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Dependency Grammars and Context-Free Grammars Steven Abney
 

Summary: Dependency Grammars and Context-Free Grammars
Steven Abney
University of Tšubingen
The question arises from time to time what the relation is between depen-
dency grammars (DG's) and phrase-structure grammars. A classic paper by
Gaifman [1] would appear to have laid the issue to rest, by proving that depen-
dency grammars are a special case of context-free grammars (CFG's). Gaifman
proves that dependency grammars are equivalent to a proper subset of phrase-
structure grammars, those of degree 1, which I will dub d1-CFG's. (As degree
cannot be explained in a few words, I will leave it undefined for the moment.)
Under a weaker notion of correspondence, which Gaifman attributes to Hays
[2], dependency grammars correspond to finite-degree CFG's, which represent
a larger subset of CFG's, but a proper subset nonetheless.
I submit, however, that Gaifman correlates DG's with a proper subset of
CFG's only by suppressing the essential property of DG's, namely, their head-
edness. I would like to show that, if we take headedness seriously, we are led
to the conclusion that DG's and CFG's both represent equivalence classes of
what I will call headed context-free grammars (HCFG's), but that neither DG's
nor CFG's subsume the other. Nonetheless, Gaifman's result is preserved in
a different form, in that the equivalence classes defined by CFG's include all

  

Source: Abney, Steven P. - School of Information, University of Michigan

 

Collections: Computer Technologies and Information Sciences