ⋮ Higher-Order Categorical Substructural Logic: Expanding the Horizon of Tripos Theory ⋮ Glivenko theorems and negative translations in substructural predicate logics ⋮ Structural and universal completeness in algebra and logic ⋮ Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL ⋮ Cut elimination and strong separation for substructural logics: an algebraic approach ⋮ An approach to Glivenko's theorem in algebraizable logics ⋮ Algebraic Kripke-style semantics for relevance logics ⋮ Fuzzy logics from substructural perspective ⋮ Double negation semantics for generalisations of Heyting algebras ⋮ Unnamed Item ⋮ Glivenko theorems revisited ⋮ A proof-theoretic approach to negative translations in intuitionistic tense logics ⋮ FIBRED ALGEBRAIC SEMANTICS FOR A VARIETY OF NON-CLASSICAL FIRST-ORDER LOGICS AND TOPOLOGICAL LOGICAL TRANSLATION

Cites Work

• Metamathematics of fuzzy logic
• Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic
• A survey of abstract algebraic logic
• Generalized MV-algebras
• Negative equivalence of extensions of minimal logic
• Algebraic foundations of many-valued reasoning
• The parameterized local deduction theorem for quasivarieties of algebras and its application
• Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL
• Cancellative residuated lattices
• Minimal varieties of residuated lattices
• THE STRUCTURE OF RESIDUATED LATTICES
• Glivenko like theorems in natural expansions of BCK-logic

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