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In this paper we introduce a modal language L T for imposing constraints on trees, and an extension LT(L r) for imposing constraints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for formalising grammatical frameworks perspicuously, 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 formalisms for linguistic theorising is discussed in some detail. . | Talking About Trees Patrick Blackburn Department of Philosophy Rijksuniversiteit Utrecht Heidelberglaan 8 3584 cs Utrecht. Email patrick@phil.ruu.nl Claire Gardent GRIL Université 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 language LT for imposing constraints on trees and an extension LT LF for imposing constraints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for formalising grammatical frameworks perspicuously and the paper illustrates this by showing how the leading ideas of GPSG 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 formalisms for linguistic theorising is discussed in some detail. 1 Introduction In this paper we introduce a modal language LT for talking about trees and an extension LT LF for talking about trees decorated with feature structures. From a logical point of view this is a natural 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 nontrivial 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
