Substructural Negations

  • Takuro Onishi Japanese Society for the Promotion of Science Postdoctoral Fellow


We present substructural negations, a family of negations (or negative modalities) classified in terms of structural rules of an extended kind of sequent calculus, display calculus. In considering the whole picture, we emphasize the duality of negation. Two types of negative modality, impossibility and unnecessity, are discussed and "self-dual" negations like Classical, De Morgan, or Ockham negation are redefined as the fusions of two negative modalities. We also consider how to identify, using intuitionistic and dual intuitionistic negations, two accessibility relations associated with impossibility and unnecessity.

How to Cite
ONISHI, Takuro. Substructural Negations. The Australasian Journal of Logic, [S.l.], v. 12, n. 4, june 2015. ISSN 1448-5052. Available at: <>. Date accessed: 23 may 2019. doi: