A Note On Higher Order Grammar

TL;DR

This paper explores how Higher Order Grammar (HOG) models syntax-phonology and syntax-semantics interfaces using higher-order logic, revealing that meanings are represented by continuous sets of equivalent logical terms.

Contribution

It formally demonstrates that in HOG, the meaning of expressions is represented by continuous sets of logically equivalent terms, not discrete ones.

Findings

Meaning is represented by continuous sets of equivalent terms.

HOG's architecture allows for a unified logical framework.

Implications for ambiguity and semantic interpretation.

Abstract

Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system. An important implication of this elegant architecture is that the meaning of a valid expression turns out to be represented not by a single, nor even by a few "discrete" terms (in case of ambiguity), but by a "continuous" set of logically equivalent terms. The note is devoted to precise formulation and proof of this observation.