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Affine logic for constructive mathematics

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 نشر من قبل Michael Shulman
 تاريخ النشر 2018
  مجال البحث
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 تأليف Michael Shulman




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We show that numerous distinctive concepts of constructive mathematics arise automatically from an antithesis translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically constructivize classical definitions, handling the resulting bookkeeping automatically.



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