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> I disagree here. My position is that your initial definition was ambiguous (and contradictory, as Logan originally pointed out) and you've been giving clarifications (which are occasionally contradictory, eg when you said everything in the sentence "refers to the topic, which is a seeing"). 

Well, that's the way I constructed it initially - topic: see, nominative: boy, accusative: house etc. I admit now that the topic is not see, but the topic is the topic of see. The difference is not so obvious. But this is exactly what I mean: if there's a mistake and you find it, I stand corrected. But it's my mistake, not a mistake of the language. Also note that the correct parse tree should be a binary one as this is a binary grammar, but I couldn't find a more suitable one. I was pretty happy with the Ironcreek parser because it somehow worked and gave me FL1.
 
> I'd say this is a working language, but a pretty obtuse and inhuman one. Here's a definition I like better. 
 
> S ->aXb	: "b has an a X" 
X -> S	: , within which, S 
S -> SS	: S and S 
X -> (empty) : (empty) 
This time the quotes don't have some obscure function. I'd get rid of them, but keeping track of the nesting would become hard. The X is to get rid of pesky extra "within which"'s. 
 
> This gives us: 
- "See has a topic, within which, "boy has a nom" and "house has an acc, within which, "hill has an on" " ". 

I think both should be acceptable as they produce the same language, right?
 
> Putting everything on one line using "and" still makes things a little difficult, and sorry about the "nothing" bit, but overall this seems to work much better. Of course we have to wrap our heads around "topic", "nom" and "acc", but that doesn't bother me much. I think their meanings end up more acceptable in this language than the first one I described. And the semantics here is more capable because we have two types of relationships, "has" and "in", both of which are between actual individual words. 

Yes, topic can be easily changed to action (or whatever), and when there's a need for a conjunction you just use that. The thing is that if there's no conjunction, the sentence won't parse, so there has to be whatever you can come up with. 'So' is a relatively neutral main clause starter, and you could use 'and' almost everywhere. A lot of the time the real meaning is something like "it_just_occured_to_me_that" or "you_know_what:". Actually my original intention was to use nominative for 'see' as well, as the neutral sentence is nominative in relation to other sentences, e.g. an accusative/object sentence such as "(He said: ) I like hamburgers."
 
> I think for good measure I'll add a third implementation, just to show we're not limited to just an awkward one and a more capable one. 
 
> S -> SS	: S and S 
S ->aXb : (X b has an a) 
X -> S	: S, within which, 
X -> (empty) : (empty) 
 
> This gives us: 
- (Boy has a nom) and ((hill has an on), within which, house has an acc), within which, see has a topic. 

I'm not objecting :)
 
> The parentheses aren't ideal. What I would really want would be something that gives: 
- Boy has a nom and hill has an on, and in that on, house has an acc, and in that nom and that acc, see has a topic. 
...But the production rules would get a little complicated. Hopefully you'll just believe me when I claim this is what I really mean. 

The production rules can be more complicated although for the research I'll probably go for the simplest possible. What I'm going to need the most is an easy way to show that FL2 is built on an FL1 which has the grammar S -> aS (or S -> a in the agglutinative mode). That's why I was looking for a grammar with aSb.
 
> So what we have here is a reversal of what the prepositional phrases are modifying - we're completely switching around what is in what. It still works, but it's different. The "topic" still belongs to "see", but it must be the sort of thing which can be within an acc and within a nom. 
 
> OK, now on to FL1. I'll be using the example sentence: 
girl-nominative-action 
house-interior-accusative-action 
cat-accusative-action 
kick-action 
 
> S -> S\nS: S, and S 
S -> A : there is A 
A -> aB : a B 
B -> -A : which has A 
B -> (empty) : . 
The "\n" represents the line break used between "words" in the example sentence. Again I've added a variable to keep the result pretty. 
 
> What we get is: 
There is girl which has nominative which has action, and there is house which has interior which has accusative which has action, and there is cat which has accusative which has action, and there is kick which has action. 
 
> That's roughly the way I was interpreting FL1 before, but as I've said, that doesn't seem to get us much meaning. Kick, nominative, and accusative all have action, but there's nothing specifying that it's the same action. 

Yeah, that's a bit tricky. In a flow of sentences the topics or actions have to be distinguishable from one another. However, we already know that the grammar is completely unambiguous because otherwise FL2 wouldn't be, and that wouldn't make any sense. The way it works in practice is that each complex sentence ends with a two-member sub-sentence. It doesn't seem to make much sense although it just has to.

It would be ideal to have 'see' as the root. Having FL2 as a postpositional language you get the sentence [see [house [hill on] acc] [boy nom] topic] which gives you:

on-hill-house-see
accusative-house-see
nominative-boy-see
topic-see

The sentences sound quite good in English. Obviously the first word modifies the next one as an adjective, but I couldn't figure out a semantic formula for the whole, unless the third-level embedding becomes a mirror image (i.e. back to [on hill]) which would give you something like a hill-top-house-see. Or maybe it's just the wrong parsing method I'm using. The compounding convention does however allow the following as it is:

[see-action [acc [on hill] house] nom-boy]

which links it all to the see-action. Of course if the next complex sentence is about an unrelated see-action, you'll have to have an anaphoric method to separate the two.

> Presumably when accusative has action, that means anything which has accusative takes the brunt of the action; while when kick has action, that means anything which has an accusative which has that same action, ends up absorbing the force of a swinging foot. I mean, that would seemingly be a part of the definition of "kick" in this language. It does seem like it would be interesting to try and define words in this way... "When X has a Y, and anything else has an A which also has Y, then..." But that means both a cat, and a house's interior, get kicked. 

But that's correct by definition, because the cat is part of the interior of the house, so kicking the cat you kick both while kicking the interior you don't necessarily kick the cat even if it's in the interior. Sounds like set theory!
 
> Really, FL1 just seems semantically different from any version of FL2, and less capable. 

Maybe it does, but that's impossible because they have the same parse tree, so they're in a way the same.

> I do like FL2 though, and it is quite pleasantly simple, and even FL2 conceptually consists of just nouns (ie, you could use nouns and a single preposition, or simply an inflectional ending.). Because the meaning of the words has to be changed around to fit into specific versions of FL2, I don't specifically see an argument that it can express anything another language could; but I see no reason to doubt it either.

I think the only way to prove it can is to test different sentence types and show it works. Of course if anyone comes up with a real counter example, then it's screwed, but I can't see any reason why that would happen, either.