Craig interpolation for semilinear substructural logics

DOI10.1002/malq.201200004zbMath1273.03075OpenAlexW2085725211MaRDI QIDQ3144874

George Metcalfe, Enrico Marchioni

Publication date: 10 December 2012

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/malq.201200004

zbMATH Keywords

algebraic semanticssubstructural logicsamalgamationsemilinearityCraig interpolation propertyR-mingleSugihara monoidspointed commutative residuated lattices

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) (06D30) Interpolation, preservation, definability (03C40)

Related Items (11)

Uniform interpolation and compact congruences ⋮ Franco Montagna's work on provability logic and many-valued logic ⋮ The Failure of The Amalgamation Property for Semilinear Varieties of Residuated Lattices ⋮ Epimorphisms in varieties of residuated structures ⋮ Structure theorems for idempotent residuated lattices ⋮ Universal algebraic methods for non-classical logics ⋮ Varieties of De Morgan monoids: minimality and irreducible algebras ⋮ Amalgamation and interpolation in ordered algebras. ⋮ Craig interpolation in the presence of unreliable connectives ⋮ Idempotent residuated structures: Some category equivalences and their applications ⋮ Theorems of Alternatives for Substructural Logics

Cites Work

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• Interpolation and Beth's property in propositional many-valued logics: a semantic investigation
• Amalgamation, congruence-extension, and interpolation properties in algebras
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• Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics
• Algebras Whose Congruence Lattices are Distributive.
• Algebraic completeness results for R-mingle and its extensions

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