15-816 Linear Logic
Lecture 5: Sequent Calculus

The system of normal natural deduction captures the structure of derivations in which introduction rules are used bottom-up and elimination rules are used top-down. This is somewhat unwieldy for proof search, so we introduce the sequent calculus in which both kinds of steps proceed bottom-up.

The sequent calculus was introduced by Gentzen as a tool to prove consistency of his natural deduction formulation of logic. We will use it in a similar way in order to show the normalization theorem for natural deductions.

As a new example, we show how to encode Petri nets in linear logic. A short introduction and a Java applet with some examples are available on the web.

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Frank Pfenning