Week5-8Alternative Parsing Formalisms

Mildly Context-sensitive grammars

-Tree substitution grammars(TSG)
- Terminals generate entire tree fragments
- TSG and CFG are formally equivalent
- Tree adjoining grammar(TAG)
- Combinatory categorical grammar(CCG)

TAG

• Like TSG but allow adjunction

Adjunction: suppose we have a parse tree with verb phrase embedded in it. Adjunction allows you to create a new node and to put it inside the tree and push the existing sub-tree further down. So we will have a new verb phrase that have the original verb phrase as its descendents.

• It can generate languages like $a^nb^nc^n$ or ww(cross-serial dependencies)(repeated same strings):
  
  • Mary gave a book and a magazine to Chen and Mike, respectively. (cannot be generated by CFG but can by TAG)
• expressive power
  
  • TAG is formally more powerful than CFG
  • TAG is less powerful than CSG

CCG

-Complex type
- X/Y, X\Y
- Take an argument of type Y, and return an object of type X.
- X/Y means that Y should appear on the right
- X\Y means that Y should appear on the left

• Expressive power
  
  • CCGs can generate the language $a^nb^nc^nd^n$, $n>0$

Semantic Parsing

• Associate a semantic expression with each node

One of the hottest areas in the next few years.