jurafsky&martin_3rdEd_17 (1).pdf

The categorial approach consists of three major

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The categorial approach consists of three major elements: a set of categories, a lexicon that associates words with categories, and a set of rules that govern how categories combine in context. Categories Categories are either atomic elements or single-argument functions that return a cat- egory as a value when provided with a desired category as argument. More formally, we can define C , a set of categories for a grammar as follows: A C , where A is a given set of atomic elements ( X / Y ), ( X \ Y ) 2 C , if X , Y 2 C The slash notation shown here is used to define the functions in the grammar. It specifies the type of the expected argument, the direction it is expected be found,
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11.6 L EXICALIZED G RAMMARS 189 and the type of the result. Thus, ( X / Y ) is a function that seeks a constituent of type Y to its right and returns a value of X ; ( X \ Y ) is the same except it seeks its argument to the left. The set of atomic categories is typically very small and includes familiar el- ements such as sentences and noun phrases. Functional categories include verb phrases and complex noun phrases among others. The Lexicon The lexicon in a categorial approach consists of assignments of categories to words. These assignments can either be to atomic or functional categories, and due to lexical ambiguity words can be assigned to multiple categories. Consider the following sample lexical entries. flight : N Miami : NP cancel : ( S \ NP ) / NP Nouns and proper nouns like flight and Miami are assigned to atomic categories, reflecting their typical role as arguments to functions. On the other hand, a transitive verb like cancel is assigned the category ( S \ NP ) / NP : a function that seeks an NP on its right and returns as its value a function with the type ( S \ NP ). This function can, in turn, combine with an NP on the left, yielding an S as the result. This captures the kind of subcategorization information discussed in Section 11.3.4 , however here the information has a rich, computationally useful, internal structure. Ditransitive verbs like give , which expect two arguments after the verb, would have the category (( S \ NP ) / NP ) / NP : a function that combines with an NP on its right to yield yet another function corresponding to the transitive verb ( S \ NP ) / NP category such as the one given above for cancel . Rules The rules of a categorial grammar specify how functions and their arguments com- bine. The following two rule templates constitute the basis for all categorial gram- mars. X / Y Y ) X (11.4) Y X \ Y ) X (11.5) The first rule applies a function to its argument on the right, while the second looks to the left for its argument. We’ll refer to the first as forward function appli- cation , and the second as backward function application . The result of applying either of these rules is the category specified as the value of the function being ap- plied.
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