Substitution Frege and extended Frege proof systems in non-classical logics

We investigate the substitution Frege (SF ) proof system and its relationship to extended Frege (EF ) in the context of modal and superintuitionistic (si) propositional logics. We show that EF is p-equivalent to tree-like SF , and we develop a “normal form” for SF proofs. We establish connections between SF for a logic L, and EF for certain bimodal… CONTINUE READING