Extensible Dependency Grammar (XDG) (Debusmann et al. 2004 COLING) is
a general framework for dependency grammar, with multiple levels of
linguistic representations called dimensions. Its approach, motivated
by the dependency grammar paradigm (Tesniere 1959; Melcuk 1988), is
articulated around a description language for multi-dimensional
attributed labeled graphs. XDG is a generalization of Topological
Dependency Grammar (TDG) (Duchier and Debusmann 2001)
For XDG, a grammar is a constraint that describes the valid linguistic signs as n-dimensional attributed labeled graphs, i.e. n-tuples of graphs sharing the same set of attributed nodes, but having different sets of labeled edges. It is central to XDG that all aspects of these signs are stipulated explicitly by principles: the class of models for each dimension, additional properties that they must satisfy, how one dimension must relate to another, and even lexicalization.
Yet, no formal account set in the XDG framework has so far explained what exactly these principles are, nor how they can be brought to bear on specific dimensions. In this paper, we show how an XDG grammar can be formally assembled from modular components called parametric principles. This yields a modular and compositional approach to grammar design. Compositional coherence is ensured by a type system whose primary novelty is to accommodate the notion of multi-dimensional graphs. Instantiation of parametric principles not only imposes grammatical constraints, but, through the type system, also determines the necessary structure of grammatical signs. In this perspective, a grammar framework is simply a library of parametric principles such as the one offered by the XDG Development Kit (XDK) (Debusmann et al. 2004 MOZ).
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