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

Remo Pareschi

REVIEW 4 major objections 4 minor 1 cited by

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

T0 review · 4 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The paper argues that LLM output can be lifted into typed compositional derivations because the prefix-by-prefix way LLMs generate text matches CCG's type-completing design.

desk verdict Worth reading as a position paper, but the central alignment claim is asserted, not measured; without that measurement the framework reduces to ordinary CCG parsing of LLM output. read the letter →

arxiv 2607.18961 v2 pith:HE62UTLD submitted 2026-07-21 cs.AI

Remo Pareschi This is my paper · ORCID

classification cs.AI

keywords largelanguagemodelsCombinatoryCategorialGrammarcompositionalsemanticsneurosymbolicAIhallucinationdetectionincrementalparsingprefix-drivengenerationsmartcontracts

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the output of an autoregressive large language model has a recoverable compositional grammar. At every prefix, the generated text can be assigned a typed category and a partial meaning in the manner of Combinatory Categorial Grammar, and this assignment is not an arbitrary overlay because LLM generation is itself prefix-driven and type-completing — each step predicts what comes next, and CCG was designed to represent exactly what a prefix requires next. If true, this gives a principled way to turn LLM text into transparent logical forms, enabling early detection of both structural errors and factual hallucinations. The same lifting extends to formal outputs like smart-contract code and query languages through the propositions-as-types correspondence, with the type system varying and the architecture held fixed.

What carries the argument

The central object is CCG itself — a lexicalized grammar in which every word carries both a syntactic category and a lambda term, and in which every prefix has a typed partial meaning, so 'John loves' is the category S/NP with the partial term λy.love(john,y). The argument leans on three properties: semantically interpreted incrementality (every prefix is a first-class typed object), derivational equivalence modulo composition (alternative derivations converge to the same lambda term, making the lifting well-defined), and the ability of modern supertaggers to assign categories to unseen words from context. These allow CCG to serve as a post-hoc lifting mechanism applied to observable LLM out

What would settle it

Run a wide-coverage CCG parser over a corpus of fluent LLM-generated text sampled from non-newswire registers, and measure the fraction of sentences that receive any typed derivation with acceptable parse confidence. If a substantial fraction fail to lift, or if the n-best analyses yield conflicting lambda terms on simple declaratives beyond known ambiguity, the central claim is refuted. A benchmark showing parse coverage on LLM output comparable to newswire coverage would support it.

Watch

Extended reading notes

Core claim

The central claim is that the prefix-driven, type-completing dynamics of autoregressive generation align closely with the incremental processing model that CCG was designed to support, so LLM outputs admit a principled, incremental, and auditable CCG reconstruction. The paper carefully does not claim LLMs implement CCG internally; it claims the outputs can be lifted post hoc into typed lambda terms, with every prefix carrying a category whose unsaturated argument matches the model's next-token expectation. Two consequences follow. First, the lifting extends beyond natural language to formal languages, because the operation of assigning a typed term to an expression is the same as type-checki

Load-bearing premise

The load-bearing premise is that existing wide-coverage CCG parsers and supertaggers can correctly assign typed derivations to LLM-generated text across registers and domains even though they are mainly trained on about a million words of newswire English; if parser coverage collapses on real LLM output, the lifting and every downstream check collapse.

Editorial extensions

If this is right

Every fluent declarative sentence produced by an LLM can be represented as an auditable typed lambda term whose components trace back to lexical entries and combinatory steps.
Hallucination detection can be formulated at the earliest structurally meaningful prefix, before the sentence is complete, by querying external knowledge sources with the predications the lifted prefix exposes.
Compositional failures in generated code become visible as type weakenings — for example, a generated smart-contract function that omits input validation has a lifted type strictly weaker than its contract's expected type.
The framework extends to any output language with a typed compositional standard, holding the LLM fixed and varying the type system, so the same architecture covers natural language, code, query languages, and formal mathematics.
A synchronous coupling of an incremental CCG parser with decoding could mask or reweight grammatically inadmissible tokens, although the paper presents this as a sketch rather than a worked proposal.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

