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A lot of interest has recently been paid to constraint-based definitions and extensions of Tree Adjoining Grammars (TAG). Examples are the so-called quasi-trees, D-Tree Grammars and Tree Description Grammars. The latter are grammars consisting of a set of formulars denoting trees. TDGs are derivation based where in each derivation step a conjunction is built of the old formular, a formular of the grammar and additional equivalences between node names of the two formulars. This formalism is more powerfull than TAGs. TDGs offer the advantages of MC-TAG and D-Tree Grammars for natural languages and they allow underspecification. However the problem is that TDGs might be unnecessarily powerfull for natural languages. To solve this problem, in this paper, I will propose a local TDGs, a restricted version of TDGs. Local TDGs still have the advantages of TDGs but they are semilinear and therefore more appropriate for natural languages. First, the notion of the semilinearity is defined. Then local TDGs are introduced, and, finally, semilinearity of local Tree Description Languages is proven.
Existing analyses of German scrambling phenomena within TAG-related formalisms all use non-local variants of TAG. However, there are good reasons to prefer local grammars, in particular with respect to the use of the derivation structure for semantics. Therefore this paper proposes to use local TDGs, a TAG-variant generating tree descriptions that shows a local derivation structure. However the construction of minimal trees for the derived tree descriptions is not subject to any locality constraint. This provides just the amount of non-locality needed for an adequate analysis of scrambling. To illustrate this a local TDG for some German scrambling data is presented.