## 15-816 Linear Logic |

The sequent rule of *Cut* expresses the substitution
principle of natural deduction in the form of an inference rule. The
validity of the substitution principle for natural deduction gives rise
to a corresponding observation in the sequent calculus: any use of the
Cut rule in a sequent derivation can be eliminated.

This *theorem of cut-elimination* (also called Gentzen's
*Hauptsatz*) is a powerful result, since it proves the
completeness of a simple bottom-up search strategy. As an immediate
consequence we can see that linear logic is consistent, and obtain
a number of independence results.

In this lecture we sketch the proof of cut elimination and investigate its consequences.

Frank Pfenning fp@cs