Emmon Bach uses in "The algebra of events" the term 'eventuality' to denote states, events, processes, etc. How can their actual existence be expressed logically? For example, when I say "John came" the eventuality e in ∃e.came(John) obtains whereas in "I want John to come" John's coming is an eventuality which doesn't obtain. Can a first-order predicate be used, something like Obtains(e)?
You can use an "obtain" predicate but it sounds very much like Meinong's distinction between being and existence, and it's not a very popular solution.
Predicates are used to denote properties but it is doubtful that existence (or "obtaining") is a property as such.
See this article for alternatives: http://plato.stanford.edu/entries/nonexistent-objects/