Analytic calculi for logics of ordinal multiples of standard t-norms
For two propositional fuzzy logics, we present analytic proof calculi, based on relational hypersequents. The logic considered first, called ML, is based on the finite ordinal sums of Lukasiewicz t-norms. In addition to the usual connectivesthe conjunction circle dot, the implication -> and the constant 0 -> we use a further unary connective interpreted by the function associating with each truth value a the greatest -idempotent below a. M is a conservative extension of Basic Logic. The second logic, called MII, is based on the finite ordinal sums of the product t-norm on (0, 1). Our connectives are in this case just the conjunction and the implication.
analytic calculi fuzzy logics basic logic