Dominance constraints for finite tree structures are widely used in several areas of computational linguistics including syntax, semantics, and discourse. In this paper, we investigate algorithmic and complexity questions for dominance constraints and their first-order theory. We present two NP algorithms for solving dominance constraints, which have been implemented in the concurrent constraint programming language Oz. The main result of this paper is that the satisfiability problem of dominance constraints is NP-complete. Despite this intractability result, the more sophisticated of our algorithms performs well in an application to scope underspecification. We also show that the existential fragment of the first-order theory of dominance constraints is NP-complete and that the full first-order theory has non-elementary complexity.

We present Logical Description Grammar (LDG), a model of grammar and the syntax-semantics interface based on descriptions in elementary logic. A description may simultaneously describe the syntactic structure and the semantics of a natural language expression, i.e., the describing logic talks about the trees and about the truth-conditions of the language described. Logical Description Grammars o er a natural way of dealing with underspeci cation in natural language syntax and semantics. If a logical description (up to isomorphism) has exactly one tree plus truth-conditions as a model, it completely speci es that grammatical object. More common is the situation, corresponding to underspeci cation, in which there is more than one model. A situation in which there are no models corresponds to an ungrammatical input.

The idea that natural language grammar and planned action are related systems has been implicit in psychological theory for more than a century. However, formal theories in the two domains have have tended to look very different. This article argues that both faculties share the formal character of applicative systems based on operations corresponding to the same two combinatory operations, namely functional composition and type-raising. Viewing them in this way suggests simpler and more cognitively plausible accounts of both systems, and suggests that the language faculty evolved in the species and develops in children by a rather direct adaptation of a more primitive apparatus for planning purposive action in the world by composing affordances of objects or tools. The knowledge representation that underlies such planning is also reflected in the natural language semantics of tense, mood, and aspect, which the paper begins by arguing provides the key to understanding both systems.

In this thesis, two requirements on Underspecified Representation Formalisms are investi-gated in detail in the context of underspecification of scope. The requirement on partial disambiguation, stating that partially disambiguated ambiguities need to be represented, does not carry much content unless it has become clear, exactly what those ambiguities are. In line with König and Reyle (1999), I argue that all theoretically possible patterns of ambiguity, i.e. subsets of readings, can occur in natural language and that therefore an underspecified representation formalism can only be regarded as expressively com-plete, if it provides representations for all of these subsets. This discussion is couched in a general formal setting, which facilitates clean definitions and allows for the derivation of formally precise results. With those formal definitions at hand, various underspeci-fied representation formalisms are evaluated. As it turns out, none of the investigated formalisms is expressively complete, which answers a corresponding question raised in (König and Reyle, 1999). These incompleteness results allow for a straightforward com-parison of the discussed approaches with respect to expressive power, which forms the

Tree descriptions based on dominance constraints are popular in several areas of computational linguistics including syntax, semantics, and discourse. Tree descriptions in the language of context unification have attracted some interest in unification and rewriting theory. Recently, dominance constraints and context unification have both been used in different underspecified approaches to the semantics of scope, parallelism, and their interaction. This raises the question whether both description languages are related. In this paper, we show for a first time that dominance constraints can be expressed in context unification. We also prove that dominance constraints extended with parallelism constraints are equal in expressive power to context unification.

We present an approach to the resolution of multimodal referential expressions in a cooperative human-machine communication setting, provided by the DenK system. We discuss how references involving multiple modalities are resolved, and we also indicate how the system can respond cooperatively in case the resolution process fails. 1

An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of (Marcus et al. 1983) has been integrated in (Vijay-Shanker 1992) with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990). We generalize Description Theory by integrating semantic information, that is, we propose to tackle both syntactic and semantic underspecification using descriptions. 1 Our focus will be on underspecification of scope. We use a generalized version of ltag, to which we shall refer as lftag. Although trees in lftag have surface strings at their leaves and are in fact very close to ordinary surface trees, there is also a strong connection with the Logical Forms (LFs) of (May 1977). We associate logical interpretations with these LFs using a technique of internalising the logical binding mechanism (Muskens 1996). The net result is that we obtain a Description Theory-like grammar in which the descriptions underspecify semantics. Since everything is framed in classical logic it is easily possible to reason with these descriptions.

Introduction: general and computational pragmatics Pragmatics is the branch of linguistics that studies the relations between linguistic phenomena and aspects of the context of language use. To understand these relations is of crucial importance in many areas of theoretical, computational, and applied linguistics. In theoretical linguistics, the analysis of such phenomena as anaphora, deixis, and tense requires taking properties into account of the context in which expressions exhibiting these phenomena can be used. Utterances which are context-dependent in such ways are called indexical. Bar-Hillel (1954) has argued that indexicality is pervasive in natural language, and speculated that more than 90% of all declarative utterances are indexical. Indexical expressions encode information about aspects of context: about objects introduced earlier in the discourse, about objects that form part of the physical and perceptual context, or about the (relative) time

2.1 Overview of underspecification research................................. 4

The constraint language for lambda-structures (CLLS) allows for a simple, integrated, and underspecified treatment of scope, ellipses, anaphora, and their interaction. CLLS features constraints for dominance, lambda binding, parallelism, and anaphoric links. In the case of antecedent contained deletion (ACD), the definition of parallelism in the original version of CLLS is slightly too restrictive due to an overly weak notion of quantifier identity. We show how to extend CLLS with an appropriate notion of quantifier identity such that ACD can be naturally analysed. This sheds some light on conflicting requirements on quantifier representations as needed for ACD and Hirschbuhler sentences.