15-816 Linear Logic

Lecture 03: Linear Natural Deduction

Starting from the notion of a linear hypothetical judgment and various common sense examples, we introduce the connectives of linear logic. Just as there are classically equivalent propositions with very different meanings in intuitionistic logic, we find that there are intuitionistically indistinguishable connectives which behave quite differently in linear logic.

Due to the limitations on the use of linear hypotheses or resources, this logic is significantly weaker than intuitionistic logic, unless we reintroduce hypothetical judgments. Following Girard, we show how this can be done in such a way that intuitionistic logic can be easily embedded into linear logic, and no expressive power is lost.

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Frank Pfenning