Tree adjoining grammars

• Basic reference: Joshi and Schabes, 1997; tutorial
• Basic elements are lexicalized trees: at least one terminal frontier node
• In addition to terminal and non-terminal symbols, a grammar consists of a set of elementary trees
  • Initial trees: non-terminal frontier nodes support substitution
  • Auxiliary trees: have a single foot node with the same category label as the root node, supports adjunction (substitution nodes also possible)
• Two kinds of operations on trees in a derivation
  • Substitution: tree with root node labeled `x` is attached to a node supporting substitution with label `x`
  • Adjunction: given an auxiliary tree `beta` with foot node and root node labeled `x` and another tree `alpha` with a non-substitution node `n` also labeled `x`,
    • the subtree of `alpha` under `n`, `t`, is excised
    • `beta` is attached at `n`
    • `t` is reattached to the foot node of `beta`
• Derivation tree: specifies how a derived tree was constructed