Formal Languages and Linguistic Descriptions

数学语言学领域在20世纪60年代创立之初经历了一阵活跃之后，在过去十年左右的时间里一直相对平静。尽管如此，仍有一些研究人员在这一领域保持活跃，并定期得出对语言学理论的一般关注产生重大影响的结果，例如证明在没有特殊约束的情况下，转换语法的生成能力比想象的要大；以及基本可学习性定理的证明。这项提案的首席研究员是那些继续探索语法系统的数学特性的研究人员之一。他是计算复杂性理论的权威，因为它适用于形式语法和解析系统。现在，他提出了一种新的形式描述语法结构的方法，这种方法将一阶逻辑的表达式与传统短语结构语法的表达式结合起来的新符号作为关键要素，并将语言视为有限逼近族。取代了传统的数学观点，即语言是有限字符串的无限集合。该项目的目的是将研究者的方法发展成一个正式的系统，该系统可以用作语言描述的工具，并且可以以新的和潜在的揭示方式研究其数学特性。研究者在这项工作中得到一位合作者的协助，他是一位有成就的描述和理论语言学家。该项目有可能对语言学理论和计算语言学做出重大的新贡献。

Abstract narrative After an initial burst of activity in the 1960s, when it was founded, the field of mathematical linguistics has been comparatively quiescent in the past decade or so. Nonetheless, a few researchers have kept active in the field, and have periodically produced results which have had a major impact on general concerns of linguistic theory, such as the demon- stration that the generative power of transformational grammars, without special constraints, is greater than supposed, and the proof of the basic learnability theorem. The Principal Investigator of this proposal is one of those researchers who have continued to explore the mathe- matical properties of grammatical systems. He is a leading authority on the theory of computational complexity as it applies to formal grammars and parsing systems. He has now formulated the outlines of a new approach to the formal des- cription of syntactic structures, which incorporates as key elements a novel notation which combines the expressions of first-order logic with the the expressions of conventional phrase-structure grammars, and a view of languages as families of finite approximations, in place of the conventional mathe- matical view of a language as an infinite set of finite strings. The aim of the project is to develop the investigator's approach into a formal system which can be used as a tool for linguistic description, and which can be studied for its mathematical properties in new and potentially revealing ways. The investigator is being assisted in this endeavor by a collaborator who is an accomplished descriptive and theoretical linguist. The project has the potential to make significant new contributions to linguistic theory and also to computational linguistics.