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.