Sorry Nate, it doesn't pan out.
In deductive logic, ~ represents logical NOT when it precedes an atom or formula, true, but the atoms themselves must be prepositions. A noun is not a preposition. For your claim to be valid, her signoff would have to be something like the following:
~a (where a = "Alison exists.")
Note that it must be lower-case, since it is an atom, and only complex formulae are represented by upper-case letters.
By the way, Alison - nice pics, but that one of you wrapped up in the blanket is [u]really[/u] unflattering.
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