Soundness and completeness of the cirquent calculus system CL6 for   computability logic
  Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic. The present article extends that result to the more expressive cirquent calculus system CL6, which is a conservative extension of both CL5 and classical propositional logic. 
Wenyan Xu and Sanyang Liu
cs.LO