 For example, Barrio, Pailos and Szmuc [2020] show that we can approximate classical logic in something called the ST-hierarchy (ST for strict-tolerant, from Cobreros, Egre, Ripley and van Rooij [2012a,b]). This allows them to avoid certain classical problems at each level of the hierarchy, like some of the paradoxes, while at the same time maintaining many of the benefits of the strength of classical logic when considering the full hierarchy.