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

We extend a methodology by Baaz and Fermüller 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).