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

This paper addresses the debate over whether Large Language Models (LLMs) possess genuine grammatical structure. Rather than arguing for or against internal linguistic competence, the author observes that the autoregressive, prefix-driven nature of LLM generation aligns perfectly with the incremental processing model of Combinatory Categorial Grammar (CCG). The proposed framework treats CCG as a post-hoc 'lifting' mechanism: it takes the output of an LLM and maps it into a typed, compositional symbolic representation using existing CCG semantic parsers.

The framework provides two major advantages for managing LLM outputs. First, it enables a two-layer checking system: a compositional layer that verifies structural integrity and a content layer that compares the lifted logical form against external knowledge sources to detect hallucinations. Second, because CCG derivations are isomorphic to type-checking in formal languages (via the Curry-Howard correspondence), this approach extends beyond natural language to programming languages like Solidity or query languages like SQL without requiring changes to the underlying LLM architecture.

By lifting fluent but opaque LLM text into transparent, auditable symbolic structures, this approach bridges the gap between neural flexibility and symbolic rigor. It allows researchers to treat LLMs as reliable producers of structured data, providing a principled way to verify the correctness of generated code or factual claims. This method requires no retraining or internal access to the model, making it a highly portable and conservative strategy for improving the reliability of neurosymbolic systems.