A modal logic is developed to deal with nite ordered binary trees as they are used in (computational) linguistics. A modal language is introduced with operators for the`mother of',` rst daughter of' and`second daughter of' relations together with their transitive re exive closures. The relevant class of tree models is de ned and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is given for which completeness is shown with respect to the class of nite ordered binary trees. A n umber of decidability results follow.

No abstract

Ever since dialogue modelling first developed relative to broadly Gricean assumptions about utter-ance interpretation (Clark, 1996), it has remained an open question whether the full complexity of higher-order intention computation is made use of in everyday conversation. In this paper we examine the phenomenon of split utterances, from the perspective of Dynamic Syntax, to further probe the necessity of full intention recognition/formation in communication: we do so by exploring the extent to which the interactive coordination of dialogue exchange can be seen as emergent from low-level mechanisms of language processing, without needing representation by interlocutors of each other’s mental states, or fully developed intentions as regards messages to be conveyed. We thus illustrate how many dialogue phenomena can be seen as direct consequences of the grammar architecture, as long as this is presented within an incremental, goal-directed/predictive model.

No abstract

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.