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 had been done in the shadow of Generative-Enumerative Syntax (GES).
In the following five years, the bulk of work has still been invested in model-theoretic reformulations of GES frameworks. Reformulations of GB can be found in (Rogers 1996), (Rogers 2003), of LFG in (Blackburn and Gardent 1995), of GPSG in (Kracht 1995) and (Rogers 1996), (Rogers 2003), of HPSG in (Kepser 2000) and (Kepser and Moennich 2003), and of TAG in (Rogers 2003).
Recently (Rogers 2004), there have been attempts to step out of the shadow of GES, and to use MTS not only to reformulate and compare existing frameworks, but to utilize the more declarative, clarifying perspective of MTS to also explore extensions of them. This is what we set out to do in this paper as well.
We base our work on the model-theoretic meta grammar formalism of Extensible Dependency Grammar (XDG) (Debusmann 2006). XDG can be used to axiomatize grammatical theories based on dependency grammar, to extend them, and to implement them using the constraint-based XDG Development Kit (XDK) (Debusmann et al. 2004), (Debusmann and Duchier 2007). XDG is novel in supporting the axiomatization of multi-dimensional grammatical theories, where the linguistic aspects of e.g. syntax and semantics can be modeled modularly by separate dependency analyses.
This paper contributes a new, previously unpublished formalization of XDG in first-order logic, and the first results on the closure properties of the string languages licensed by XDG. The closure properties are proven based on the operation of grammar composition, where the string language resulting from the composition of two grammars G1 and G2 is the difference, union or intersection of that of G1 and G2.
We recap the axiomatization of Context-Free Grammar (CFG) of (Debusmann 2006), which we employ as our launch pad to go beyond CFG. First, we explore the relaxation of the contiguity criterion of CFG, and second, we explore the intersection of CFGs. This brings us into the position to formulate a simple and elegant account of German scrambling loosely based on (Duchier and Debusmann 2001).
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