  In this paper we study frame definability in finitely-valued modal logics and
establish two main results via suitable translations: (1) in finitely-valued
modal logics one cannot define more classes of frames than are already
definable in classical modal logic (cf.~\citep[Thm.~8]{tho}), and (2) a large
family of finitely-valued modal logics define exactly the same classes of
frames as classical modal logic (including modal logics based on finite Heyting
and \MV-algebras, or even \BL-algebras). In this way one may observe, for
example, that the celebrated Goldblatt--Thomason theorem applies immediately to
these logics. In particular, we obtain the central result from~\citep{te} with
a much simpler proof and answer one of the open questions left in that paper.
Moreover, the proposed translations allow us to determine the computational
complexity of a big class of finitely-valued modal logics.
