“…those logics the algebraic semantics of which is given by varieties of normal/regular lattice expansions (LEs), and their expansions with fixed points [5, 3] [5]. Not only this very high level of generality allows to extend the benefits of correspondence and canonicity results to many well known logical systems such as bi-intuitionistic (modal) logic, the Lambek-Grishin calculus [24], and the multiplicative-additive fragment of linear logic [16], but this new point of view paves the way to several developments and connections among the meta-theories of several logical frameworks, examples of which are a general perspective on Gödel-McKinsey-Tarski translations and correspondence/canonicity transfer results [13,15], systematic connections among different relational semantics of a given logic [4], and systematic connections between correspondence-theoretic results and the proof-theoretic behaviour of logical frameworks [21,23,2,22,20].…”