A Meta-Level Grammar: Redefining Synchronous TAG for Translation and Paraphrase

In applications such as translation and paraphrase, operations are carried out on grammars at the meta level. This paper shows how a meta-grammar, defining structure at the meta level, is useful in the case of such operations; in particular, how it solves problems in the current definition of Synchronous TAG (Shieber, 1994) caused by ignoring such structure in mapping between grammars, for applications such as translation. Moreover, essential properties of the formalism remain unchanged. 1 I n t r o d u c t i o n A grammar is, among other things, a device by which it is possible to express structure in a set of entities; a grammar formalism, the constraints on how a grammar is allowed to express this. Once a grammar has been used to express structural relationships, in many applications there are operations which act at a 'meta level' on the structures expressed by the grammar: for example, lifting rules on a dependency grammar to achieve pseudo-projectivity (Kahane et al, 1998), and mapping between synchronised Tree Adjoining Grammars (TAGs) (Shieber and Schabes, 1990; Shieber 1994) as in machine translation or syntax-to-semantics transfer. At this meta level, however, the operations do not themselves exploit any structure. This paper explores how, in the TAG case, using a meta-level grammar to define meta-level structure resolves the flaws in the ability of Synchronous TAG (S-TAG) to be a representation for applications such as machine translation or paraphrase. This paper is set out as follows. It describes the expressivity problems of S-TAG as noted in Shieber (1994), and shows how these occur also in syntactic paraphrasing. It then demonstrates, illustrated by the relative structural complexity which occurs at the meta level in syntactic paraphrase, how a meta-level grammar resolves the representational problems; and it further shows that this has no effect on the generative capacity of S-TAG. 2 S T A G a n d M a c h i n e T r a n s l a t i o n Synchronous TAG, the mapping between two Tree Adjoining Grammars, was first proposed by Shieber and Schabes (1990). An application proposed concurrently with the definition of S-TAG was that of machine translation, mapping between English and French (Abeill~ et al, 1990); work continues in the area, for example using S-TAG for English-Korean machine translation in a practical system (Palmer et al, 1998). In mapping between, say, English and French, there is a lexicalised TAG for each language (see XTAG, 1995, for an overview of such a grammar). Under the definition of TAG, a grammar contains elementary trees, rather than flat rules, which combine together via the operations of substitution and adjunction (composition operations) to form composite structures--derived trees--which will ultimately provide structural representations for an input string if this string is grammatical. An overview of TAGs is given in Joshi and Schabes (1996). The characteristics of TAGs make them better suited to describing natural language than Context Free Grammars (CFGs): CFGs are not adequate to describe the entire syntax of natural language (Shieber, 1985), while TAGs are able to provide structures for the constructions problematic for CFGs, and without a much greater generative capacity. Two particular chaxacteris-