Is there a way to do compositional semantics without possible worlds?

Especially in the case of semantics of fictional objects.

I was trying to think of fictional objects as 'grammatical object' so they don't demand a referent the way objects tend to do. So I guess, one would have to do semantics without referents. what kind of extensions would one take in this case? Or better yet, how can this problem be solved without resorting to extensions?


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