From Dependency to Compositionality: A Neurosymbolic Lifting of LLM Outputs via Combinatory Categorial Grammar

2026-07-21

AI Summary

This work addresses the tendency of large language models (LLMs) to generate outputs lacking verifiable syntactic structure, often resulting in structural errors and hallucinations. The authors propose a neurosymbolic framework that, for the first time, dynamically aligns the incremental derivation mechanism of Combinatory Categorial Grammar (CCG) with the prefix-driven generation process of LLMs. By leveraging the Curry–Howard isomorphism, the approach lifts model outputs into typed compositional derivations. This enables unified structural reconstruction across both natural language and formal languages—including SQL, Solidity, and OWL—and incorporates a two-tier verification mechanism to enforce structural consistency and enable early detection of factual inaccuracies in generated content.

Abstract

Large language models (LLMs) generate fluent text by incrementally predicting the next token from a prefix. Critics in the generative tradition argue that such systems lack genuine grammar; influential replies from the dependency-grammar perspective hold that LLM behavior is well described by local head-dependent structure built word by word. We argue that a sharper observation has been overlooked: the prefix-driven, type-completing dynamics of autoregressive generation align closely with the incremental processing model that Combinatory Categorial Grammar (CCG) was originally designed to support. On this basis we propose a neurosymbolic framework in which LLM outputs are lifted into typed compositional derivations -- not claiming that LLMs implement CCG internally, but that their outputs admit a principled, incremental, and auditable CCG reconstruction. Two consequences follow. First, through the Curry-Howard correspondence the lifting extends beyond natural language to the formal languages LLMs also produce -- programming languages such as Solidity, description-logic and query languages such as OWL and SQL -- with the type system varying and the architecture held fixed. Second, the lifting supports two layers of checking: a compositional layer that catches structural failures directly, and a content layer that checks the lifted structure against external knowledge sources, enabling the earliest possible flagging of hallucinated content. The account thereby requires of a producer not cognition but a prefix-driven generative profile. We close with a sketch of synchronous LLM-CCG coupling as one direction the framework opens.

Problem

• Large Language Models
• Combinatory Categorial Grammar
• Compositionality
• Hallucination
• Neurosymbolic

Innovation

• neurosymbolic
• Combinatory Categorial Grammar
• type system
• incremental compositionality
• hallucination detection