Defining Natural Language Grammars in GPSG

1 Overview Three central goals of work in the generalized phrase structure grammar (GPSG) linguistic framework, as stated in the leading book "Generalized Phrase Structure Grammar" Gaz-dar et al (1985) (hereafter GKPS), are: (1) to characterize all and only the natural language grammars, (2) to algorithmically determine membership and generative power consequences of GPSGs, and (3) to embody the universalism of natural language entirely in the formal system, rather than by statements made in it. 1 These pages formally consider whether GPSG's weak context-free generative power (wcfgp) will allow it to achieve the three goals. The centerpiece of this paper is a proof that it is unde-cidable whether an arbitrary GPSG generates the nonnatural language ~'. On the basis of this result, I argue that GPSG fails to define the natural language grammars, and that the gen-erative power consequences of the GPSG framework cannot be algorithmically determined, contrary to goals one and two. 2 In the process, I examine the linguistic universalism of the GPSG formal system and argue that GPSGs can describe an infinite class of nonnatural context-free languages. The paper concludes with a brief diagnosis of the result and suggests that the problem might be met by abandoning the weak context-free generative power framework and assuming substantive constraints. 1.1 The Structure of GPSG Theory A generalized phrase structure grammar contains five language-particular components (immediate dominance (ID) rules, metarules , linear precedence (LP) statements, feature co-occurrence IGKPS clearly outline their goals. One, uto arrive at a constrained metalanguage capable of defining the grammars of natural languages, but not the grammar of, say, the set of prime numbers2(p.4). Two, to construct an explicit linguistic theory whose formal consequences are clearly and easily determinable. These 'formal consequences' include both the generative power consequences demanded by the first goal and membership determination: GPSG regards languages "as collections whose membership is definitely and precisely specifiable."(p.1) Three, to define a linguistic theory where ~lhe universalism [of natural language] is, ultimately, intended to be entirely embodied in the formal system, not ezpressed by statements made in it.'(p.4, my emphasis) 2The proof technique make use of invalid computations, and the actual GPSG constructed is so simple, so similar to the GPSGs proposed for actual natural languages, and so flexible in its exact formulation that the method of proof suggests there may be no simple reformulations of GPSG that avoid this problem. The proof also suggests that …