A Simple Reconstruction of GPSG

Like most linguistic theories, the theory of generalized phrase structure grammar (GPSG) has described language axiomatically, that is, as a set of universal and language-specific conattaints on the well-formedncss of linguistic elements of some sort. The coverage atttl detailed analysis of English grammar in the ambitious recent volume by Gazdar, Klein, Pullum, and Sag entitled Generalized Phrase Structure Grammar [2] are impressive, in part because of the complexity of the axiomatic system developed by the authors. In this paper, we examine the possibility that simpler descriptions of the same theory can be achieved through a slightly different, albeit still axiomatic, method. Rather than characterize the well-formed trees directly, we progress in two stages by procedurally characterizing the well-formedness axioms themselves, which in turn characterize the trees. 1 I n t r o d u c t i o n I Like most llngafistic theories, the theory of generalized phrase structure grammar (GPSG) has described language axiomatically, that is, as a set of universal and language-specific constraints on the we[l-formedncss of linguistic elements of some sort. In the case of GPSG, these elements are trees whose nodes are themselves structured entltics from a domain of categories (a type of feature ~trueture [6]). The proposed axioms have become quite complex, culminating in the ambitious recent volume by Gazdar, Klein, Pullum, and Sag entitled Generalized Phrase Structure Grammar [2]. The coverage and detailed analysis of English grammar in this work are impressive, in part because of the complexity of the axiomatic system developed by the a u t h o r . In this paper, we examine the possibility that simpler descriptions of the same theory can be achieved through a slightly different, albeit still axiomatic, method. Rather than characterize the well-formed trees driectly, we progress in two stages by procedurally characterizing tim well-formedaess axioms themselves, which in turn charaetei'ize the trees. In particular, we give a procedure which converts GPSG g ramma~ into g r amma~ written lThls research was m~de possible by a gift. from the System Development Foundation. I am indebted to Lauri K~rttuncn and Ray Perrault for their eomrael~te on earlier drafts, and to Roger Evans, Gerald Gszdsr~ Ivan S~.$t ltenry Thompson, and members of the Foundations of Grammar project at the Center for the Study of Language and Information for their helpful discussions during the development of this work. in a unification-b~qed formalism, the PATR-II formalism developed at SRI International (henceforth PATR) [5], which h~s its own declarative semmltics, and which can therefore be viewed &s an axiomatization of string well-formedness constraints. 2 The characterization of GPSG thus obtained is simpler and better defined than the version described by Gazdar et al. The semantics of the formalism is given directly through the reduction to PATR. Also, the PATR axiomatization has a clear construetire interpretation, unlike that used in Gazdar et al., thus making the system more amenable to computational implementation. Finally, the characteristics of the coml~ilation--the difficulty or ease with which the various devices can be encoded in PATR-can provide a measure of the expressiveness and indispensability of these devices in GPSG. 2 T h e G P S G A x i o m s 2 .1 A S u m m a r y o f t h e P r i n c i p l e s GPSG describes natural languages in terms of various types of constraints on local sets of nodes in trees. Pcrtlncnt to the ensuing discussion are the following: • ID (immediate dominance) rules, which state constraints of immediate dominance among categories; • metarules, which state generalizations coI~ccraing classes of ID rules; ¢ LP (linear precedence) rules, which constrain the Ihwar order of sibling categories; • feature cooccurrencc restrictions (FCR), which constrain the feature structures as to which arc permissiHe categories; a feature specification defaults (FS1)), which provide values for features that are otherwise unspecified; and, most importantly, 21towever, a caveat is ]n order th:~t the detailed ~u~alysis from this perspective of the full range of GPSG devices (especially immediate dominance (ID) rules, and feature cooccurrence restrictions) is not discussed fillly here, nor do I completely understand them. (See Section 3.4.} And while in a confessional mood, I should add that the Msorlthm given here has not actually been implemented.