Analytic Calculi for Logics of Ordinal Multiples of Standard t-Norms

For two propositional fuzzy logics, we present analytic proofcalculi, based on relational hypersequents. The logic consideredfirst, called M, is based on the finite ordinal sums of ukasiewiczt-norms. In addition to the usual connectives—the conjunction, the implication and the constant 0—we use a furtherunary connective interpreted by the function associating witheach truth value a the greatest -idempotent below a. M is aconservative extension of Basic Logic. The second logic, called M, is based on the finite ordinal sumsof the product t-norm on (0, 1]. Our connectives are in thiscase just the conjunction and the implication.