What are the different ways of, in effect, incorporating propositional atoms into first-order logic?
For instance: Halbach, in The Logic Manual, in effect makes $0$-place predicates serve as atoms, but then takes the semantic value of these predicates to be truth-values (whereas he takes the semantic value of an $n$-place predicate to be, as is usual, an $n$-place relation).
There are obviously other possibilities (though most of the other texts I've looked at don't have an equivalent for propositional atoms at all). I'm looking for pointers to texts which have these other possibilities.