Diversification of Object-Languages for Propositional Logics

I argue in favour of object languages of logics to be diversely-generated, that is, not having identical (or equivalent) immediate sub-formulas. In addition to diversely-generated object languages constituting a more appropriate abstraction of the use of sentential connectives in natural language, I show that such language lead to a simplifications w.r.t. some specific issues: the identity of proofs, the factual equivalence (in logics of grounding) and the Mingle axiom in Relevance logics. I also point out that some of the properties of classical logic based on freely-generated object languagest.