In this paper we study the solvability of the equality negation task in a simple wait-free model where two processes communicate by reading and writing shared variables or exchanging messages. In this task, the two processes start with a private input value in the set $\{0,1,2\}$, and after communicating, each one must decide a binary output value, so that the outputs of the processes are the same if and only if the input values of the processes are different. This task is already known to be unsolvable; our goal here is to prove this result using the dynamic epistemic logic (DEL) approach introduced by Goubault et al. (2018) [18]. We show that in fact, there is no epistemic logic formula that explains why the task is unsolvable. Furthermore, we observe that this task is a particular case of an epistemic covering task. We thus establish a connection between the existing DEL framework and the theory of covering spaces in topology, and prove that the same result holds for any epistemic covering task: no epistemic formula explains the unsolvability.

在本文中，我们研究了一个简单的免等待模型中的平等否定任务的可解性，其中两个进程通过读写共享变量或交换消息进行通信。在此任务中，两个过程以集合中的私有输入值开始$\{0，\mathrm{1个}，2\}$，并且在进行通信后，每个人都必须确定一个二进制输出值，以便当且仅当进程的输入值不同时，进程的输出才相同。众所周知，该任务是无法解决的。我们的目标是使用Goubault等人提出的动态认知逻辑（DEL）方法来证明这一结果。（2018）[18]。我们表明，实际上，没有解释该任务为何无法解决的认知逻辑公式。此外，我们观察到该任务是认知覆盖任务的特殊情况。因此，我们在现有的DEL框架与覆盖拓扑中的空间理论之间建立了联系，并证明对于任何认知覆盖任务都具有相同的结果：没有认知公式可以解释不可解性。