This post is a sequel to my previous post here. If you have not read it, read that one first.
In the previous post we assumed that there was a single belief function. But peoples belief can change over time and differ between people, so one should create a belief function for each person for each point in time.
Image one changes Moore's statement to use a different time or person, for example "it is raining but you don't belief it is raining" or "it was raining but I did not belief it was raining". It is obvious from the text that this is not a contradiction of an absurdity. The math reflects this:
$$M_1(s) \land M_1(M_2(s))$$
As there are two different belief functions, the self-consiousness axiom does not apply, and this cannot be reduced further, making this statement undecided.
Now that we have a working framework, one can build more Moore's statements. For example:
$$s \oplus M(s)$$
This translates to "I do not belief this statement", which looks like the classic liars paradox, but isn't a paradox, and can be true or false. But If one checks if the person who tells the statement beliefs it, one gets the following.
$$M(s) \oplus M(M(s)) = \bar{F}$$
Which is a contradiction.