Higher Order Grammar

在美国国家科学基金会的支持下，卡尔·波拉德博士将对高阶语法（HOG）的规范和实施进行两年的研究，这是一种新的理论和计算语言学的正式框架，旨在作为头部驱动短语结构语法（HPSG）的继任者。该研究也有望对其他形式语言框架（如词汇功能语法（LFG）、类型逻辑语法（TLG）和可能世界语义）产生重大影响。HPSG是pollard等人在20世纪80年代和90年代开发的，仍然是最广泛使用的正式语言框架之一，但由于其高度非标准和特殊的数学基础，它有许多不受欢迎的特征，这使得非专业人员学习和使用它变得不必要的困难，并为与邻近学科（特别是数学、逻辑和计算机科学）的同事合作创造了障碍。在保留HPSG的基本模型理论（或基于约束的）方法特征的同时，HOG试图通过转向更成熟和更容易理解的数学基础，即直觉命题逻辑（IPL）及其相关证明理论，来消除这些问题。与意义相关的特别有趣的事实是，可能世界的概念在HOL中是可定义的，这使得命题可以被视为原语和已定义的世界（因此与标准卡纳普-克里普克-蒙塔古传统中的情况相反）；这种设置为我们提供了所有我们需要的世界（但不是不可能的世界），同时为哲学逻辑学家所熟悉的长期存在的语义难题（如逻辑全知（或粒度）问题和hesperus -磷问题）提供了新颖而令人惊讶的简单解决方案。还将注意句法-语音界面，根据语音解释可以被视为与语义解释在形式上相同的假设（就范畴逻辑而言，句法-语义和句法-语音界面都是部分逻辑内函子）。

With National Science Foundation support, Dr. Carl Pollard willconduct two years of research on the specification and implementationof Higher Order Grammar (HOG), a new formal framework for theoreticaland computational linguistics intended as a successor to Head-DrivenPhrase Structure Grammar (HPSG). The research is also expectedto have significant consequences for other formal linguisticframeworks such as lexical-functional grammar (LFG), type-logicalgrammar (TLG), and possible-worlds semantics. HPSG, developed byPollard and others in the 1980's and 1990's, is still one of the mostwidely employed formal linguistic framweworks, but has manyundesirable features that arise from its highly nonstandard andidiosyncratic mathematical foundations, which make it unnecessarilydifficult for nonspecialists to learn and use, and which create abarrier to collaboration with colleagues in adjacent disciplines(especially mathematics, logic, and computer science). Whilepreserving the underlying model-theoretic (or constraint-based)approach characteristic of HPSG, HOG seeks to eliminate these problems by shifting to more established and better understood mathematicalfoundations, namely intuitionistic propositional logic (IPL) and itsassociated proof theory.Of particular interest in connection with meaning is the fact that thenotion of POSSIBLE WORLD is definable in the HOL, enablingpropositions to be treated as primitives and worlds as defined (thereverse of the situation in the standard Carnap-Kripke-Montaguetradition); this setup gives us all the worlds we need (but noimpossible worlds), while at the same time leading to novel andsurprisingly simple solutions of longstanding semantic conundrumsfamiliar to philosophical logicians (such as the logical omniscience(or granularity) problem and the Hesperus-Phosphorus problem). Attention will also be given to the syntax-phonology interface, working from the hypothesis that phonological interpretation can be treated asformally on a par with semantic interpretation (in terms of categoricallogic,the syntax-semantics and syntax-phonology interfaces are bothpartial logical endofunctors).