Talking About Trees

Talking About Trees Patrick Blackburn Department of Philosophy, Rijksuniversiteit Utrecht Heidelberglaan 8, 3584 CS Utrecht. Email: patrick@phil.ruu.nl Claire Gardent GRIL, Universit4 de Clermont Ferrand, France, and Department of Computational Linguistics, Universiteit van Amsterdam Spuistraat 134, 1012 VB Amsterdam. Email: claire@mars.let.uva.nl Wilfried Meyer-Viol Centrum voor Wiskunde en Informatica Kruislaan 413, 1098 SJ Amsterdam. Email: W.Meyer.Viol@cwi.nl Abstract In this paper we introduce a modal lan- guage L T for imposing constraints on trees, and an extension LT(L r) for imposing con- straints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for for- malising grammatical frameworks perspic- uously, and the paper illustrates this by showing how the leading ideas of GPS6 can be captured in LT(LF). In addition, the role of modal languages (and in particular, what we have called layered modal languages) as constraint for- malisms for linguistic theorising is discussed in some detail. 1 Introduction In this paper we introduce a modal language L 7 for talking about trees, and an extension L'r(L F) for talking about trees decorated with feature struc- tures. From a logical point of view this is a nat- ural thing to do. After all, the trees and feature structures used in linguistics are simple graphical objects. To put it another way, they are merely rather simple Kripke models, and modal languages are probably the simplest languages in which non- trivial constraints can be imposed on such structures. Moreover the approach is also linguistically natural: many of the things linguists need to say about trees (and feature structures) give rise to modal operators rather naturally, and indeed our choice of modalities has been guided by linguistic practice, not logical convenience. There are several reasons why we think this path is an interesting one to explore, however two are of particular relevance to the present paper. 1 First, we believe that it can lead to relatively simple and natural formalisations of various grammatical frame- works. In our view, neither simplicity nor natural- ness are luxuries: unless a formalisation possesses a high degree of clarity, it is unrealistic to hope that it can offer either precise analyses of particular sys- tems or informative comparisons of different frame- works. We believe our approach has the requisite clarity (largely because it arose by abstracting from linguistic practice in a rather direct manner) and much of this paj?er is an attempt to substantiate this. Second, L r can be combined in a very nat- ural way with feature logics to yield simple systems which deal with configurational concepts, complex categories and their interaction. The key idea is to perform this combination of logics in a highly con- strained way which we have called layering. Layer- ing is a relatively new idea in modal logic (in fact the only paper devoted exclusively to this topic seems to be [Finger and Gabbay 1992]), and it seems to pro- vide the right level of expressive power needed to model many contemporary grammar formalisms. The paper is structured …

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