WH-Domain Learning in CCG

• The paper introduces a probabilistic CCG framework that models long-range wh-dependencies using a minimal set of combinatory rules.
• It employs an EM algorithm with Bayesian Dirichlet priors to achieve high accuracy in parsing wh-questions, with key metrics such as 90% word order accuracy.
• The study demonstrates that robust syntax–semantics coupling can explain child acquisition of wh-movement without relying on pre-encoded innate movement mechanisms.

WH-domain learning encompasses the process by which linguistic agents, such as children or computational models, acquire the capacity to represent, interpret, and generalize the long-range dependencies characteristic of wh-questions and related constructions. In generative syntax, the WH-domain, or CP-domain, is the locus for the movement or fronting of wh-phrases (e.g., what, who, where), resulting in filler–gap dependencies such as “What did you see ___?”. For language acquisition and computational modeling, WH-domain learning thus refers to the acquisition of both the syntactic categories associated with wh-expressions and the compositional operations or rules that mediate these non-local relations (Mahon et al., 17 Mar 2025).

1. Formal Characterization of the WH-Domain

The WH-domain is structurally defined as the grammatical region in which wh-phrases are licensed to appear in clause-initial position, forming dependencies with argument positions (“gaps”) within embedded syntactic structures. In theoretical syntax, this domain is often associated with the CP (complementizer phrase) layer. Successful WH-domain learning involves acquiring morphosyntactic and semantic representations that encode both the special status of wh-words and the procedural mechanisms (movement, filler–gap binding, or combinatory composition) supporting long-range dependencies. In child language acquisition, the challenge is to develop, from exposure to child-directed speech, an analysis of these constructions that enables correct interpretation and production.

2. Probabilistic Model Architecture for WH-Domain Acquisition

Mahon, Johnson, and Steedman (2024) (Mahon et al., 17 Mar 2025) present a framework in which the learner adopts Combinatory Categorial Grammar (CCG), a strongly lexicalized, mildly context-sensitive formalism sufficient for encoding wh-dependencies (2-MCFG expressivity). The grammar is defined through a minimal set of combinatory rules: Forward Application, Backward Application, and Forward Composition, supplemented by type-raising to facilitate wh-question derivations. Each lexical item is paired with a syntactic category and a logical form (LF) in the lambda calculus. Critically, the model jointly learns the lexicon (syntactic and semantic types) and grammar by training on utterance–LF pairs, with logical forms serving as strong semantic supervision.

The model architecture involves the following factorization for the probability of words, meanings, and derivations: $$p(w, m, T \mid \theta) = p_r(r) \prod_{\text{non-leaf } s'} p_t(s'_1, s'_2 \mid s') \prod_{\text{leaf } s} \Bigl[p_t(\text{leaf} \mid s) p_h(e_s \mid s) p_l(m_s \mid e_s) p_w(w_s \mid m_s)\Bigr]$$ where $w$ is the word sequence, $m$ is the meaning (LF), $T$ is the parse tree, $p_r$ is the root prior, $p_t$ governs splitting or declaring leaves, $p_h$ predicts shell-LFs, $p_l$ predicts full LFs, and $p_w$ generates words from meanings.

3. Learning and Inference Algorithms

The learning objective is to maximize the marginal log-likelihood over the observed pairs $(w_i, m_i)$: $$\mathcal{L}(\theta) = \sum_{i} \log p_\theta(w_i, m_i) = \sum_{i} \log \left(\sum_T p_\theta(w_i, m_i, T)\right)$$ Parameter estimation is achieved using an EM (Expectation–Maximization) procedure with Bayesian Dirichlet-process priors. The E-step computes soft counts over possible parses; the M-step updates multinomial parameters using expected sufficient statistics. Smoothing is imposed by combining empirical counts with base power-law distributional priors. Semantic-type constraints are enforced to prune the parse space, ensuring only type-compatible derivations are considered.

