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Proof theory for locally finite many-valued logics: Semi-projective logics
Agata Ciabattoni1, Franco Montagna
1Vienna University of Technology, Austria.
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.
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