I infer that the framework's value depends less on which LLM is used than on the availability of wide-coverage CCG parsing, so the most decisive next experiment is a parser-coverage benchmark on in-the-wild LLM text.
A testable extension: implement the lifted typing for smart-contract code and check whether the predicted type weakenings correlate with the empirically observed low functional-correctness rates of generated contracts.
The paper's 'types as interfaces' idea suggests content checking could be typed by the query form each predication licences — membership, referent resolution, subsumption — which could be formalized into a typed protocol between the lifted term and the knowledge source.
I infer that the alignment claim is robust at word boundaries but becomes fuzzy at subword token boundaries; a full synchronous implementation will need a buffering layer, as the paper itself notes.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Worth a look for the observation that autoregressive next-token prediction and CCG's prefix-by-prefix type completion have the same shape of incrementality. That observation is the best thing here, and I don't think it appears in the Gibsonian dependency-grammar line the paper starts from. The lifting is honestly scoped: no claim that LLMs implement CCG internally, post-hoc reconstruction, derivational equivalence used to make the lifting well-defined. The two-layer check distinction (compositional vs content) is clear, and the Curry-Howard extension to Solidity, OWL, and SQL is a coherent research program rather than hype. The paper is well-written and unusually candid about its limitations. This is a real position paper, and a reasonable one.

The load-bearing step, however, is not demonstrated. The paper asserts that LLM next-token distributions align with CCG's type-completing expectations at each prefix, but the only evidence is 'John loves Mary', where the lexical categories are hand-supplied and the alignment is built into the example. The paper's own subword caveat means the lockstep holds only at word boundaries, and nothing shows that the boundary-filtered distribution still tracks CCG types. Lexical and attachment ambiguity mean there usually isn't a unique unsaturated argument; the n-best policy acknowledges this but doesn't connect it to the LLM's probabilities. Nothing in the autoregressive training objective rewards CCG-type-completing continuations. If the alignment is absent, the lifting is still useful as a post-hoc semantic parse of LLM text, but it is no longer 'principled' in the paper's sense, and the synchronous early-flagging architecture in §6 loses its claimed rationale. That is a bigger problem than the parser-coverage concern the paper flags in §7, and it is exactly what needs direct measurement.

Minor but relevant: the Solidity case is explicitly a sketch, and the empirical motivation rests on an unpublished co-authored manuscript, so the 20–26% correctness figure cannot currently be checked. The paper acknowledges both, which is to its credit. The self-citation is not a problem; the old Pareschi and Steedman result is the right reference for derivational equivalence.

Who is this for? People working on neurosymbolic verification, hallucination detection, or controllable generation. It deserves serious peer review as a vision paper, with the expectation that reviewers will push for an actual test of the alignment claim and a concrete parser-coverage experiment. I probably would not cite it in my own work yet, but I would bring it to a reading group.

Referee Report

4 major / 4 minor

Summary. The paper proposes a neurosymbolic framework for lifting LLM outputs into typed CCG derivations. Its central claim is that autoregressive, prefix-driven generation and CCG's incremental, type-completing processing are closely aligned, and that this alignment makes the lifting 'principled, incremental, and auditable.' The framework is developed in two layers: a compositional CCG layer that produces lambda terms, and a content layer that checks the lifted structure against external knowledge sources, enabling early flagging of hallucinations. The paper extends the lifting, via the Curry-Howard correspondence, to formal languages such as Solidity, SQL, and OWL, and sketches a synchronous LLM-CCG coupling. It repeatedly disclaims any claim that LLMs internally implement CCG and candidly identifies implementation and parser-coverage limitations.

