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Did the Miller--Fink scheme of 2009, which I admired but never got my head
around, also involve four inflections? I dimly recall it had two.
 On Jun 27, 2013 3:50 AM, "Herman Miller" <[log in to unmask]> wrote:

> Here's a variation on an idea Alex Fink was talking about back in 2009
> ("Unambiguous prosody for trees"). The nice thing is that in the simple
> cases, it looks like something that might be found in a reasonable spoken
> language. I'll illustrate with names of birds from English.
>
> First, the simple part: adding adjectives to noun phrases. Adjectives get
> one inflection (a tone, suffix, or whatever), and the head of the noun
> phrase gets a different inflection. I'll label them as A and N. You can
> string any number of adjectives together, and they group with the noun one
> by one to make longer phrases.
>
> black-A bird-N
> (black bird)
> blackbird
>
> rusty-A black-A bird-N
> (rusty (black bird))
> Rusty Blackbird
>
> Japan-A green-A wood-A pecker-N
> (Japanese (green (wood-pecker)))
> Japanese Green Woodpecker
>
> Basically the phrase can be extended indefinitely by replacing N with the
> sequence A N. But what if you want to expand an A into a more complex
> sequence? You need a new kind of phrase which I'll call a "descriptive
> phrase". Start with a phrase like "red tail" (A N), then change the N to a
> new inflection, D. English does something like this in names like
> "Red-tailed Hawk", where the adjective "red" and the noun "tail" are
> combined to make a new adjective "red-tailed".
>
> red-A tail-D hawk-N
> ((red tail) hawk)
> Red-tailed Hawk
>
> red-A wing-D black-A bird-N
> ((red wing) (black bird))
> Red-winged Blackbird
>
> north-A rough-A wing-D swallow-N
> (north ((rough wing) swallow))
> Northern Rough-winged Swallow
>
> Note that in a sequence like A A D, only the last A combines with the D.
> Since A D reduces to A, A A D N is equivalent to A A N. If you want more
> than one A to combine with a D, you need another inflection, what I'll call
> the combining form (C). Imagine for instance that English doesn't have a
> word for "nape", but instead uses the phrase "neck-A back-N" for "back of
> the neck". So to make a compound adjective "red-naped" you'll need this
> construction:
>
> red-A neck-C back-D sap-A sucker-N
> ((red (neck back)) (sap sucker))
> Red-naped Sapsucker
>
> Note how "neck-A back-N" becomes "neck-C back-D" when used as the second
> part of a descriptive phrase.
>
> So far we've got:
>
> N -> A N
> A -> A D
> D -> C D
>
> Now here's the cool part. To expand a C, the left-hand side is inflected
> like a C, and the right-hand side is like an N.
>
> C -> C N
>
> I can't come up with an actual bird name that illustrates this, but here's
> the simplest case that requires this construction.
>
> A C N D N
> A (C N) D N = A C D N
> A ((C N) D) N = A D N
> (A ((C N) D)) N = A N
>
> Here's a few other examples to illustrate how it works.
>
> (A ((A ((C N) D)) N))
> ((A ((C (A N)) D)) N)
> ((A (C ((C N) D))) N)
> ((A ((C N) (C D))) N)
> ((A ((C N) D)) (A N))
> (((A ((C N) D)) D) N)
> ((A (((C N) N) D)) N)
> (((A D) ((C N) D)) N)
>
> So with just four relatively simple rules you can represent arbitrarily
> complex trees, and at least the first two or three of the rules look like
> something that might work in a reasonable spoken language.
>