Higher Order Grammar

在美国国家科学基金会的支持下，Carl Pollard博士将对高阶语法（HOG）的规范和实现进行为期两年的研究，HOG是一种新的理论和计算语言学的正式框架，旨在作为头驱动短语结构语法（HPSG）的继承者。该研究也有望对其他形式语言学框架，如词汇功能语法（LFG），类型逻辑语法（TLG）和可能世界语义学产生重大影响。Pollard等人在20世纪80年代和90年代开发的HPSG仍然是最广泛使用的形式语言框架之一，但由于其高度非标准的特殊数学基础，它具有许多不受欢迎的特征，这使得非专业人员难以学习和使用，并阻碍了与相邻学科同事的合作（特别是数学、逻辑和计算机科学）。在保留基本模型理论的同时HOG是HPSG（或基于约束的）方法的特征，HOG试图通过转向更成熟和更好理解的证明基础来消除这些问题，即直觉命题逻辑（IPL）及其相关的证明理论。与意义有关的特别有趣的是，HOL中的可能世界概念是可定义的，使命题能够被视为原语和定义的世界（与标准的卡尔纳普-克里普克-蒙塔格传统相反）;这个设置给了我们所有需要的世界（但没有不可能的世界），同时也为哲学逻辑学家所熟悉的长期存在的语义难题提供了新颖而又令人惊讶的简单解决方案（例如逻辑全知（或粒度）问题和Hesperus-磷问题）。注意也将给予语法-音系学接口，从语音解释可以被视为正式等同于语义解释的假设（在范畴逻辑方面，语法-语义和语法-音系学接口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).