Mathematics of unbounded duplicative and columnar constructions in chinese
Susumu Kuno, Daniel Radzinski · Medical Entomology and Zoology · 1990
This dissertation deals with the relationship between natural languages and formal languages. After surveying the published arguments on generative capacity issues in connection with natural language, we study the very central construction of yes-no A-not-A questions in Chinese, which displays arbitrarily long duplicative strings similar in pattern to those of the formal copy language $\{ WW \vert W \in (a + b)*\}$. We show how this construction could be used to demonstrate that Chinese is not a Context-Free Language from the perspective of internal classification of constructions, i.e. classificatory capacity. We then look at the construction of number-names in Chinese which displays columnar strings of arbitrary length like those of the canonical formal language $\{ab\sp{k1} ab\sp{k2} \... ab\sp{kn} \vert k1 > k2 >\... kn >0\}.$ This construction serves to show that the number-name system of Chinese is beyond the scope of single- or multiple-component Tree Adjoining Grammar, a formalism whose generative power lies between Context-Free Grammar and Context-Sensitive Grammar. The interesting implications this holds for the language as a whole are also discussed. On this matter we conclude that our formal results bear directly either on the syntax of Chinese or on the interface between Chinese and the cognitive component responsible for arithmetic reasoning. Consequently, either Tree Adjoining Grammars, as currently defined, fail to generate the class of natural languages in a way that discriminates between linguistically warranted sub-languages, or formalisms with generative power equivalent to Tree Adjoining grammar cannot serve as a basis for the interface between the human linguistic and mathematical faculties. Similar results hold for Chinese distributive numerals in strings of arbitrary length exhibiting duplication and columniation like those in strings of arbitrary length exhibiting duplication and columniation like those in the formal language $\{ab\sp{k1} ab\sp{k2} \... ab\sp{kn} ab\sp{k1} ab\sp{k2} \... ab\sp{kn} \vert k1>k2>\... >kn>0\}.$ The Indexed Grammars generate all of the phenomena discussed.