Significance. If the alignment claim held, the framework would provide a principled basis for incremental compositional auditing of LLM output, with substantial potential for hallucination detection and verification of LLM-generated code and formal-language artifacts. The paper is valuable for articulating a clear layered architecture, for correctly positioning existing machinery (ccg2lambda, incremental CCG parsers, constrained decoding), and for stating its limitations honestly rather than overclaiming. However, the central empirical premise is currently supported only by a single toy example with hand-supplied categories; the contribution is therefore best read as a research program or a conceptual proposal rather than a demonstrated result. The paper's careful non-claim about LLM internals and its explicit acknowledgment of the parser-coverage gap are strengths, but they do not by themselves establish the framework's operational viability.

major comments (4)

[§3.1, Table 1 and note 2] The central claim that LLM next-token expectations and CCG typed expectations 'agree' is not measured; the only evidence is 'John loves Mary' with hand-supplied lexical categories. This agreement is the basis for calling the lifting 'principled' and for the synchronous early-flagging architecture of §6. The granularity caveat (subword vs word) and the n-best policy acknowledge complications but do not connect them to an actual LLM distribution. If the alignment is absent or weaker than claimed, the lifting reduces to ordinary CCG parsing of LLM text, and the distinctive 'operational alignment' and prevention claims lose their basis. The paper should either provide measurements of agreement between LLM continuations and CCG-admissible continuations on real LLM outputs, or explicitly reframe 'alignment' as a hypothesis and separate it from the framework's usefulness.
[§7, Limitations and next steps] The framework's applicability depends on wide-coverage CCG parsers handling LLM-generated text across registers, domains, and degrees of formality. The paper acknowledges this, citing supertagger generalization to biomedical text as partial mitigation, but provides no evaluation on actual LLM output. The residual concern is structural and register-level rather than lexical, and it is most pressing in the synchronous regime where parser failures would directly constrain generation. Because the lifting is load-bearing for both checking layers, a demonstration on a small but non-toy corpus of LLM-generated text parsed with an existing CCG parser is needed to establish feasibility. Without such a demonstration, the framework remains a plausible but untested proposal.
[§4.5 and §6] The 'earliest possible flagging' claim relies on maintaining incremental parser state and issuing an external query at mid-prefix. In the Zeus example, the flag at the fourth prefix depends on a specific lexical treatment ('The Aztec god Zeus' as an NP with a conjunctive modifier) and on an ontology lookup whose mapping is not specified. The synchronous regime in §6 is explicitly a sketch, and the paper itself names the parser-induced garden-path hazard. The text should clearly separate the conceptual possibility of early flagging from an operational claim; as written, §4.5 reads as stronger than the acknowledged implementation status supports.
[§5.3, Figure 1] The Solidity lifting is a hand-constructed type sketch: no lexicon, parser, or algorithm is given, and the type weakening from (A) to (B) is asserted rather than derived. The caption does label it 'hypothesized,' which is appropriate, but the surrounding text uses this example to support the cross-domain claim that type-checking can verify generated code. The paper should state more explicitly that the formal-language extension is an unverified research direction and should not be read as empirical evidence for the framework's viability. The acknowledgment that 'we do not develop the Solidity lifting in detail here' is honest, but it means the section functions as a research agenda rather than a demonstration.

minor comments (4)

[References] In the Wijnholds et al. entry, 'Proceedingsofthe24thConferenceonComputationalNaturalLanguageLearning' lacks spaces between words; please fix the bibliography formatting.
[§3.1, Table 1] The row for t=3 says 'sentence is complete; punctuation expected' but 'punctuation expected' is not a CCG type and is not part of the typed state. Clarify that this is an informal LLM-side expectation, not part of the CCG lifting.
[§2.2] The statement that alternative derivations yield 'equivalent terms' could be more precise: the lambda terms are equivalent up to beta-eta conversion. Adding this would preempt a technical objection.
[§4.5] The 'brother of Esau was Elijah' example is attributed to a personal communication. If the episode is not publicly documented, consider anonymizing it or adding a public reference, so that the claim is verifiable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the lifting is a post-hoc architecture; the central alignment claim is an asserted empirical analogy, not a fit, and the worked examples are explicitly hand-constructed sketches.

