Frame definability in finitely valued modal logics

In this paper we study frame definability in finitely valued modal logics and establish two main results via suitable translations: (1) one cannot define more classes of frames than are already definable classical logic (cf. [27, Thm. 8]), (2) a large family exactly the same as (including based on finite Heyting MV-algebras, or even BL-algebras). way may observe, for example, that celebrated Goldblatt–Thomason theorem applies immediately to these logics. particular, obtain central result from [26] with much simpler proof answer open questions left paper. Moreover, proposed translations allow us determine computational complexity big class