15-816 Linear Logic
A standard strategy in proof search for natural deduction is to work upwards from the desired judgment by using introduction rules and to work downwards from the hypotheses by using elimination rules. We finish a proof or subproof when hypothesis and conclusion match.
Formalizing this strategy amounts to writing down a new deductive system in which there are three judgments "A is a hypothesis", "A is a linear hypothesis", and "A is a true conclusion". This deductive system is a refinement of Gentzen's sequent calculus.
We exhibit the one-to-many relationship between natural deductions and sequent derivations and show how proof search strategies can be expressed at the level of the sequent calculus.
We also discuss the description of concurrent computation as another application of linear logic.