jurafsky&martin_3rdEd_17 (1).pdf

To see some of the ways that ambiguity arises in a

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the grammatical rules. To see some of the ways that ambiguity arises in a categorial framework, consider the following example. (13.34) United diverted the flight to Reno. Our grasp of the role of the flight in this example depends on whether the prepo- sitional phrase to Reno is taken as a modifier of the flight , as a modifier of the entire verb phrase, or as a potential second argument to the verb divert . In a context-free grammar approach, this ambiguity would manifest itself as a choice among the fol- lowing rules in the grammar. Nominal ! Nominal PP VP ! VP PP VP ! Verb NP PP In a phrase-structure approach we would simply assign the word to to the cate- gory P allowing it to combine with Reno to form a prepositional phrase. The sub- sequent choice of grammar rules would then dictate the ultimate derivation. In the categorial approach, we can associate to with distinct categories to reflect the ways in which it might interact with other elements in a sentence. The fairly abstract combinatoric rules would then sort out which derivations are possible. Therefore, the source of ambiguity arises not from the grammar but rather from the lexicon. Let’s see how this works by considering several possible derivations for this example. To capture the case where the prepositional phrase to Reno modifies the flight , we assign the preposition to the category ( NP \ NP ) / NP , which gives rise to the following derivation. United diverted the flight to Reno NP ( S \ NP ) / NP NP / N N ( NP \ NP ) / NP NP > > NP NP \ NP < NP > S \ NP < S Here, the category assigned to to expects to find two arguments: one to the right as with a traditional preposition, and one to the left that corresponds to the NP to be modified. Alternatively, we could assign to to the category ( S \ S ) / NP , which permits the following derivation where to Reno modifies the preceding verb phrase.
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232 C HAPTER 13 S TATISTICAL P ARSING United diverted the flight to Reno NP ( S \ NP ) / NP NP / N N ( S \ S ) / NP NP > > NP S \ S > S \ NP < B S \ NP < S A third possibility is to view divert as a ditransitive verb by assigning it to the category (( S \ NP ) / PP ) / NP , while treating to Reno as a simple prepositional phrase. United diverted the flight to Reno NP (( S \ NP ) / PP ) / NP NP / N N PP / NP NP > > NP PP > ( S \ NP ) / PP > S \ NP < S While CCG parsers are still subject to ambiguity arising from the choice of grammar rules, including the kind of spurious ambiguity discussed in Chapter 11, it should be clear that the choice of lexical categories is the primary problem to be addressed in CCG parsing. 13.7.2 CCG Parsing Frameworks Since the rules in combinatory grammars are either binary or unary, a bottom-up, tabular approach based on the CKY algorithm should be directly applicable to CCG parsing. Recall from Fig. 13.3 that PCKY employs a table that records the location, category and probability of all valid constituents discovered in the input. Given an appropriate probability model for CCG derivations, the same kind of approach can work for CCG parsing.
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