Parsing with HPSG

Signs and HPSG Rules vs. Ordinary CFG Rules

• Each sign or HPSG rule consists of SYNSEM, DTRS, and PHON parts.
• The SYNSEM part specifies how the syntax and semantics of the phrase (or word) are constrained. It corresponds roughly to the left-hand side of CFG rules but contains much more information.
• The DTRS part specifies the constituents that make up the phrase (if it is a phrase). (Each of these constituents is a complete sign.) This corresponds to part of the information on the right-hand side of CFG rules, but not to ordering information.
• The PHON part specifies the ordering of the constituents in DTRS (where this is constrained) and the pronunciation of these (if this is specifiable). This corresponds to the the ordering information on the right-hand side of CFG rules.

A Sketch of a Bottom-Up Parsing Algorithm

• Unify input lexical-signs with lexical-signs in the lexicon.
• Until no more such unifications are possible
  • Unify instantiated signs with the daughters of instantiated phrasal signs or with phrasal signs in the grammar.
• If
  • All instantiated signs but one saturated one (S) are associated with daughters of other instantiated signs and
  • the PHON value of all instantiated signs is completely specified
  return the complete S structure
• Else fail.

Example

• The words in the sentence specify only their pronunciations and their positions.

  1 [PHON ((0 1 kim))]
  
  2 [PHON ((1 2 walks))]
  

• Unifying 1 with the lexical entry for Kim gives

  3 [PHON ((0 1 kim))
     SYNSEM [CAT [HEAD noun SUBCAT ()]
             CONTENT [INDEX *1* [PER 3rd NUM sing]]
             CONTEXT [BACKGR {[RELN naming BEARER *1* NAME Kim]}]]]
  

  We now know something about the meaning of Kim (it refers to somebody named Kim) and something about its syntactic properties (it is third person singular).

• Unifying 2 with the lexical entry for walks gives

  4 [PHON ((1 2 walks))
     SYNSEM [CAT [HEAD [VFORM fin]
                  SUBCAT ([CAT [HEAD noun SUBCAT ()]
                           CONTENT [INDEX *1* [PER 3rd NUM sing]]])]
             CONTENT [RELN walk WALKER *1*]]]
  

  We know that walks refers to walking and that it requires a subject noun phrase which refers to the walker but doesn't require any object.

• We have the following grammar rule, which states that one kind of phrase consists only of the head and subcategorizes for the thing that the head requires. It applies in this case, where a VP consists of just an intransitive verb.

  [SYNSEM [CAT [HEAD *1* SUBCAT (*2*)]
           CONTENT *4*]
   DTRS [HEAD-DTR [SYNSEM [CAT [HEAD *1* SUBCAT (*2*)]
                           CONTENT *4*]
                   PHON *3*]
         COMP-DTRS ()]
   PHON *3*]
  

  Unifying 4 with the HEAD-DTR of this rule gives

  5 [SYNSEM [CAT [HEAD [VFORM fin]
                  SUBCAT ([CAT [HEAD noun SUBCAT ()]
                           CONTENT [INDEX *1* [PER 3rd NUM sing]]])]
             CONTENT [RELN walk WALKER *1*]]
     DTRS [HEAD-DTR [SYNSEM [CAT [HEAD [VFORM fin] SUBCAT (...)]]
                     CONTENT [...]
                     PHON ((1 2 walks))]
           COMP-DTRS ()]
     PHON ((1 2 walks))]
  

  Now we have a VP with the transitive verb walks as its head (and only constituent).

• We also have the following grammar rule, which states that a saturated phrase can consist of a head phrase which categorizes for a complement which is an X and an X and that the complement precedes the head. This applies here because our VP only requires a subject.

  6 [SYNSEM [CAT [HEAD *1* SUBCAT ()]
             CONTENT *4*]
     DTRS [HEAD-DTR [SYNSEM [CAT [HEAD *1* SUBCAT (*2*)]
                             CONTENT *4*]
                     PHON *3*]
           COMP-DTRS ([PHON *5*
                       SYNSEM *2*])]
     PHON (*5* < *3*)]
  

  Unifying 5 with the HEAD-DTR of this rule gives

  7 [SYNSEM [CAT [HEAD [VFORM fin SUBCAT ()]]
             CONTENT [RELN walk WALKER *1*]]
     DTRS [HEAD-DTR [SYNSEM [CAT [HEAD [VFORM fin]
                                  SUBCAT ([CAT [HEAD noun SUBCAT ()]
                                           CONTENT [INDEX *1*
                                                          [PER 3rd NUM sing]]])]
                             CONTENT [RELN walk WALKER *1*]]
                     PHON ((1 2 walks))]
           COMP-DTRS ([PHON *2*
                       SYNSEM [CAT [HEAD noun SUBCAT ()]
                               CONTENT [INDEX *1*]]])]
     PHON (*2* < ((1 2 walks)))]
  

  That is, we now have a sentence (subcategorizing for nothing), but its subject (the complement) doesn't have its phonology specified so we're not done.

• Unifying 3 with the COMP-DTR of 7 gives

  8 [SYNSEM [CAT [HEAD [VFORM fin SUBCAT ()]]
             CONTENT [RELN walk WALKER [PER 3rd NUM sing]]]
     DTRS [HEAD-DTR [SYNSEM [CAT [HEAD [VFORM fin]
                                  SUBCAT ([CAT [HEAD noun SUBCAT ()]
                                           CONTENT [INDEX [PER 3rd NUM sing]]])
                             CONTENT [RELN walk WALKER [PER 3rd NUM sing]]]
                     PHON ((1 2 walks))]
           COMP-DTRS ([PHON ((0 1 kim))
                       SYNSEM [CAT [HEAD noun SUBCAT ()]
                               CONTENT [INDEX [PER 3rd NUM sing]]])]
     PHON ((0 1 kim) (1 2 walks))]
  

  Now the subject of the sentence is pronounceable, and we're done.

[L645 Syllabus]