A Specification Language for Lexical Functional Grammars

A Specification Language for Lexical Functional Grammars Patrick Blackburn and Claire Gardent Computerlinguistik Universit£t des Saarlandes Postfach 1150, D-66041 Saarbrficken Germany {patrick, claire)©coli, uni-sb, de Abstract This paper defines a language Z~ for spe- cifying LFG grammars. This enables constraints on LFG's composite onto- logy (c-structures synchronised with f- structures) to be stated directly; no ap- peal to the LFG construction algorithm is needed. We use f to specify schemata annotated rules and the LFG uniquen- ess, completeness and coherence princip- les. Broader issues raised by this work are noted and discussed. 1 Introduction Unlike most linguistic theories, LFG (see Kaplan and Bresnan (1982)) treats grammatical relations as first class citizens. Accordingly, it casts its lin- guistic analyses in terms of a composite ontology: two independent domains -- a domain of consti- tuency information (c-structure), and a domain of grammatical function information (f-structure) -- linked together in a mutually constraining man- ner. As has been amply demonstrated over the last fifteen years, this view permits perspicuous analyses of a wide variety of linguistic data. However standard formalisations of LFG do not capture its strikingly simple underlying intuitions. Instead, they make a detour via the LFG con- struction algorithm, which explains how equatio- nal constraints linking subtrees and feature str.uc- tures are to be resolved. The main point of the present paper is to show that such detours are unnecessary. We define a specification language £ in which (most of) the interactions between c- and f-structure typical of LFG grammars can be stated directly. The key idea underlying our approach is to think about LFG model theoretically. That is, our first task will be to give a precise -- and trans- parent -- mathematical picture of the LFG onto- logy. As has already been noted, the basic enti- ties underlying the LFG analyses are composite structures consisting of a finite tree, a finite fea- ture structure, and a function that links the two. Such structures can straightforwardly be thought of as models, in the usual sense of first order model theory (see Hodges (1993)). Viewing the LFG on- tology in such terms does no violence to intuition: indeed, as we shall see, a more direct mathemati- cal embodiment of the LFG universe can hardly be imagined. Once the ontological issues have been settled we turn to our ultimate goal: providing a specifica- tion language for LFG grammars. Actually, with the ontological issues settled it is a relatively sim- ple task to devise suitable specification languages: we simply consider how LFG linguists talk about such structures when they write grammars. That is, we ask ourselves what kind of constraints the linguist wishes to impose, and then devise a lan- guage in which they can be stated. Thus we shall proceed as follows. After a brief introduction to LFG, 1 we isolate a class of models which obviously mirrors the composite nature of the LFG ontology, and then turn to the task of de- vising a language for talking about them. We opt …

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