The definition of combinatory categorial grammar (CCG) in the literature varies quite a bit from author to author. However, the differences between the definitions are important in terms of the language classes of each CCG. We prove that a wide range of CCGs are strongly context-free, including the CCG of CCG-bank and of the parser of Clark and Cur-ran (2007). In light of these new results, we train the PCFG parser of Petrov and Klein (2007) on CCGbank and achieve state of the art results in supertagging accuracy, PARSEVAL measures and dependency accuracy.
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