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

arXiv: https://arxiv.org/abs/1405.6678 · HTML: https://mlsanity.com/paper/1405.6678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2014.

## Built on by (most cited first, 2 of 2)

- [First order linear logic and tensor type calculus for categorial grammars](https://mlsanity.com/paper/2112.15253/) (2021)
- [Making first order linear logic a generating grammar](https://mlsanity.com/paper/2206.08955/) (2022)

## Abstract (arXiv)

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.