15-816 Linear Logic

Lecture 24: Natural Deduction Revisited

We recall the system of linear natural deduction and present an encoding in the linear logical framework. We further show an encoding of the intuitionistic sequent calculus and begin to show the translations between derivations in the two calculi, establishing the soundness and completeness of sequent calculus for natural deduction proof search.

The encoding of this proof is a relation between natural deductions and sequent calculus derivations. This translation can be used operationally, relying on the operational semantics of LLF.

As a side remark, we also show an non-standard encoding of intuitionistic logic in linear logic which does not take advantage of the unrestricted context, but relies on the additive connectives for context contraction (alternative conjunction) and weakening (additive truth).

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Frank Pfenning