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

arXiv: https://arxiv.org/abs/2607.18961 · HTML: https://mlsanity.com/paper/2607.18961/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 8 of 8)

- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Synchromesh: Reliable code generation from pre-trained language models](https://mlsanity.com/paper/2201.11227/) (2022)
- [Verbalizable Representations Form a Global Workspace in Language Models](https://mlsanity.com/paper/2607.15495/) (2026)
- [A* CCG Parsing with a Supertag and Dependency Factored Model](https://mlsanity.com/paper/1704.06936/) (2017)
- [Human-Artificial Interaction in the Age of Agentic AI: A System-Theoretical Approach](https://mlsanity.com/paper/2502.14000/) (2025)
- [Beyond Code Similarity: Benchmarking the Plausibility, Efficiency, and Complexity of LLM-Generated Smart Contracts](https://mlsanity.com/paper/2511.16224/) (2025)

## Abstract (arXiv)

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.