full rationale

The paper's central claim is that autoregressive LLM generation and CCG share a prefix-driven, type-completing dynamic. This is not derived from the framework's inputs by construction. In §3.1 the 'John loves Mary' table shows a hand-chosen CCG derivation alongside asserted LLM next-token expectations; the CCG categories are assigned by lexical entry, not fitted to the LLM distribution, and the paper repeatedly disclaims any claim that LLMs implement CCG (§3.1: 'does not claim that LLMs internally store symbolic grammatical rules'). The coherence property used to make the lifting well-defined rests on the associativity of CCG composition cited to Pareschi & Steedman 1987; this is an external mathematical fact about combinatory rules, not an input-to-output reduction of the paper's own prediction. The Solidity lifting in Figure 1 is explicitly labeled a 'hypothesized typed lifting' and 'a sketch... presenting them by hand'; the content-check examples are synthetic minimal-pair illustrations. The paper's own §7 limitations state that no end-to-end implementation exists and that parser robustness on LLM text is unassessed, and §6 declines to present the synchronous regime as more than a sketch. These are gaps in empirical support, not circular derivations. No load-bearing step equates a fitted parameter with a prediction, imports a uniqueness theorem to forbid alternatives, or smuggles an ansatz via self-citation. Self-citations (Pareschi & Steedman 1987; Salzano et al. 2026) support secondary or motivational claims and are not the sole justification of the central alignment thesis.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper is a conceptual framework; it does not fit parameters or introduce new entities. Its claims rest on standard results (CCG semantics, Curry-Howard) and on domain assumptions about parser generalization and external knowledge availability that the paper itself flags as open problems.

assumptions (5)

standard math CCG combinatory rules and the Curry-Howard correspondence are the correct compositional semantics for natural and formal languages.
Invoked throughout Sections 2.2 and 5.1 as the warrant for lifting and cross-domain extension.
domain assumption LLM outputs are prefix-driven at the granularity of words once subword tokens are buffered.
Footnote 2 of Section 3.1 acknowledges the token/word mismatch and assumes a buffering layer resolves it.
domain assumption Existing wide-coverage CCG parsers/supertaggers generalize to LLM-generated text across registers and unseen vocabulary.
Section 2.2 cites biomedical porting; Section 7 flags the residual structural gap as untested.
domain assumption Reliable external knowledge sources exist and can be queried for the reference of lifted predications.
Section 4.3-4.4 depend on ontology lookups; the paper states source trustworthiness is a meta-question not resolved.
standard math The propositions-as-types correspondence licenses identification of CCG derivations with type-checking in programming languages.
Section 5.1 uses this to extend the framework to Solidity, SQL, OWL.

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Cite this review

Pith. "Pith review of From Dependency to Compositionality: A Neurosymbolic Lifting of LLM Outputs via Combinatory Categorial Grammar." pith.science (2026). https://pith.science/paper/HE62UTLD

@misc{pith2026260718961,
  author       = {Pith},
  title        = {Pith review of: From Dependency to Compositionality: A Neurosymbolic Lifting of LLM Outputs via Combinatory Categorial Grammar},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HE62UTLD}},
  note         = {Machine review of arXiv:2607.18961}
}

read the original 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.

Figures

Figures reproduced from arXiv: 2607.18961 by the authors.

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Forward citations

Cited by 1 Pith paper

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Reference graph

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Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

Linguist Philos 4(4):517--558

Ades AE, Steedman MJ (1982) On the order of words. Linguist Philos 4(4):517--558

1982

[2] [2]

Front Hum Dyn 7:1579166

Borghoff UM, Bottoni P, Pareschi R (2025) Human--artificial interaction in the age of agentic AI : a system-theoretical approach. Front Hum Dyn 7:1579166. https://doi.org/10.3389/fhumd.2025.1579166

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