Abstract
We define a general family of hypersequent systems with well-behaved logical rules, of which the known hypersequent calculus for (propositional) Godel logic, is a particular instance. We present a method to obtain (possibly, non-deterministic) many-valued semantics for every system of this family. The detailed semantic analysis provides simple characterizations of cut-admissibility and axiom-expansion for the systems of this family.
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