jurafsky&martin_3rdEd_17 (1).pdf

Both kinds of composition are signalled by a b in ccg

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to the right for the relevant arguments. Both kinds of composition are signalled by a B in CCG diagrams, accompanied by a < or > to indicate the direction. The next operator is type raising . Type raising elevates simple categories to the Type raising status of functions. More specifically, type raising takes a category and converts it to function that seeks as an argument a function that takes the original category
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11.6 L EXICALIZED G RAMMARS 191 as its argument. The following schema show two versions of type raising: one for arguments to the right, and one for the left. X ) T / ( T \ X ) (11.9) X ) T \ ( T / X ) (11.10) The category T in these rules can correspond to any of the atomic or functional categories already present in the grammar. A particularly useful example of type raising transforms a simple NP argument in subject position to a function that can compose with a following VP . To see how this works, let’s revisit our earlier example of United serves Miami . Instead of clas- sifying United as an NP which can serve as an argument to the function attached to serve , we can use type raising to reinvent it as a function in its own right as follows. NP ) S / ( S \ NP ) Combining this type-raised constituent with the forward composition rule ( 11.7 ) permits the following alternative to our previous derivation. United serves Miami NP ( S \ NP ) / NP NP > T S / ( S \ NP ) > B S / NP > S By type raising United to S / ( S \ NP ) , we can compose it with the transitive verb serves to yield the ( S / NP ) function needed to complete the derivation. There are several interesting things to note about this derivation. First, is it provides a left-to-right, word-by-word derivation that more closely mirrors the way humans process language. This makes CCG a particularly apt framework for psy- cholinguistic studies. Second, this derivation involves the use of an intermediate unit of analysis, United serves , that does not correspond to a traditional constituent in English. This ability to make use of such non-constituent elements provides CCG with the ability to handle the coordination of phrases that are not proper constituents, as in the following example. (11.11) We flew IcelandAir to Geneva and SwissAir to London. Here, the segments that are being coordinated are IcelandAir to Geneva and SwissAir to London , phrases that would not normally be considered constituents, as can be seen in the following standard derivation for the verb phrase flew IcelandAir to Geneva . flew IcelandAir to Geneva ( VP / PP ) / NP NP PP / NP NP > > VP / PP PP > VP In this derivation, there is no single constituent that corresponds to IcelandAir to Geneva , and hence no opportunity to make use of the < F > operator. Note that complex CCG categories can can get a little cumbersome, so we’ll use VP as a shorthand for ( S \ NP ) in this and the following derivations. The following alternative derivation provides the required element through the use of both backward type raising ( 11.10 ) and backward function composition ( 11.8 ).
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192 C HAPTER 11 F ORMAL G RAMMARS OF E NGLISH flew IcelandAir to Geneva ( VP / PP ) / NP NP PP / NP NP < T > ( VP / PP ) \ (( VP / PP ) / NP ) PP < T VP \ ( VP / PP ) < B VP \ (( VP / PP ) / NP ) < VP Applying the same analysis to
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