Title of article :
Order-enriched categorical models of the classical sequent calculus
Carsten Fuhrmann، نويسنده , , David Pym، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2006
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.
Journal title :
Journal of Pure and Applied Algebra