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 L03 FS: Feature structures with CFG


        Features and CFG

We have already seen that feature structures (FS) can be
associated with words in the lexicon:

+ FS associated with 'child' in lexicon
 
    [ ROOT      child          ]
    [ CAT       n              ]
    [ AGRMNT    [ NUMBER  sg ] ]
    [           [ PERSON   3 ] ]

+ FS associated with 'a' in lexicon
    [ SPEC      indef          ]
    [ AGRMNT    [ NUMBER  sg ] ]
    [           [ PERSON   3 ] ]

o  Features can be put in context free grammar (CFG)
   -  Associate FS with both terminals & non-terminals
   -  Specify constraints on the CFG 

+ Example CF rule 1 with constraint 
    +  NP  ->   det n
    +  Constraint:
         FS(NP) = FS(det)  U  FS(n)

    -  That is, NP consists of a det followed by an n,
        * provided, the FS of det and n unify.
        * resulting FS of NP is the result of unification

    +  Resulting FS (of NP for 'a child') 

         [ ROOT      child          ]
         [ CAT       n              ]
         [ SPEC      indef          ]
         [ AGRMNT    [ NUMBER  sg ] ]
         [           [ PERSON   3 ] ]
      

o  Continuing the example:
    +  CF rule 3:
         VP  ->  v  NP
       Constraints:
         FS(VP).act   =  FS(v).root
         FS(VP).obj   =  FS(NP)

    +  CF rule 2:
         S  ->  NP  VP
       Constraints:
         FS(S).agent   = FS(NP)
         FS(S).patient = FS(VP).obj
         FS(S).act     = FS(VP).act

o Builds a semantic structure above for the sentence
  + 'a child eats the cake':

         [ CAT      S              ]
         [ AGENT    [ ROOT child ] ]
         [          [   ...      ] ]
         [                         ]
         [ ACT      [ ROOT eat   ] ]
         [          [   ...      ] ]
         [                         ]
         [ OBJ      [ ROOT cake  ] ]
         [          [   ...      ] ]
      
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o  Subj-verb agreement rule can also be expressed by
   means of feature structures:
    +  CF rule 2:
         S  ->  NP  VP
       Additional constraint:
         FS(NP).AGRMNT = FS(VP).AGRMNT

    -  S can be rewritten to: NP followed by VP, provided:
        *  Value of attribute AGRMNT in FS associated
           with NP, unifies with that in VP

    +  CF rule 3:
         VP  ->  v  NP
       Additional constraints:
         FS(VP).AGRMNT  =  FS(v).AGRMNT
         FS(VP).TENSE   =  FS(v).TENSE
       Note: VP gets its agreement features from v, and not NP

o  Example application of rules with input sentence:
     A child sees the toys.

   -  FS with 'picks' and VP (constraint with rule 3):
             
        [TENSE   prsnt         ]
        [AGRMNT  [NUMBER   sg] ]

   -  Constraint with rule 2 succeeds because values of
      AGRMNT feature are compatible.
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