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Publication Detail
Order-enriched categorical models of the classical sequent calculus
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Journal Article
  • Authors:
    Führmann C, Pym D
  • Publication date:
    01/01/2006
  • Pagination:
    21, 78
  • Journal:
    Journal of Pure and Applied Algebra
  • Volume:
    204
  • Issue:
    1
  • Status:
    Published
  • Print ISSN:
    0022-4049
Abstract
It is well-known that weakening and contraction cause naïve categorical models of the classical sequent calculus to collapse to Boolean lattices. Starting from a convenient formulation of the well-known categorical semantics of linear classical sequent proofs, we give models of weakening and contraction that do not collapse. Cut-reduction is interpreted by a partial order between morphisms. Our models make no commitment to any translation of classical logic into intuitionistic logic and distinguish non-deterministic choices of cut-elimination. We show soundness and completeness via initial models built from proof nets, and describe models built from sets and relations. © 2005 Elsevier B.V. All rights reserved.
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