LTL works with Boolean propositions. People probably studied extensions to non-Boolean propositions... Do you know a good starting reference?
(I am aware of STL, but it also seems to talk about clocks, is there a variant without clocks?)
Update: the question is not about "true, false, maybe" but rather about LTL where we can refer to integers, for example. Example: one might want to write
G(i+1 == X(i)), meaning that value
i should increment.