## 15-816 Linear Logic |

In the search for proofs in intuitionistic linear logic, we can restrict ourselves to cut-free derivations. This is one important consequence of the cut elimination theorem. Proof search then proceeds via a purely bottom-up construction of a derivation, always reducing the goal of proving a sequent to the subgoal of proving the premisses of an applicable inference rule.

In this process, many non-deterministic choices remain: which left
or right rule do we apply, and how do we split the resources in the
multiplicative rules? To obtain feasible, yet complete theorem proving
strategies these choices should be restricted further. For example, it
is a complete strategy to *always* apply the right rule for
alternative conjunction, when the proposition we want to prove has the
right form.

Thus the simplest form of strategy arises from *inversion
principles*: whenever the conclusion of an inference rule is
provable, then the premisses of the rule are also derivable. Thus we
will not miss a possibly true proposition, if we apply the rule in the
backward direction. In this lecture we investigate which inference
rules are invertible in this sense, and which critical choices remain in
the search for a derivation.

In upcoming lectures we will develop further techniques to limit the non-determinism and postpone choices that are difficult to make.

- Next: Lecture 08: Unification
- Previous: Lecture 06: Cut Elimination
- Schedule

Frank Pfenning fp@cs