Correspondence Theory for Atomic Logics

We develop the correspondence theory for the framework of atomic and molecular logics on the basis of the work of Goranko & Vakarelov. First, we show that atomic logics and modal polyadic logics can be embedded into each other. Using this embedding, we reformulate the notion of inductive formulas introduced by Goranko & Vakarelov into our framework. This allows us to prove correspondence theorems for atomic logics by adapting their results