Copying in natural languages, context-freeness, and queue grammars

TLDR: The absence of mirror-image constructions in human languages means that it is not enough to extend Context-free Grammars in the direction of context-sensitivity, and a class of grammars must be found which handles (context-sensitive) copying but not ( context-free) mirror images, suggesting that human linguistic processes use queues rather than stacks.

Abstract: The documentation of (unbounded-length) copying and cross-serial constructions in a few languages in the recent literature is usually taken to mean that natural languages are slightly context-sensitive. However, this ignores those copying constructions which, while productive, cannot be easily shown to apply to infinite sublanguages. To allow such finite copying constructions to be taken into account in formal modeling, it is necessary to recognize that natural languages cannot be realistically represented by formal languages of the usual sort. Rather, they must be modeled as families of formal languages or as formal languages with indefinite vocabularies. Once this is done, we see copying as a truly pervasive and fundamental process in human language. Furthermore, the absence of mirror-image constructions in human languages means that it is not enough to extend Context-free Grammars in the direction of context-sensitivity. Instead, a class of grammars must be found which handles (context-sensitive) copying but not (context-free) mirror images. This suggests that human linguistic processes use queues rather than stacks, making imperative the development of a hierarchy of Queue Grammars as a counterweight to the Chomsky Grammars. A simple class of Context-free Queue Grammars is introduced and discussed.