Distributive residuated frames and generalized bunched implication algebras

DOI10.1007/s00012-017-0456-xzbMath1420.03139OpenAlexW2761182803MaRDI QIDQ1686325

Peter Jipsen, Nikolaos Galatos

Publication date: 21 December 2017

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://digitalcommons.chapman.edu/scs_articles/547

zbMATH Keywords

cut eliminationdecidabilitysubstructural logicfinite model propertyresiduated latticeGentzen systemresiduated framefinite embeddability property

Mathematics Subject Classification ID

Lattices of varieties (08B15) Logical aspects of lattices and related structures (03G10) Cut-elimination and normal-form theorems (03F05) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47)

Related Items (12)

The convolution algebra ⋮ Weakening Relation Algebras and FL$$^2$$-algebras ⋮ The FEP for some varieties of fully distributive knotted residuated lattices ⋮ Deciding Equations in the Time Warp Algebra ⋮ Representable and diagonally representable weakening relation algebras ⋮ An algebraic glimpse at bunched implications and separation logic ⋮ Unnamed Item ⋮ Join-completions of partially ordered algebras ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Complexity of the universal theory of bounded residuated distributive lattice-ordered groupoids ⋮ The structure of generalized BI-algebras and weakening relation algebras

Cites Work

• Algebraic proof theory for substructural logics: cut-elimination and completions
• MacNeille completions of FL-algebras
• Generalized Kripke frames
• Residuated lattices. An algebraic glimpse at substructural logics
• Distributive full Lambek calculus has the finite model property
• The FEP for some varieties of fully distributive knotted residuated lattices
• Cayley's and Holland's theorems for idempotent semirings and their applications to residuated lattices
• The semantics and proof theory of the logic of bunched implications
• The semantics of BI and resource tableaux
• Residuated frames with applications to decidability
• On the finite embeddability property for residuated ordered groupoids

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