Dependency Grammars and Context-Free Grammars

نویسنده

  • Steven Abney
چکیده

The question arises from time to time what the relation is between dependency 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 dependency grammars are a special case of context-free grammars (CFG’s). Gaifman proves that dependency grammars are equivalent to a proper subset of phrasestructure 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 headedness. 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 HCFG’s, but the equivalence classes defined by DG’s include only finite-degree HCFG’s. In particular, each HCFG has a unique characteristic grammar, a CFG that abstracts away from the choice of heads in the HCFG. Each HCFG also has a unique projection grammar, a DG representing the dependencies among projections in the headed trees generated by the HCFG. The projection grammar abstracts away from the order in which dependent projections are combined with governing projections. Each relation defines equivalence classes: the class of HCFG’s having the same characteristic grammar, the class of HCFG’s having the same projection grammar. But the equivalence classes are incomparable. There are HCFG’s that have the same characteristic grammar, but different projection grammars; and there are HCFG’s with the same projection grammar, but different characteristic grammars. To flesh out this sketch, we need to define some terms. A DG is a tuple G = (Σ; P; S), where Σ is a set of word categories, P is a set of productions, and S μ Σ is the set of start symbols. Productions are of the form X(fi;fl), where X is a category, and fi; fl are sequences of categories. The productions license dependency trees. A dependency tree is licensed by G iff every node is licensed by some production of G. A production X(Y1; : : : ; Ym;Z1; : : : Zn)

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تاریخ انتشار 1994