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In this paper we extend the fuzzy-set-theoretic approach to semantics of sequent calculi, developed in (Fuzzy Sets Systems, 121 (2001) 397), by allowing the truth lattices of fuzzy sets involved to be not necessarily distributive. The main result of our paper is that a (propositional) sequent consequence (in Tarski's sense) satisfies weak structural rules, that is, structural rules with Cut splitted...
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