I think that's a pretty good working definition. I would hope that G and G' are both consistent enough that the transform from State to State' via Unwritten Rule will be consistent from today to tomorrow, but for proving incompleteness it's enough to show that there's no existing unique mapping from State to State'.
I disagree. ANY such game would not be just 'complete' it would be NECESSARILY CLOSED, only being able to describe a finite number of situations, just like a board game!
When a player says "I tie the magic sword to a long wooden shaft to produce a magic polearm", does it work?
Here's the Dungeon World answer to that:
Is it outright impossible in a fictional position sense (IE are the materials required simply unavailable and not plausibly acquired within the scope of the move). If fictional plausibility exists (decided by the whole table, not just the GM) then we go on to whether or not saying 'yes' or 'no' to the PRACTICALITY of it (IE can you make a sturdy enough polearm from the supplied materials). This MIGHT still be a fictional position thing, or it might be a question of asking whether or not the given characters are acting within their competency, or even whether or not ANYONE could perform such a regardless of ability and materials. We know naginatas were made in EXACTLY this way, from swords, so that dispenses with that last question. Given that we are presumably not weapon smiths, the decidability is not present at the table, so we cannot say 'no' based on any of these factors.
Now, this is not a GM move, so it is NOT GOVERNED by the GM's principles and agenda. There is, on p12, however, an answer to the question "Why play Dungeon World?" and there are 3 answers:
1. To see the characters do amazing things.
2. To see them struggle together.
3. Because the world still has so many places to explore.
So, at the root of it, you must simply ask if 'yes' addresses 'why?'. I would say making a magic polearm probably falls under 1 and 2. Thus the table (and this is a TABLE decision, NOT A GM DECISION) should decide, and IMHO they are supposed to say 'yes' here.
When a player says "I use my knowledge of bagpipes and a bunch of lamp oil to make a flamethrower," does he get a flamethrower, and if so how does it work? Some RPGs might be complete w/rt these specific examples but no RPG I know of is; I doubt any RPG is complete (in the sense clearstream has defined) w/rt all examples.
Again, I think we do exactly as we did above, but in this case I'm guessing most tables are going to come down on the side of this not being a practical plan. I mean, maybe, but I really doubt it would work in anything like reality, so its more of a question of 'rule of cool', which is largely asking the same questions as above. I think if the PC has some cache as a creator of gizmos and contraptions and such, or he's working with insane gnome clockworkers or something, then SURE! If its a last second "I pour oil in my bagpipe!" then my thinking is DD to avoid actually bursting into flames yourself, and if you want to throw the now flaming bagpipes at your enemy, VOLLEY AWAY! lol. While you might think of this as incompleteness, I still think of it as "I applied the agenda and principles in a reasonable way." Its funny, it shows the PC struggling and still doing something cool or at least amusing.
Tone may also apply here, but AGAIN, the table has absolute authority in terms of deciding if this works or not! The rules cover the process of making these situations happen, whatever that means, entirely. Nothing is left hanging. It just isn't decided on some sort of mechanical or 'simulationist' basis. Even the 'it must make fictional sense' restriction isn't about REALISM, its about being able to have a narrative structure and a fiction to work from at all.