How do we classify formal systems' (propositional logic, first-order logic, second-order logic,  higher-order logic, Hoare logic and type theory) expressivity? In the same way that grammars (CSG, CFG, ...), languages (CSL, tree-adjoining language, ...) and abstract machines (Turing machine, ...) 'fit' into the Type 0-3 range of the Chomsky hierarchy, can we also classify the formal systems into it?Or, is there another yardstick for describing the relative expressive power of formal systems? 
Expressive power of formal systems
formal languages;formal grammars;logic;chomsky hierarchy