In this paper, we bring up the problem of logical omniscience in epistemic logic. One way of avoiding the problem is through Rantala models, where non-normal worlds are introduced. Such models are vulnerable to criticism, as we show. One of many issues that occur is the Bjerring result, which states that incorporating non-normal worlds makes the agent logically incompetent. For this reason, we propose a different solution based on positional logics.