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_4: The editor of this volume, who is also author or coauthor of five of the contributions, has provided an introduction that not only affords an overview of the separate articles but also interrelates the basic issues in linguistics, psycholinguistics and cognitive studies that are addressed in this volume. The twelve articles are grouped into three sections, as follows: "I. Lexical Representation: " The Passive in Lexical Theory (J. Bresnan); On the Lexical Representation of Romance Reflexive Clitics (J. Grimshaw); and Polyadicity (J. Bresnan)."II. Syntactic Representation: " Lexical-Functional Grammar: A Formal Theory for Grammatical Representation (R. Kaplan and J. Bresnan); Control and Complementation (J. Bresnan); Case Agreement in Russian (C. Neidle); The Representation of Case in Icelandic (A. Andrews); Grammatical Relations and Clause Structure in Malayalam (K. P. Monahan); and Sluicing: A Lexical Interpretation Procedure (L. Levin)."III. Cognitive Processing of Grammatical Representations: " A Theory of the Acquisition of Lexical Interpretive Grammars (S. Pinker); Toward a Theory of Lexico-Syntactic Interactions in Sentence Perception (M. Ford, J. Bresnan, and R. Kaplan); and Sentence Planning Units: Implications for the Speaker's Representation of Meaningful Relations Underlying Sentences (M. Ford).
summary: In Lexical Functional Grammars @cite_4 , grammatical functions are loosely coupled with phrase structure, which seems to be just the opposite of what is done in a GIG, in which functional edges are part of the phrase structure. Nonetheless, these two approaches share the concern of bringing out a functional structure, even if much of what enters into an f-structure (i.e. a functional structure) in LFG is to be addressed by the semantic component ---a topic for further research--- in GIG.