## Section: New Results

### Meta-level focusing and object-level proof system

Participants : Vivek Nigam, Dale Miller.

It is well known how to use an intuitionistic meta-logic to specify natural deduction systems. It is also possible to use linear logic as a meta-logic for the specification of a variety of sequent calculus proof systems
[51] . Nigam and Miller have shown that adopting different
*focusing* annotations for such linear logic specifications, a range of other proof systems can also be specified. In particular, they have shown that natural deduction (normal and non-normal), sequent proofs (with and without cut), tableaux, and proof systems using general elimination
and general introduction rules can all be derived from essentially the same linear logic specification by altering focusing annotations. By using elementary linear logic equivalences and the completeness of focused proofs, we are able to derive new and modular proofs of the soundness and
completeness of these various proofs systems for intuitionistic and classical logics.