## 15-816 Linear Logic |

We begin with two examples for uses of linear logic: the first
transcribes a menu from English, the second models the *blocks
world* which has been used in artificial intelligence as a standard
planning problem. In each case, the expressiveness of linear logic
gives rise to compact and natural encodings.

Next, we show how intuitionistic logic can be embedded into linear logic, if we do not directly use intuitionistic implication. It is the fact that this embedding exists in the presence of the modal "of course" operator which makes linear logic interesting. This realization is one of the important contribution by Girard, who described linear logic in its modern form.

The proof of the correctness of the embedding employs the principle of structural induction over derivations, which will be one of the main proof principles we use in this course.

- Next: Lecture 05: Sequent Calculus
- Previous: Lecture 03: Linear Natural Deduction
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Frank Pfenning fp@cs