On the Universality of Atomic and Molecular Logics via Protologics

After observing that the truth conditions of connectives non–classical logics are generally defined in terms formulas first–order logic, we introduce ‘protologics’, a class whose by arbitrary formulas. Then, atomic and molecular logics, which two subclasses protologics generalize our gaggle behave particularly well from theoretical point view. We also study notion equi-expressivity between based on different classes models. prove that, according to notion, every pure predicate logic with $$k\ge 0$$ variables constants is as expressive some sort logic. equally logics. That formally supports claim somehow ‘universal’. Finally, identify subclass call constitutes its representative core: