Open AccessSubstructural Negations
Author(s) -
Takuro Onishi
Publication year - 2015
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v12i4.2225
Subject(s) - negation , impossibility , dual (grammatical number) , mathematics , duality (order theory) , modalities , calculus (dental) , algebra over a field , pure mathematics , linguistics , philosophy , medicine , social science , dentistry , sociology , political science , law
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.