Efficient Processing Of Flexible Categorial Grammar

From a processing point of view, however, flexible categorial systems are problematic, since they introduce spurious ambiguity. In this paper, we present a flexible categorial grammar which makes extensive use of the p roduc t -ope ra to r , f i rs t in t roduced by Lambek (1958). The grammar has the property that for every reading of a sentence, a strictly left-branching derivation can be given. This leads to the definition of a subset of the grammar, for which the spurious ambiguity problem does not arise and efficient processing is possible. 1. Flexibility vs. Ambiguity Categorial Grammars owe much of their popularity to the fact that they allow for various degrees of flexibility with respect to constituent structure. From a processing point of view, however, flexible categorial systems are problematic, since they introduce spurious ambiguity. The best known example of a flexible categorial grammar is a grammar containing the reduction rules appl icat ion and c o m p o sition, and the category changing rule raising 1 • * I would like to thank Esther K0nig, Erik-Jan van der Linden, Michael Moortgat, Adriaan van Paassen and the participants of the Edinburgh Categorial Grammar Weekend, who made useful comments to earlier presentations of this material. All remaining errors and misconceptions are of course my own. 1 Throughout this paper we will be using the notation of Lambek (1958), in which A/B and B\A are a right-directional and a ( i ) application : A/B B ==> A B B\A ==> A composition: A/B B/C ==> NC C\B B~, ==> C ~ raising : A ==> (B/A)\B A ==> B/(A\B) With this grammar many alternative constituent structures for a sentence can be generated, even where this does not correspond to semantic ambiguities. From a linguistic point of view, this has many advantages. Various kind of arguments for giving up traditional conceptions of constituent structure can be given, but the most convincing and well-documented case in favour of flexible constituent structure is coordination (see Steedman (1985), Dowty (1988), and Zwarts (1986)). The standard assumption in generative grammar is that coordination always takes place between between constituents. Rightnode raising constructions and other instances of non-constituent conjunction are problematic, because it is not clear what the status of the coordinated elements in these constructions is. Flexible categorial grammar presents an elegant solution for such cases, since, next to canonical constituent structures, it also admits various other constituent structures. Therefore, the sentences in (2) can be considered to be ordinary instances of coordination (of two categories slap and ( v p / a p ) \ v p , respectively). (2) a. John sold and Mary bought a book s/vp vp/np s/vp vp/np np