title: Proof theory for locally finite many-valued logics: Semi-projective logics.
abstract: 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 [Formula: see text]-contraction axiom ([Formula: see text]). The introduced calculi are used to prove that the decidability problem in these logics is Co-NP complete.
authors.affiliation: Vienna University of Technology, Austria.
authors.forename: Agata
authors.initials: A
authors.lastname: Ciabattoni
authors.forename: Franco
authors.initials: F
authors.lastname: Montagna
keywords: Analytic calculi; Many valued logic; Sequents of relations