Formal Constraints on Metarules

Metagrammaticai formalisms that combine context-free phrase structure rules and metarules (MPS grammars) allow concise statement of generalizations about the syntax of natural languages. Unconstrained MPS grammars, tmfortunately, are not cornputationally "safe." We evaluate several proposals for constraining them, basing our amae~ment on computational tractability and explanatory adequacy. We show that none of them satisfies both criteria, and suggest new directions for research on alternative metagrammatical formalisms. 1. I n t r o d u c t i o n The computational-linguistics community has recently shown interest in a variety of metagrammatical formalisms for encoding grammars of natural language. A common technique found in these formalisms involves the notion of a metarule, which, in its most common conception, is a device used to generate grammar rules from other given grammar rules. 1 A metarule is essentially a statement declaring that, if a grammar contains rules that match one specified pattern, it also contains rules that match some other specified pattern. For example, the following metarule (1) VP . .V V P ~ V P * Y ADVP VP [+/;-I [+o.~i states that, if there is a rule that expands a finite V P into a finite auxiliary and a nonfinite VP, there will also be a rule that expands the V P as before except for an additional adverb between the auxiliary and the nnnfinite VP. 2 The patterns may contain variables, in which case they characterize "families ~ of related rules rather than individual pairs. *This reeearch was supported by the National Science Foundation grant No. IST-8103550. The views and conclusions expressed in this document are those of the authors and should not be interpreted as represent,.tive of the views of the National Science Foundation or the United States government. We are indebted to Fernando Pereira, Stanley Peters, and Stanley Roscnscheln for many helpful discun~ons leading to the writing of this paper. IMetarules were first utilized for natural-language research and are most extensively developed within the theory of Generalized Phrase Structure Grammar (GPSG) [Ga2dar end Pullum, 1082; Gawron et ~., 1982; Thompson. 1082 I. 2A metarule similar to our example was proposed by Gazdar, Pullum, and sag [10s2, p. oorl. The metarule notion is a seductive one, intuitively allowing generalizations about the grammar of a language to be stated concisely. However, unconstrained metarule formalisms may possess more expressive power than is apparently needed, and, moreover, they are not always compatationally "safe." For example, they may generate infinite sew of rules and describe arbitrary languages, lu this paper we examine both the formal and linguistic implications of various constraints on metagrammatical formalisms consisting of a combination of context-free phrase structure rules and metarules, which we will call metarule phrase.structure (MPS] grammars. The term "MPS grammar" is used in two ways in this paper. An MPS grammar can be viewed as a grammar in its own right that characterizes a language directly. Alternatively, it can be viewed as a metagrammar, that is, as a generator of a phrase structure obiect grammar, the characterized language being defined as the language of the object grammar. Uszkoreit and Peters [1982] have developed a formal definition of MPS grammars and have shown that an unconstrained MPS grammar can encode any recursively enumerable language. As long am the framework for grammatical description is not seen am part of a theory of natural language, this fact may not alt'ect the usefulness of MPS grammars am tools for purely descriptive linguistics research; however, it has direct and obvious impact on those doing research in a computational o r theoretical linguistic paradigm. Clearly, some way of constraining the power of MPS grammars is necessary to enable their use for encoding grammars in a ¢omputationally feasible way. In the sections that follow, we consider several formal proposals for constraining their power and discuss some of their computational and linguistic ramifications. In our discussion of the computational ramifications of the proposed constraints, we will use the notion of weak-generative capacity as a barometer of the expressive power of a formalism. Other notions of expre~ivity are possible, although some of the traditional ones may not be applicable to MPS grammars. Strong*generative capacity, for instance, though well-defined, seems to be an inadequate notion for comparison of MPS grammars, since it would have to be extended to include information about rule derivations am well am tree derivations. Similarly, we do not mean to imply by our arguments that the class of natural languages corresponds to some class that ranks low in the Chomsky hierarchy merely because the higher classes are less constrained in weak-generative power. The appropriate characterization of possible natural languages may not coincide at all