It may not present a full definition but it does state a "unique" attribute and therefore an attribute without which no vehicle for game purposes can qualify as an "armoured halftrack."
Nope. That is
absolutely not what that statement is saying.
"I am human, and only humans can eat ice cream." does not logically equal "You are only human if you can eat ice cream". It does not take into account humans that
can't eat ice cream -- but are still humans, regardless.
The fact that armoured half-tracks are allowed to do something that things that aren't armoured half-tracks cannot do, is
not the same as saying that vehicles that can't do that thing therefore cannot be armoured half-tracks.
You don't however need an understanding of the transitive properties of statements in logic to parse this. All you need to do is: a) be aware that there is no "formal" definition of armoured half-track in the rules; b) realise that without such a definition, the only way to know when a vehicle is an "armoured half-track" is to use normal English grammar and realise that the vehicle must therefore be a half-track that is armoured; c) look up the vehicle listing in Chapter H, consult the "type" column of the vehicle to determine the "type"; and then d) look at the "AF" column to see if there is a number there.
In this particular case, page H12, line "SPW251/2" gives us a "type" = "ht" and "AF" = "1". Therefore: it's a half-track, and it's armoured.
Compare and contrast with line "SdKfz 10/4" which has "type" = "AAht" and "AF" = "star". Therefore: it's a half-track, but it's
not armoured.
The English phrase "armoured half-track" does not include the inherent concept "and can carry Passengers". Such a concept would require a
formal definition, in the
rules, that says "you are only an armoured half-track if you are an armoured half-track that can carry Passengers". No such formal definition exists, therefore
it cannot be true. COWTRA!