jurafsky&martin_3rdEd_17 (1).pdf

Given these rules and a simple lexicon lets consider

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Given these rules and a simple lexicon, let’s consider an analysis of the sentence United serves Miami . Assume that serves is a transitive verb with the category ( S \ NP ) / NP and that United and Miami are both simple NP s. Using both forward and backward function application, the derivation would proceed as follows: United serves Miami NP ( S \ NP ) / NP NP > S \ NP < S
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190 C HAPTER 11 F ORMAL G RAMMARS OF E NGLISH Categorial grammar derivations are illustrated growing down from the words, rule applications are illustrated with a horizontal line that spans the elements in- volved, with the type of the operation indicated at the right end of the line. In this example, there are two function applications: one forward function application indi- cated by the > that applies the verb serves to the NP on its right, and one backward function application indicated by the < that applies the result of the first to the NP United on its left. With the addition of another rule, the categorial approach provides a straight- forward way to implement the coordination metarule described earlier on page 181 . Recall that English permits the coordination of two constituents of the same type, resulting in a new constituent of the same type. The following rule provides the mechanism to handle such examples. X CONJ X ) X (11.6) This rule states that when two constituents of the same category are separated by a constituent of type CONJ they can be combined into a single larger constituent of the same type. The following derivation illustrates the use of this rule. We flew to Geneva and drove to Chamonix NP ( S \ NP ) / PP PP / NP NP CONJ ( S \ NP ) / PP PP / NP NP > > PP PP > > S \ NP S \ NP < F > S \ NP < S Here the two S \ NP constituents are combined via the conjunction operator < F > to form a larger constituent of the same type, which can then be combined with the subject NP via backward function application. These examples illustrate the lexical nature of the categorial grammar approach. The grammatical facts about a language are largely encoded in the lexicon, while the rules of the grammar are boiled down to a set of three rules. Unfortunately, the basic categorial approach does not give us any more expressive power than we had with traditional CFG rules; it just moves information from the grammar to the lexicon. To move beyond these limitations CCG includes operations that operate over functions. The first pair of operators permit us to compose adjacent functions. X / Y Y / Z ) X / Z (11.7) Y \ Z X \ Y ) X \ Z (11.8) The first rule, called forward composition , can be applied to adjacent con- Forward composition stituents where the first is a function seeking an argument of type Y to its right, and the second is a function that provides Y as a result. This rule allows us to compose these two functions into a single one with the type of the first constituent and the argument of the second. Although the notation is a little awkward, the second rule, backward composition is the same, except that we’re looking to the left instead of Backward composition to the right for the relevant arguments. Both kinds of composition are signalled by a
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