On multiple context-free grammars

There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms, namely, combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining grammars. Each of these formalisms is known to generate a larger class of languages than context-free grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages.

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The equivalence of four extensions of context-free grammars

5 The Passive in a TAG 49 5.1 The link between raising and the passive . . . . . . . . . . . . . . . . 49 5.2 A TAG analysis of the passive . . . . . . . . . . . . . . . . . . . . . . 52 5.3 Impersonal and raising passives . . . . . . . . . . . . . . . . . . . . . 55 ∗This work was supported in part by NSF grants MCS8219196-CER, MCS8207294 and a grant from the Alfred P. Sloan Foundation for a Program in Cognitive Science, Grant No. 84-4-15.

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The Linguistic Relevance of Tree Adjoining Grammar

Investigations of classes of grammars that are nontransformational and at the same time highly constrained are of interest both linguistically and mathematically. Context-free grammars (CFG) obviously form such a class. CFGs are not adequate (both weakly and strongly) to characterize some aspects of language structure. Thus how much more power beyond CFG is necessary to describe these phenomena is an important question. Based on certain properties of tree adjoining grammars (TAG) an approximate characterization of class of grammars, mildly context-sensitive grammars (MCSG), has been proposed earlier. In this paper, we have described the relationship between several different grammar formalisms, all of which belong to MCSG. In particular, we have shown that head grammars (HG), combinatory categorial grammars (CCG), and linear indexed grammars (LIG) and TAG are all weakly equivalent. These formalisms are all distinct from each other at least in the following aspects: (a) the formal objects and operations in each formalism, (b) the domain of locality over which dependencies are specified, (c) the degree to which recursion and the domain of dependencies are factored, and (d) the linguistic insights that are captured in the formal objects and operations in each formalism. A deeper understanding of this convergence is obtained by comparing these formalisms at the level of the derivation structures in each formalism. We have described a formalism, the linear context-free rewriting system (LCFR), as a first attempt to capture the closeness of the derivation structures of these formalisms. LCFRs thus make the notion of MCSGs more precise. We have shown that LCFRs are equivalent to muticomponent tree adjoining grammars (MCTAGs), and also briefly discussed some variants of TAGs, lexicalized TAGs, feature structure based TAGs, and TAGs in which local domination and linear precedence are factored TAG(LD/LP). Disciplines Computer Sciences Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-90-01. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/539 The Convergence Of Mildly Context-Sensitive Grammar Formalisms MS-CIS-90-01 LINC LAB 161 Aravind K. Joshi K. Vijay Shanker David Weir Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104-6389

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The Convergence of Mildly Context-Sensitive Grammar Formalisms

Tree Adjoining Grammar (TAG) is a formalism for natural language grammars. Some of the basic notions of TAG's were introduced in [Joshi, Levy, and Takahashi 1975] and by [Joshi, 1983]. A detailed investigation of the linguistic relevance of TAG's has been carried out in [Kroch and Joshi, 1985]. In this paper, we will describe some new results for TAG's, especially in the following areas: (1) parsing complexity of TAG's, (2) some closure results for TAG's, and (3) the relationship to Head grammars.

Kelly Roach

Papers

Formal Properties of Head Grammars