15-816 Linear Logic

Lecture 04: Interpreting Intuitionistic in 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.

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Frank Pfenning