Undead logic

BTW, Gavin, I figured out what the opposite of the opposite of undead is... Not dead AND not not dead.

One could say that undead is not dead, so it would be best expressed as ¬P (not P), where P is the statement "is dead". However, ¬(¬P) = P (i.e. is dead) which can't be the opposite (or complement) of 'undead'. Certainly, humans, orcs and other races are not undead and they are not always dead. Thus, the above formulation results in a contradiction of the following form:
1. Undead ⇒ not P
2. Humans ⇒ not Undead
∴ Humans ⇒ P

(This is the fallacy of assuming the converse.)

I parse the term 'undead' to mean ¬(P ∨ ¬P) (i.e. not (P or not P)). This, of course, can be written as ¬P ∧ P, a contradiction. But it is perfectly reasonable to suppose P ∨ ¬P applies to humans, orcs, trolls, etc. They're either dead or they're not dead. Thus, despite the contradiction I stand by the formulation of undead as ¬(P ∨ ¬P).

The contradiction is the undeads' not mine.