dominance

[LFG List]

Date: Thu, 21 Oct 1999 14:37:37 +1000 (EST)
From: Avery Andrews <andaling at pretty.anu.edu.au>
Message-Id: <199910210437.OAA13267 at pretty.anu.edu.au>
To: LFG at LINGUIST.LDC.UPENN.EDU, fridmar at mail.cosapidata.com.pe
Subject: Re: dominance
X-Sun-Charset: ISO-8859-1


Poking around some more in my older books, I find that Ginsberg (1966)
`the Mathematical Theory of Context Free Languages' does indeed define
trees using sets of sequences of whole numbers, but also that
Chomsky (1961) `On the notion: "Rule of Grammar"' (in Fodor & Katz,
_The Structure of Language_, also in _Proceedings of the Twelfth
Symposium in Applied Mathematics_) does use trees (described as
labelled brackettings rather than P-markers), and even defines `dominance',
but what gets defined as dominance is just the `rewrites as' relation
for a rewriting system:

 \phi dominates \psi (\phi \doublearrow \psi) if there is a derivation
 \sig_1, .. \sig_n such that \sig_1 = \phi and \sig_n=\psi.

This is not what people normally mean by `dominates' because its not
relativized to a specific structure, where for example S might dominate
the sequence `John to like pizza' in the structure for one example but
not for another.

So the issue is indeed confused....

  - Avery.Andrews at anu.edu.au

> 
> I have some questions on the history of a popular hierarchical relation
> that is part of the formal apparatus of most generative grammars:
> "dominance".
> 
> 1. Who was the first linguist that employed the term?
> 2. Where did the term appear for the first time in linguistics?
> 3. What were the formal or mathematical properties that were for the first
> time assigned to this hierarchical relation?
> 4. Was the notion of "dominance" created "out of nothing" or was it built on
> a previous concept from another discipline?
> 5. Does the notion of "dominance" in early transformational generative
> grammar have some relationship with the notion of "representation" (THE
> LOGICAL STRUCTURE OF A LINGUISTIC THEORY, 1955: 173)? This concept was
> stated as follows:
> 
> "The level P is based on a relation of representation which we will denote
> by p ("rho"). This is the relation holding, in English, between NP and
> the^old^man, between Sentence and NP^VP, between the latter and
> John^came^home,
> and between N and John. Tentatively, the converse of p can be read as "is
> a".
> That is,
> 
> 2.  p(NP, the^man) if and only if the^man is a NP.
> The relation p has the following properties:
> 3. p is irreflexive, asymmetrical, transitive and nonconnected.
> 
> Thus p gives a partial ordering of the strings of P. There is a unique prime
> of P which essentially stands "first" in this ordering. This is the prime
> Sentence (S). S is the unique prime that represents every grammatucal
> string. There are also certain primes that are last" in this ordering, i.e.,
> that bear the relation `p to no string. We will call the set containing just
> these primes and the strings formed from them the set P."
> 
> Please respond to venuspeter at latinmail.com. Any hints on this most welcome.
> I shall post a summary.
> 
> 
> Marco Antonio Young Rabines
> Departamento de Lingüística
> Universidad Nacional Mayor de San Marcos
> Av. Venezuela s/n
> Lima 1
> Perú
>