The modal logic I am considering is the "Simplest Quantified Modal Logic" which combines first-order predicate logic with identity, with S5 in the most straightforward way, described here and slightly differently here (with no accessibility relation, but with S5 it doesn't matter here). The semantics are possibilist.
Suppose in our world, w0, Pegasus is not actual, and has wings (much like he would be described in mythology, and how, I think, most people would think of him). We can describe a possible world, w1, exactly like w0 except that that Pegasus is not actual and Pegasus does not in fact have wings (perhaps the possible object was born with a mutation at w1), and so does not fall within the extension of "has wings" in w1. So in both worlds, we have a non-actual object, and an accidental property of this non-actual object which it has in one world but not the other.
Using formal notation, we can describe the situation by letting the constant p denote Pegasus, A stand for the "is actual" predicate, and W stand for the "is winged" predicate:
V(p) ∉ [V(A)](w0) and V(p) ∉ [V(W)](w0)
V(p) ∉ [V(A)](w1) and V(p) ∈ [V(W)](w1)
Aside from this one difference, the values of all other constants and predicates are exactly the same
To me, this seems bizarre and unintuitive. In both worlds all of the facts about actual objects in the world are the same, including all of the facts about history, the myths we tell about Pegasus, anything believed about Pegasus, the evolution of the world from beginning to end, and so on. Just as a matter of fact, the non-actual object Pegasus falls within the extension of "has wings" in one world, and does not fall within the extension of "has wings" in the other. At the very least, it seems on any empiricist epistemology, the facts of the matter about the accidental properties possible objects like Pegasus seem, in principle, unknowable.
I like possibilist semantics because of its simplicity, but this really irks me for some reason. I tried googling around a bit, but couldn't find any possibilists who talk about something like this issue of accidental properties of possibile objects. Or, is it even an issue? Is it just flexibility in the possibilist semantics that possibilists accept?