A Proposed Mathematical Theory Explaining Word Order Typology

Abstract

In this paper I attempt to lay the groundwork for an algorithm that measures sentence competency. Heretofore, competency of sentences was determined by interviewing speakers of the language. The data compiled forms the basis for grammatical rules that establish the generative grammar of a language. However, the generative grammar, once established, does not filter out all incompetent sentences. Chomsky has noted that there are many sentences that are grammatical but do not satisfy the notion of competency and, similarly, many non-grammatical constructions that do. I propose that generative grammar constructions as well as formal theory frameworks such as Transformational Grammar, Minimalist Theory, and Government and Binding do not represent the most irreducible component of a language that determines sentence competency. I propose a Mathematical Theory governing word order typology that explains not only the established generative grammar rules of a language but, also, lays the groundwork for understanding sentence competency in terms of irreducible components that has not been accounted for in previous formal theories. I have done so by relying on a mathematical analysis of word frequency relationships based upon large, representative corpuses that represents a more basic component of sentence construction overlooked by current text processing and artificial intelligence parsing systems and unaccounted for by the generative grammar rules of a language.