Abstract
For a long time there has been a debate about whether CFGs are sufficiently powerful to describe natural languages. Several approaches have used CFGs, oftentimes enriched with some additional mechanism of transformation (Chomsky, 1956) or with features (Gazdar et al., 1985) for natural languages. These approaches were able to treat a large range of linguistic phenomena.
However, in the 1980s Stuart Shieber was able to prove in (1985) that there are natural languages that cannot be generated by a CFG. Before that, Bresnan et al. (1982) made a similar argument but their proof is based on the tree structures obtained with CFGs while Shieber argues on the basis of weak generative capacity, i.e., of the string languages.
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Kallmeyer, L. (2010). Grammar Formalisms for Natural Languages. In: Parsing Beyond Context-Free Grammars. Cognitive Technologies, vol 0. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14846-0_2
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