Hybrid Type-Logical Grammars, First-Order Linear Logic and the Descriptive Inadequacy of Lambda Grammars

TL;DR

This paper demonstrates that hybrid type-logical grammars are a fragment of first-order linear logic, offering new proof strategies, clarifying their foundations, and highlighting their computational complexity and limitations compared to lambda grammars.

Contribution

It establishes a direct embedding of hybrid type-logical grammars into first-order linear logic, providing new proof methods and insights into their computational and descriptive properties.

Findings

Hybrid type-logical grammars are a fragment of first-order linear logic.

NP-completeness of hybrid type-logical grammars is established.

Lambda grammars suffer from over-generation and syntax-semantics interface issues.

Abstract

In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby clarifying the proof-theoretic foundations of hybrid type-logical grammars, but, since the translation is simple and direct, it also provides several new parsing strategies for hybrid type-logical grammars. Second, NP-completeness of hybrid type-logical grammars follows immediately. The main embedding result also sheds new light on problems with lambda grammars/abstract categorial grammars and shows lambda grammars/abstract categorial grammars suffer from problems of over-generation and from problems at the syntax-semantics interface unlike any other categorial grammar.