Inference for novel utterances proceeds via beam search over leaf spans, followed by a CKY-style chart parser for CCG derivations. The goal is to find $$(m^*, T^*) = \arg\max_{m, T} p(w, m, T \mid \theta_{\mathrm{final}})$$. The leaf search algorithm ranks likely (category, LF) pairs before full-sentence parsing.

4. Modeling Long-Range WH-Dependencies

CCG enables unbounded wh-filler–gap constructions via its combinatory apparatus. Wh-words receive type-raised categories (e.g., $S_{whq}/(S_q/NP)$ for “what”), auxiliaries are annotated accordingly, and verbs carry argument structure. Composition and application rules combine these over arbitrary distances, allowing the derivation of logical forms for examples like “What did you lose?” without recourse to movement traces. This construction is formally equivalent to a filler–gap dependency and exploits the mildly context-sensitive power of CCG and 2-MCFGs. The probability model automatically learns the distribution of wh-constructions through their frequency and categorical regularities, without the need to pre-encode movement mechanisms.

5. Empirical Evaluation and Metrics

Empirical validation is carried out using the Brown–Adam CHILDES corpus (9,314 tokens, 5,320 utterances), with each utterance paired to a logical form via UD→LF mapping. Approximately 21.6% of utterances are object-wh questions. Ten percent of the corpus is reserved for test evaluation. The key metrics and results include the following:

• P(SVO) for word order exceeds 90% after 500 examples.
• Logical form accuracy for the 50 most frequent words is around 90%; category accuracy is roughly 70%.
• Utterance–meaning inference (“select acc”): 88% correct with 4 distractor LFs; 80% correct when only the utterance is available; 85% excluding unseen words.
• Construction-specific accuracies: transitives (75%), modals (80%), progressives (78%), negations (82%), wh-questions (80%).
• Assignment of wh-word categories: 85% correct at train time, 70% at test time.
• Robustness is maintained under up to 8 distractor meanings.
• One-trial learning for nonce words: correct LF for a new transitive predicate obtains posterior >0.8 after a single exposure, extending to complex constructions including wh-questions.

Qualitative parse example: For “what did you lose?” the system assigns what : $S_{whq}/(S_q/NP)$ : $\lambda p.p~WHAT$, did : $S_q/VP/NP$ : $\lambda x.\lambda p.did(p~x)$, you : NP : you, lose : $VP/NP$ : $\lambda x.\lambda y.lose~x~y$, and combines these to yield LF $did(lose~WHAT~you)$ through $>$ and $>B$ combinators.

6. Theoretical Significance and Implications

The results demonstrate that a universal, minimally specified inventory of CCG rules (application, composition, type-raising) together with logical form supervision is sufficient to induce both the abstract syntactic categories for wh-phrases and the algebraic operations supporting arbitrarily deep filler–gap structures. The findings support the hypothesis that children can leverage strong syntax–semantics coupling (“semantic bootstrapping”) to acquire wh-movement patterns, relying on compositional structure building rather than innate movement-specific mechanisms. The model’s robustness to distractor meanings parallels the empirical resilience of children in ambiguous referential settings.

7. Limitations and Prospects

The CCG learning model assumes tokenized inputs and does not explicitly model morphology or phonology; a neural morphophonological module or finite-state transducer could address this limitation. Pragmatic or discourse context effects are not present, but could sharpen meaning inference if integrated. Supertagging currently emerges via DP induction and might benefit from a neural supertagger for computational efficiency. Extension to typologically diverse languages (e.g., Hebrew) is required to evaluate universality across differing wh-word ordering. Further, incorporating real acoustic input could ground logical form acquisition in perceptual data (Mahon et al., 17 Mar 2025).

A plausible implication is that children do not require a densely innate inventory of wh-movement schemas if learning is supported through richly informative utterance–meaning supervision and a combinatorially expressive syntactic formalism. The probabilistic CCG learner thus constitutes a formal, data-efficient model of WH-domain acquisition, simultaneously capturing both the logical structure and the linguistic generalizations necessary for the mastery of wh-questions.