## From positive and intuitionistic bounded arithmetic to monotone proof complexity

We study versions of second-order bounded arithmetic where induction and comprehension formulae are positive or where the underlying logic is intuitionistic, examining their relationships to monotone and deep inference proof systems for propositional logic. In the positive setting a restriction of a Paris-Wilkie (PW) style translation yields quasipolynomial-size monotone propositional proofs from Π01 arithmetic theorems, …