Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semantic side of logic: model-theoretic syntax (MTS). MTS takes grammars to be sets of statements of which (algebraically idealized) well-formed expressions are models. We clarify the difference between the two kinds of framework and review their separate histories, and then argue that the generative perspective has misled linguists concerning the properties of natural languages. We select two elementary facts about natural language phenomena for discussion: the gradient character of the property of being ungrammatical and the open nature of natural language lexicons. We claim that the MTS perspective on syntactic structure does much better on representing the facts in these two domains. We also examine the arguments linguists give for the infinitude of the class of all expressions in a natural language. These arguments turn out on examination to be either unsound or lacking in empirical content. We claim that infinitude is an unsupportable claim that is also unimportant. What is actually needed is a way of representing the structure of expressions in a natural language without assigning any importance to the notion of a unique set with definite cardinality that contains all and only the expressions in the language. MTS provides that.

In this paper we describe an approach to constraint based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the assignments which make the formulas true. We show that this allows an efficient representation of knowledge about the content of constraints which can be used as a practical tool for grammatical theory verification.

Context-free grammars and tree automata, because they are required to be finite, are limited to defining sets of trees in which the branching is bounded by a finite constant. As a result they cannot capture accounts of syntactic phenomena in which no such a priori bound exists---in flat accounts of coordination, for instance. This mismatch led Langendoen in 1976 and Gazdar, et al., in 1985 (GPSG) to propose varieties of two level grammars, in the one case infinite grammars that are themselves generated by other grammars, in the other grammars that permit regular expressions on the right-hand side of rewrite rules. In earlier work, we have characterized the local sets (the sets of trees generated by CFGs) and the recognizable sets (those accepted by tree automata) by definability in the logical language L 2 K;P . In defining such sets of trees in L 2 K;P , however, one must explicitly bound the branching. In this paper we explore the consequences of relaxing these bounds. We show, f...

The analysis of human communication, in all its forms, increas-ingly depends on large collections of texts and transcribed record-ings. These collections, or corpora, are often richly annotated with structural information. These data sets are extremely large so manual analysis is only successful up to a point. As such, sig-nificant effort has recently been invested in automatic techniques for extracting and analyzing these massive data sets. However, further progress on analytical tools is confronted by three major challenges. First, we need the right data model. Second, we need to understand the theoretical foundations of query languages on that data model. Finally, we need to know the expressive requirements for general purpose query language with respect to linguistics. This thesis has addressed all three of these issues. Specifically, this thesis studies formalisms used by linguists and

Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by definability in the monadic second*order theory of certain structures. More recently, these descriptive characterizations have been used to obtain complexity results for constraint- and principle-based theories of syntax and to provide a uniform model-theoretic flamework for exploring the relationship between theories expressed in disparate formal terms. These results have been limited, to an extent, by the lack of descriptive characterizations of language classes beyond the context-free. Recently, we have shown that tree-adjoining languages (in a mildly generalized form) can be characterized by recognition by automata operating on three-dimensional tree manifolds, a three-dimensional analog of trees. In this paper, we exploit these automata- theoretic results to obtain a characterization of the tree-adjoining languages by definability in the monadic second-order theory of these three-dimensional tree manifolds. This not only opens the way to extending the tools of modeltheoretic syntax to the level of TALs, but provides a highly flexible mechanism for defining TAGs in terms of logical constraints.

This paper explores commonalities and differences between Dachs, a variant of Dependency Grammar, and Lexical-Functional Grammar. Dachs is based on traditional linguistic insights, but on modern mathematical tools, aiming to integrate different knowledge systems (from syntax and semantics) via their coupling to an abstract syntactic primitive, the dependency relation. These knowledge systems correspond rather closely to projections in LFG. We will investigate commonalities arising from the usage of the projection approach in both theories, and point out differences due to the incompatible linguistic premises. The main difference to LFG lies in the motivation and status of the dimensions, and the information coded there. We will argue that LFG confounds dioeerent information in one projection, preventing it to achieve a good separation of alternatives and calling the motivation of the projection into question.

This paper uses classical logic for a simultaneous description of the syntax and semantics of a fragment of English and it is argued that such an approach to natural language allows procedural aspects of linguistic theory to get a purely declarative formulation. In particular, it will be shown how certain construction rules in Discourse Representation Theory, such as the rule that inde nites create new discourse referents and de nites pick up an existing referent, can be formulated declaratively if logic is used as a metalanguage for English. In this case the declarative aspects of a rule are highlighted when we focus on the model theory of the description language while a procedural perspective is obtained when its proof theory is concentrated on. Themes of interest are Discourse Representation Theory, resolution of anaphora, resolution of presuppositions, and underspeci cation.

Five years after the first ESSLLI workshop on Model-Theoretic Syntax (MTS), Pullum and Scholz (2001) stated that since the work on MTS had largely focused on reformulating existing GES frameworks, in a sense, it

This paper explores commonalities and differences between Dachs,