Busaniche, M and Cignoli, R., "Constructive logic with strong negation as a substructural logic", a publicar en Journal of Logic and Computation ; doi: 10.1093/logcom/exn081.
Abstract: Spinks and Veroff have shown that constructive logic
with strong negation (CLSN for short), can be considered as a
substructural logic. We use algebraic tools developed to study substructural
logics to investigate some axiomatic extensions of CLSN. For instance we prove
that Nilpotent Minimum Logic is the extension of CLSN by the prelinearity
axiom. This generalizes the well known result by Monteiro and Vakarelov that
three-valued \Lukasiewicz logic is an extension of CLSN.
A Glivenko-like theorem relating CLSN and three-valued \Lukasiewicz
logic is proved.