We extend the methodology in Baaz and Fermüller (1999)  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. © 2013 Elsevier B.V. All rights reserved.
Ciabattoni, A., & Montagna, F. (2013). Proof theory for locally finite many-valued logics: Semi-projective logics. Theoretical Computer Science, 480, 26–42. https://doi.org/10.1016/j.tcs.2013.02.003