We propose a lexicalized formulation of dependency grammar which extends the non-projective account of syntax of extitAxiomatizing Dependency
Parsing Using Set Constraints [Duchier 1999] with an account of linear precedence
inspired by the classical model of topological fields [Bech, 1955].
In this framework, an analysis
consists of two mutually constraining trees: a tree of syntactic
dependencies (ID tree) and a tree of topological dependencies (LP
tree). The ID tree is non-ordered and non-projective, and its edges
are labeled by syntactic relations. The LP tree is partially ordered
and projective, and its edges are labeled by topological fields. The
shape of the LP tree is a flattening of the ID tree's obtained by an
emancipation process allowing nodes to `climb up'. Our theory is
formulated in term of lexicalized constraints and of principles
governing climbing conditions.
In extitTopological Dependency Trees: A Constraint-based Account of Linear
Precedence [Duchier, Debusmann, 2001], we described
its application to an account of word-order phenomena in the German
verb complex. In the present article, we focus on its formalization
and state a formal well-formedness condition that precisely
characterizes the valid analyses. Furthermore, this condition can
also be interpreted as a constraint program and forms the basis of our
implementation.