Let $\mathsf{KP\omega}_0$ be Kripke-Platek set theory with Infinity but Foundation (or $\in$-Induction) restricted to $\Delta_0$-formulas. $\mathsf{ZF}$ proves $\in$-Induction holds for arbitrary formulas, but it is because we have Full Separation which is unavailable over $\mathsf{KP\omega}_0$, so $\in$-Induction on more complex formulas become a non-trivial statement over $\mathsf{KP\omega}_0$.


I wonder whether the following is known: 

> **Question.** Working over $\mathsf{KP\omega}_0$,
> 1. Does $\Pi_1$-Foundation prove $\Sigma_1$-Foundation or vice versa?
> 1. What about their consistency strength? Does $\Pi_1$-Foundation have a higher consistency strength than that of $\Sigma_1$-Foundation?