On the cut rule in the calculus of structures
نویسنده
چکیده
We investigate the proof complexity of analytic subsystems of the deep inference proof system SKSg (the calculus of structures). Exploiting the fact that the so-called cut rule of SKSg does not correspond to cut in the sequent calculus, but to the ¬-left rule, we establish that the “analytic” system KSg + c↑ has essentially the same complexity as the monotone Gentzen calculus MLK . In particular, KSg + c↑ quasipolynomially simulates SKSg , and admits polynomial-size proofs of some variants of the pigeonhole principle.
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