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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.