Tree Insertion Grammar (TIG)

Overview

Tree insertion grammar (TIG) is a grammar formalism derived from tree adjoining grammars (TAG). This formalism consists of a tree-lexicon with trees describing word phrases in a grammatical context and two operations (adjunction,substitution), which can be applied to create a correct sentence in the language.
More precisely, a correct sentence is a consistent derivation over the trees in the grammar. Derivation means iteratively performing the possible operations (adjunction, substitution) with entrys of the tree-lexicon.

Tree - structure

The entrys in the language lexicon have a ordinary tree structure with some further conditions. Each node in the tree can have one of the following types : NONTERM , TERM , SUBST , EPS , RFOOT , LFOOT. Nodes of type NONTERM are always inner-nodes, all types have to occur as leaf-nodes. Additionally each node in the tree has a specified categorie, except the nodes of type NONTERM. Those nodes represent a lexical expression in the underlying language and has this expression as label value. The nodes of type SUBST indicating a possible substitution operation.
The nodes of type RFOOT or type LFOOT have to occur uniqueliy in a tree, such that there aren't any trees with more than one RFOOT typed node and LFOOT typed node in that tree. These trees are named auxiliary trees and are important for the adjunction operation.
Each tree has to have at least one node of type NONTERM.

Auxiliary trees

Adjunction

Substitution

The substitution operation can be performed on any tree with a leaf node of type SUBST and a further tree in which the categorie of the root node is equivalent to the categorie in that leaf node. Such trees could be combined by attaching the second tree at the SUBST typed leaf node.