The sentence, The Current King of France is ill, presupposes the existence of an extant French king. That sentence translates to, ∃!x(Kx ⋀ Ix), which is false.
Similarly, the sentence, The Wolverine has an Adamantium Skeleton, translates to ∃!x(Wx ⋀ Ax), which is true.
Similarly, the sentence, Socrates had a beard, translates to ∃!x(Sx ⋀ Bx), which is true. However, for all I know , Socrates could also reference a fiction.
How does logic reference fictional characters?
This is a hot topic at the intersection of contemporary metaphysics and logic, so see, for example the relevant parts of SEP articles on Fiction and Existence.
My own, admittedly naive view, is that talk of fictional entities and fictional truths can be handled simply by introducing special quantifiers that range over fictions. Let's use 'Ê' to stand for the fictional existential quantifier, which is to be used as follows:
Ê(f, x, φ) ≡ ∃x( x ∈ Df ∧ φ(x) ).
Df is the 'fictional domain' or the set of fictional entities and ∃ is an unrestricted existential quantifier. We have the option of simply including fictional entities along with real entities in a single domain D and then giving a special treatment for the 'real' quantifiers as opposed to the fictional ones as we've done here.
With the fictional quantifier 'Ê' we can then talk about Wolverine and Socrates as if they are fictions:
(1) Ê! (f1, x, (Wx ∧ Ax) )
(2) Ê! (f2, x, (Sx ∧ Bx) )
In (1), f1 is the index of that fictional domain that includes Wolverine in it, say the x-men world. (1) then says that there is a unique entitiy in that world that is Wolverine and has Adamantium skeleton. In (2), the index might be a reference to a fictional domain called 'history of western philosophy', some of which might not overlap with reality. (2) simply makes the assertion that there is a unique entity in the history of western philosophy, who is Socrates and has a beard. No claim is being made about this entity (viz. Socrates) belonging to the domain of real entities, but that might be the case, who knows.
This is just a first thought and I'm willing to change my answer if you convince me in the comments.
In this case, the optimal choice would be using modal logic (see this SEP article to get started). Machinery of modal logic was designed to deal with situations similiar to yours, i.e. talking about a thing and its counterparts in all possible worlds. This way, there is this historical figure named Socrates, which is a part of our (i.e. actual) world, and also there are other fictional Socrateses, who inhabit other possible fictional worlds.
A very snide Model Theorist would ask you to axiomatically specify your universe of discourse first.
I am a very snide Model Theorist.
Can you axiomatically specify your universe of discourse?
The trouble with using logic to reason about the world around us, is that definitions are true in every world; so they tell us nothing that helps distinguish this one.
No matter what convoluted thought experiment universe you might construe, if I write down the twenty-or-so axioms of PA, and then "Therefore S(S(0)) + S(S(0)) = S(S(S(S(0))))" then I have just correctly stated that 2+2=4.
This, nothing can prevent from being true. Mathematics hitches on the fact that if you start out with certain symbol strings and apply certain well-defined transformations in a well-defined order, you always get the same result.
Mathematics, effectively is a different universe. Inside our brains we happen to have a bundle of neurons which behave as a "universe of discourse," i.e. it obeys the rules of mathematical reasoning; which is why we can reason about mathematics (to an extent.)
Also, there is at one point in the canonical series, two wolverines with adamantium skeletons.
If you want to reason about the real world, might I recommend bayesian statistics in stead?
Sources: Eliezer Yudkowsky's A Human's Guide to Words, 2008
