Some languages, including Mandarin and Cantonese, have a dedicated belief verb that one uses for describing false beliefs. For instance, in Mandarin, yiwei is used to describe beliefs that the speaker wants to emphasize are false; xiang is a neutral belief verb, like English 'think' and 'believe,' and can be used to describe any belief, regardless of whether the speaker considers it true or false. (You might translate yiwei into English as "be under the mistaken impression that.")
There's been a lot of research on these verbs in developmental psychology. (The question is, roughly, "If a child grows up speaking a language that has a special false-belief verb, do they acquire the concept of false belief or the ability to think about false beliefs any faster?" This meta-analysis refers to a number of studies on this question in Chinese languages, if anyone's interested.) But I haven't seen any linguistic work on the subject.
Can anyone point me towards any linguistic work on false-belief verbs, in any language?