Various calculi exist for graded modal logics and all generate vast amounts of case distinctions.
In this paper we present an optimized translation from graded modal logic into many-sorted predicate logic. In many cases the length of proofs for theorems of this calculus is independent of the cardinalities. The translation is sound and complete. Translating graded modalities into predicate logic. The complexity of concept languages - Donini, Lenzerini et al.