Putting Some Weakly Context-Free Formalisms in Order

A number of formalisms have been proposed in order to restrict tree adjoining grammar (TAG) to be weakly equivalent to context free grammar (CFG): for example, tree substitution grammar (TSG), tree insertion grammar (TIG), and regular-form TAG (RF-TAG); in the other direction, tree-local multicomponent TAG (TL-MCTAG) has been proposed as an extension to TAG which is weakly equivalent to TAG. These formalisms have been put to use in various applications. For example, Kroch and Joshi (1987) and others use TL-MCTAG for linguistic description; Bod (1992) uses TSG, and Chiang (2000) uses TIG, for statistical parsing; Shieber (1994) proposes to use TSG for generating synchronous TAG derivations for translation, and Dras (1999) uses RF-TAG for the same purpose. Although it is understood that these formalisms are useful because they have greater strong generative capacity (henceforth SGC) than their weakly-equivalent relatives, it is not always made clear what this actually means: sometimes it is understood in terms of phrase structures, sometimes in terms of a broader notion of structural descriptions (so Chomsky (1963)). We take the latter view, and follow Miller (1999) in seeing phrase structures as just one of many possible interpretations of structural descriptions (alongside, for example, dependency structures). For Miller, structural descriptions themselves should never be compared (since they vary widely across formalisms), but only their interpretations. Thus SGC in the phrase-structure sense is one of several ways of testing SGC in the broader sense. However, not much effort has been made to demonstrate precisely how formalisms compare in these other ways. In this paper we examine four formalisms—CFG, TIG, RF-TAG, and what we call component-local scattered context grammar (CL-SCG)—under four different interpretations, and find that TIG, RF-TAG, and CL-SCG all extend the expressivity of CFG in different ways (see Figure 1). These results show that it is possible to make formally precise statements about notions of generative capacity other than weak generative capacity (henceforth WGC), as a step towards articulating desiderata of formal grammars for various applications.