Section: Scientific Foundations

Focused proof systems

Several team members have continued their efforts to understand and apply focusing proof systems. Since Andreoli's first focused proof system for full linear logic [23] , several efforts have attempted to provide focused proof systems for intuitionistic and classical logics. Liang and Miller [14] have provided the LJF and LKF proof systems that appear to be the most general such focusing systems for intuitionistic and classical logics, respectively. In a second work [18] , Liang and Miller have also presented a focusing proof system for combinations of classical, intuitionistic, and linear logics that manage to uncover the previous three proof systems as well as allows proofs in these different systems to communicate via the cut inference rule.

Baelde has also focused proof systems found in his PhD thesis [27] to reconstruct and design useful algorithms used within the model checking literature [15] .