The Linguistic Relevance of Tree Adjoining Grammar∗Anthony Kroch and Aravind JoshiUniversity of PennsylvaniaMS-CIS-85-16June 1985Contents1 Introduction 21.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Factoring recursion and co-occurrence restrictions . . . . . . . . . . . 41.3 The plan of the paper . . . . . . . . . . . . . . . . . . . . . . . . . . 52 An introduction to the Tree Adjoining Grammar formalism 62.1 Tree Adjoining Grammar–TAG . . . . . . . . . . . . . . . . . . . . . 62.2 TAG’s with ‘links’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 TAG’s with local constraints on adjoining . . . . . . . . . . . . . . . 162.4 Some formal properties of TAG’s . . . . . . . . . . . . . . . . . . . . 233 Some linguistic examples 244 Raising and equi constructions in a TAG 394.1 The basic issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 The problem of nominalizations . . . . . . . . . . . . . . . . . . . . . 444.3 Further considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 475 The Passive in a TAG 495.1 The link between raising and the passive . . . . . . . . . . . . . . . . 495.2 A TAG analysis of the passive . . . . . . . . . . . . . . . . . . . . . . 525.3 Impersonal and raising passives . . . . . . . . . . . . . . . . . . . . . 55∗This work was supported in part by NSF grants MCS8219196-CER, MCS8207294 and a grantfrom the Alfred P. Sloan Foundation for a Program in Cognitive Science, Grant No. 84-4-15.16 Wh- movement in a TAG 576.1 Subjacency in a TAG . . . . . . . . . . . . . . . . . . . . . . . . . . 576.2 The that-trace effect in a TAG . . . . . . . . . . . . . . . . . . . . . 646.3 A further example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717 Conclusions 748 References 779 Notes 8221 Introduction1.1 MotivationIn this paper we apply a new notation for the writing of natural language grammarsto some classical problems in the description of English.1The formalism is the TreeAdjoining Grammar (TAG) of Joshi, Levy and Takahashi 1975, which was studiedinitially only for its mathematical properties but which now turns out to be an inter-esting candidate for the proper notation of meta-grammar; that is for the universalgrammar of contemporary linguistics. Interest in the application of the TAG for-malism to the writing of natural language grammars arises out of recent work on thepossibility of writing grammars for natural languages in a metatheory of restrictedgenerative capacity (for example, Gazdar 1982 and Gazdar et al. 1985). There havebeen also several recent attempts to examine the linguistic metatheory of restrictedgrammatical formalisms, in particular, context-free grammars. The inadequacies ofcontext-free grammars have been discussed both from the point of view of stronggenerative capacity (Bresnan et al. 1982) and weak generative capacity (Shieber1984, Postal and Langendoen 1084, Higginbotham 1984, the empirical claims of thelast two having been disputed by Pullum (Pullum 1984)). At this point the TAGformalism becomes interesting because while it is more powerful than context-freegrammar, it is only “mildly” so. This extra power of TAG is a direct corollaryof the way TAG factors recursion and dependencies, and it can provide reasonablestructural descriptions for constructions like Dutch verb raising where context-freegrammar apparently fails. These properties of TAG and some of its mathematicalproperties were discussed by Joshi 1983.It is our hope that the presentation below will support the claim, currentlycontroversial, that the exploration of restrictive mathematical formalisms as meta-languages for natural language grammars can produce results of value in empiricallinguistics. In spite of the fact that the syntactic theory of natural languages andmathematical linguistics share a common origin, the relevance of the latter to theformer is a matter of contention. Linguists agree that an explanatory theory oflanguage requires a restrictive specification of universal grammar since that notiondefines the space of possible human languages. Without a restrictive universal gram-mar the problem of language acquisition becomes intractable for the child, who hasto entertain so many hypotheses as to the correct grammar for his language that thelimited primary data of his experience will not allow him to choose among them.Linguists also agree that the formalization of transformational-generative grammar(TG) as it is used in the Aspects and related models is far too permissive. In thesearch for a more restrictive theory, however, different researchers have taken verydifferent tacks. Some have claimed that progress can best be made by reanalyzingthe syntax of English and other languages that have received extensive treatment inTG grammar within systems of grammar that are provably less powerful in genera-tive capacity than transformational grammars are. Only in this way can researchersbe sure that the grammars they construct will not only be learnable but also us-able in the real-time linguistic activities of parsing and generation that grammati-3cal knowledge underlies. Under this approach transformational grammars must beexcluded by the theory of universal grammar because, since they can generate non-recursive sets, the languages they generate cannot be expected to be parsable withinreasonable (i.e., polynomial) time bounds (Generalized Phrase Structure Grammar(GPSG) of Gazdar takes this approach). Other linguists, most notably Chomsky,have argued that a restrictive theory of universal grammar can and should be devel-oped by the empirically driven discovery of constraints on rules and representationsand that these constraints cannot be expected to restrict the generative capacityof grammars in any interesting way. Chomsky appears to believe that the effectof the constraints that comprise universal grammar on the mathematically definedgenerative capacity of possible human language grammars has little linguistic rel-evance (Chomsky 1977, 1980). For him the learnability problem is the only onethat should constrain universal grammar. The parsability of languages is not a goalthat universal grammar should aim to account for because it is doubtful that thecomplete set of grammatical sentences of a human language is necessarily parsableand it may even be that parsing is not algorithmic.The thrust of GPSG and similar approaches is to elaborate a formal