Constructive logic with strong negation is a substructural logic. II

DOI10.1007/s11225-008-9138-1zbMath1166.03010OpenAlexW4232798335MaRDI QIDQ1005940

Matthew Spinks, Robert Veroff

Publication date: 17 March 2009

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://boris.unibe.ch/117792/1/11225_2008_Article_9138.pdf

zbMATH Keywords

substructural logicconstructive logicdeductive systemresiduated latticestrong negationNelson algebradefinitional equivalenceregularly algebraisable logic

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47)

Related Items (16)

Twist structures and Nelson conuclei ⋮ Strong negation in intuitionistic style sequent systems for residuated lattices ⋮ Paraconsistent constructive logic with strong negation as a contraction-free relevant logic ⋮ Disentangling \textsf{FDE}-based paraconsistent modal logics ⋮ On the provable contradictions of the connexive logics \(\mathbf{C}\) and \(\mathbf{C3}\) ⋮ Belnap Constants and Nelson Logic ⋮ Prelinearity in (quasi-)Nelson logic ⋮ Intuitionistic logic is a connexive logic ⋮ Constructive logic with strong negation is a substructural logic. I ⋮ Rough Sets - Past, Present and Future: Some Notes ⋮ Quasi-discriminator varieties ⋮ Constructive logic with strong negation is a substructural logic. II ⋮ Compatibly involutive residuated lattices and the Nelson identity ⋮ Quasi-subtractive varieties ⋮ Inference rules in Nelson's logics, admissibility and weak admissibility ⋮ Extensions of Lambek Calculi

Uses Software

• Prover9

Cites Work

• Linear logic
• Fregean logics
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• Constructive logic with strong negation is a substructural logic. I
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• Some investigations of varieties of \({\mathcal N}\)-lattices
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• Rule separation and embedding theorems for logics without weakening
• Automated deduction in equational logic and cubic curves
• Parameterized verification of linear networks using automata as invariants
• Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL
• Equational characterization of Nelson algebra
• Ternary and quaternary deductive terms for Nelson algebras
• THE STRUCTURE OF RESIDUATED LATTICES
• ASSERTIONALLY EQUIVALENT QUASIVARIETIES
• Constructive Logic with Strong Negation as a Substructural Logic
• Logics Preserving Degrees of Truth from Varieties of Residuated Lattices
• Logics without the contraction rule
• Algebraizable logics
• Fregean subtractive varieties with definable congruence
• Solving open questions and other challenge problems using proof sketches
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