Proof theory for locally finite many-valued logics: Semi-projective logics

We extend the methodology in Baaz and Fermüller (1999) [5] to systematically construct analytic calculi for semi-projective logics-a large family of (propositional) locally finite many-valued logics. Our calculi, defined in the framework of sequents of relations, are proof search oriented and can be used to settle the computational complexity of the formalized logics. As a case study we derive sequent calculi of relations for Nilpotent Minimum logic and for Hajek's Basic Logic extended with the n-contraction axiom (n≥1). The introduced calculi are used to prove that the decidability problem in these logics is Co-NP complete.