Higher Order Grammar

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

With National Science Foundation support, Dr. Carl Pollard will conduct two years of research on the specification and implementation of Higher Order Grammar (HOG), a new formal framework for theoretical and computational linguistics intended as a successor to Head-Driven Phrase Structure Grammar (HPSG). The research is also expected to have significant consequences for other formal linguistic frameworks such as lexical-functional grammar (LFG), type-logical grammar (TLG), and possible-worlds semantics. HPSG, developed by Pollard and others in the 1980's and 1990's, is still one of the most widely employed formal linguistic framweworks, but has many undesirable features that arise from its highly nonstandard and idiosyncratic mathematical foundations, which make it unnecessarily difficult for nonspecialists to learn and use, and which create a barrier to collaboration with colleagues in adjacent disciplines (especially mathematics, logic, and computer science). While preserving 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 mathematical foundations, namely intuitionistic propositional logic (IPL) and its associated proof theory. Of particular interest in connection with meaning is the fact that the notion of POSSIBLE WORLD is definable in the HOL, enabling propositions to be treated as primitives and worlds as defined (the reverse of the situation in the standard Carnap-Kripke-Montague tradition); this setup gives us all the worlds we need (but no impossible worlds), while at the same time leading to novel and surprisingly simple solutions of longstanding semantic conundrums familiar 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 as formally on a par with semantic interpretation (in terms of categorical logic,the syntax-semantics and syntax-phonology interfaces are both partial logical endofunctors).