Constructive logic with strong negation as a substructural logic. (English) Zbl 1205.03040

Spinks and Veroff have shown that constructive logic with strong negation (CLSN) can be considered as a substructural logic.
This result paves the way for the application of algebraic techniques developed for the study of substructural logics to CLSN.
The authors prove that nilpotent minimum logic is the extension of CLSN by a prelinearity equation. This generalizes the well-known result by Monteiro and Vakarelov that three-valued Łukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued Łukasiewicz logic is proved.


03B60 Other nonclassical logic
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03G25 Other algebras related to logic
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