text: Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a syntactic representation of a sentence as each successive lexeme is read. A GIG rule specifies a set of parse configurations that trigger its application and an operation to perform on a matching configuration. Rules are partly context-sensitive; furthermore, they are reversible, meaning that their operations can be undone, which allows the parsing process to be nondeterministic. These two factors confer enough expressive power to the formalism for parsing natural languages.
  @cite_2: In this paper, a tree generating system called a tree adjunct grammar is described and its formal properties are studied relating them to the tree generating systems of Brainerd (Information and Control14 (1969), 217-231) and Rounds (Mathematical Systems Theory 4 (1970), 257-287) and to the recognizable sets and local sets discussed by Thatcher (Journal of Computer and System Sciences1 (1967), 317-322; 4 (1970), 339-367) and Rounds. Linguistic relevance of these systems has been briefly discussed also.
summary: Graph interpolation can be viewed as an extension of tree adjunction to parse graphs. And, indeed, TAGs @cite_2 , by introducing a 2-dimensional formalism into computational linguistics, have made a decisive step towards designing a syntactic theory that is both computationally tractable and linguistically realistic. In this respect, it is an obligatory reference for any syntactic theory intent on satisfying these criteria.