This paper describes a new interpretation of Tree Adjoining Grammars (TAG) that allows the embedding of TAG in the unification framework in a manner consistent with the declarative approach taken in this framework. In the new interpretation we present in this paper, the objects manipulated by a TAG are considered to be descriptions of trees. This is in contrast to the traditional view that in a TAG the composition operations of adjoining and substitution combine trees. Borrowing ideas from Description Theory, we propose quasi-trees as a means to represent partial descriptions of trees. Using quasi-trees, we are able to justify the definition of feature structure-based Tree Adjoining Grammars (FTAG) that was first given in Vijay-Shanker (1987) and Vijay-Shanker and Joshi (1988). In the definition of the FTAG formalism given here, we argue that a grammar manipulates descriptions of trees (i.e., quasi-trees); whereas the structures derived by a grammar are trees that are obtained by taking the minimal readings of such descriptions. We then build on and refine the earlier version of FTAG, give examples that illustrate the usefulness of embedding TAG in the unification framework, and present a logical formulation (and its associated semantics) of FTA G that shows the separation between descriptions of well-formed structures and the actual structures that are derived, a theme that is central to this work. Finally, we discuss some questions that are raised by our new interpretation of the TAG formalism: questions dealing with the nature and definition of the adjoining operation (in contrast to substitution), its relation to multi-component adjoining, and the distinctions between auxiliary and initial structures.
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