Hybrid Type-Logical Grammars, First-Order Linear Logic and the Descriptive Inadequacy of Lambda Grammars
This work addresses theoretical foundations and computational properties for computational linguists, though it appears incremental as it builds on existing grammar frameworks.
The authors demonstrated that hybrid type-logical grammars are a fragment of first-order linear logic, leading to a new proof theory, parsing strategies, and NP-completeness proof. They also argued that this reveals lambda grammars/abstract categorial grammars have unique over-generation and syntax-semantics interface issues compared to other categorial grammars.
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.