Constructive logic with strong negation is a substructural logic. I

DOI10.1007/s11225-008-9113-xzbMath1145.03013OpenAlexW2000140686MaRDI QIDQ931408

Robert Veroff, Matthew Spinks

Publication date: 25 June 2008

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

Full work available at URL: https://doi.org/10.1007/s11225-008-9113-x

zbMATH Keywords

varietysubstructural logicconstructive logicresiduated latticestrong negationNelson algebrafull Lambek calculus with exchange and weakening

Mathematics Subject Classification ID

Mechanization of proofs and logical operations (03B35) Other algebras related to logic (03G25) Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (03B47) Varieties of lattices (06B20)

Related Items (22)

Kleene algebras with implication ⋮ 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 ⋮ On the provable contradictions of the connexive logics \(\mathbf{C}\) and \(\mathbf{C3}\) ⋮ Belnap Constants and Nelson Logic ⋮ Prelinearity in (quasi-)Nelson logic ⋮ BELNAP–DUNN MODAL LOGICS: TRUTH CONSTANTS VS. TRUTH VALUES ⋮ Fragments of quasi-Nelson: residuation ⋮ Intuitionistic logic is a connexive logic ⋮ A note on contraction-free logic for validity ⋮ The categorical imperative: category theory as a foundation for deontic logic ⋮ Quasi-discriminator varieties ⋮ Constructive logic with strong negation is a substructural logic. II ⋮ Behavioral algebraization of logics ⋮ Paraconsistent Modal Logics ⋮ Compatibly involutive residuated lattices and the Nelson identity ⋮ Quasi-subtractive varieties ⋮ Quasi-Nelson algebras ⋮ Inference rules in Nelson's logics, admissibility and weak admissibility ⋮ Extensions of Lambek Calculi ⋮ Quasi-Nelson algebras and fragments

Uses Software

• Prover9

Cites Work

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