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This paper proposes a neurosymbolic framework that maps Large Language Model outputs onto Combinatory Categorial Grammar (CCG), enabling auditable, incremental reconstruction of generative text. By leveraging the Curry-Howard correspondence, this approach extends structural verification beyond natural language to formal programming and query languages like Solidity and SQL. The method introduces dual-layer checking mechanisms—compositional for syntax errors and content-based against external knowledge—to significantly reduce hallucinations in LLM-generated code and logic.
From Dependency to Compositionality: A Neurosymbolic Lifting of LLM Outputs via Combinatory Categorial Grammar
arXiv:2607.18961v1 Announce Type: new 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.
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.
27 pages. Under review
Artificial Intelligence (cs.AI)
I.2.7; F.4.1; F.4.2; D.2.4
arXiv:2607.18961 [cs.AI]
(or arXiv:2607.18961v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.18961 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 335 words
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