Correspondence Theory for Atomic Logics
Guillaume Aucher · HAL (Le Centre pour la Communication Scientifique Directe) · 2022
The correspondence theory for the framework of atomic and molecular logics is developed on the basis of the work of Goranko & Vakarelov. First, we show that modal polyadic logics can be embedded into atomic logics. 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. We apply our general results to FDE, the family of relevance logics, intuitionistic logic and intermediate logics. We obtain novel axiomatizations of these logics that include Boolean connectives.