Beyond Simple CFGs

• Problems with Context-Free Grammars (RTNs)
  • Agreement (in Swahili)

       Wavulana watatu wadogo walianguka.
       boys     three  small  fell
       `Three small boys fell.'
    
       Viti   vitatu vidogo vilianguka.
       chairs three  small  fell
       `Three small chairs fell.'
    
       Nyumba   tatu  ndogo zilianguka.
       house(s) three small fell
       `Three small houses fell.'
    
       Meno  matatu madogo yalianguka.
       teeth three  small  fell
       `Three small teeth fell.'
    

    • In a CFG for Swahili, we seem to need separate NP networks and separate S networks for each class of nouns. For English Ss (which are much simpler), we would have

      

  • Long-distance dependencies
    • What did you say you thought Bill wanted to wear?
    • The ordinary rules fail to apply here because wear, a transitive verb, does not have an immediately following direct object. We seem to need separate rules for each way in which a clause like Bill wanted to wear (something) can be embedded in a question which asks about the "something". We seem to need rules like the following (where "TVP-NP" means "transitive VP without its normal NP"):

      

      But there would need to be many of these, they would not permit embedding at an arbitrary level, and they would not show how questions are related to the corresponding statements.

• Alternatives
  • Old
    • Transformations: rules which move, delete, or insert constituents, relating "deep" and "surface" structures
    • Augmented transition networks
      • Registers: global and local to subnetworks
      • Tests: evaluating arbitrary LISP expressions
      • Actions: evaluating arbitrary LISP expressions

        

    • Both of these approaches have the disadvantages of being
      • Largely unconstrained
      • Procedural: not usable for variety of tasks
  • New
    • Context-free grammars with complex categories
      • Handling agreement

        ((cat S)) -> (((cat NP) (number ?n)) ((cat VP) (number ?n)))
        ((cat NP) (number ?n)) -> (((cat N) (number ?n))))
        ((cat VP) (number ?n)) -> (((cat V) (arg1 0) (number? n)))
        Willard: ((cat N) (number sing) (lex willard))
        people: ((cat N) (number plur) (lex person))
        dances: ((cat V) (arg1 0) (number sing) (lex dance))