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LIT-851: Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools

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Properties7
StatusActive — read in full 2026-10-09 (NOTE-654); worth reading as the paper that measures how much signalling there is in natural-language meaning selection, and that gives signalling a causal reading. Its Proposition 1 shows that in a binary cyclic system the CbD quantity Δ is twice the sum, over contents, of the least direct influence of context that any of Jones's canonical (causal) models of the data must posit, each the total-variation distance between a content's two marginals. Applied to 90 rank-2 noun–verb systems from the BNC and ukWaC, Δ averages about 1.35 in every class of ambiguity, and homonymous verbs carry about 70% of it against about 50% for polysemous verbs (14 against 55 systems; my recomputation from its appendix gives a Welch t of 2.0, two-sided p ≈ 0.06). It tests no system for contextuality. Read with the caveat that most systems rest on very few corpus occurrences: 51 of the 90 have Δ exactly 0, 2 or 4.
Tagscontextuality, linguistics, cognition, probabilistic-modeling, quantum-foundations
ExtendsLIT-842 — On the Quantum-like Contextuality of Ambiguous Phrases, LIT-777 — Context–content systems of random variables: The Contextuality-by-Default theory
SupportsCLAIM-219 — A change in the global compatibility of a fixed scenario is either a change in contextuality proper, which the behavioural data read show none of, or a change in overlap consistency, which is ordinary context dependence and moves by at most 2ε when each context moves by ε, CLAIM-235 — The line's proposed quantities have no finite-data estimators: plug-in signalling from one or a few occurrences per context is positive in expectation when the true marginals agree, so the contextual fraction is undefined on raw tables, and deficiency over text-valued renderings has no estimator, CLAIM-245 — Under Contextuality-by-Default, a deterministic context-wise recoding can make a noncontextual signalling source maximally contextual, or turn a contextual source into pure signalling, so per-content signalling is not monotone under such maps and the quantity to bound is joint overlap discrepancy, CLAIM-325 — The behavioural data the record has read show no contextuality proper: none of the five kinds of data Dzhafarov, Zhang and Kujala re-analyse is contextual, Wang et al. test none of their 90 language systems for it, and no documented test of pragmatic or meaning judgements finds it at adequate power
Cited as “grounds” byARG-037 — The signalling counts read off Wang et al.'s appendix show that signalling is typical of language data
Cited as “paper” byNOTE-654 — Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools
Cited as “source” byTHEORY-177 — In a binary cyclic system, the Contextuality-by-Default measure of signalling is twice the sum, over contents, of the least direct influence of context that a canonical causal model of the data must place on each content, and each content's least influence is the total-variation distance between its two marginals

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Daphne Wang, Mehrnoosh Sadrzadeh, Samson Abramsky and Víctor H. Cervantes (2021), Journal of Cognitive Science 22(3):391–420 — DOI-10.17791/jcs.2021.22.3.391; author copy at UCL Discovery, eprint 10146180

Key takeaways

  • Signalling, given a causal reading (Proposition 1, proved). For a binary cyclic system, Δ = Σ|⟨R_q^c⟩ − ⟨R_q^{c′}⟩|, the CbD measure of signalling, equals 2 Σ_q Δ*(F_q). Δ*(F_q) is the least probability, over all of Jones’s canonical models that reproduce the data, that switching context changes content q’s value with the background held fixed. It equals 1 − Σ_v min(P[R_q^c = v], P[R_q^{c′} = v]), the total-variation distance between the two marginals. The proof combines CbD’s maximal couplings with Jones’s correspondence between couplings and canonical models (his Proposition 8.4, quoted, not proved).
  • The data. 90 rank-2 cyclic systems: a verb and a noun, each with two interpretations, read as verb–object and as subject–verb, with probabilities from hand-labelled BNC and ukWaC occurrences. 32 verbs (from Pickering and Frisson, and Shutova) and 20 nouns (from Rayner and Duffy, and Tanenhaus et al.). Systems whose uncertainty on Δ exceeded the range of possible values were dropped. Counts per system are not reported; 51 of the 90 have Δ exactly 0, 2 or 4.
  • Δ does not separate ambiguity types. The mean Δ is about 1.35 in all four verb × noun classes (1.24 ± 0.29 to 1.50 ± 0.43, standard errors). The appendix reproduces these values.
  • Homonymous verbs carry more of it. Among systems with Δ > 0, the verb’s share 2Δ_v/Δ averages about 70% for verbs with several meanings (14 systems from six verbs) and about 50% for verbs with several senses (55 systems). The paper says the difference holds “with more than 95% confidence” and names no test. From its appendix I get 0.70 against 0.48, Welch t = 2.0 on about 20 degrees of freedom, so p ≈ 0.03 one-sided and ≈ 0.06 two-sided. Nouns split about 50% whatever their ambiguity. Over all 69 systems the verb’s share is 52% ± 4%, which does not bear out the introduction’s claim that verbs carry more on average.
  • No contextuality test. No system is tested for CbD contextuality. The paper notes that Δ > 2 rules it out in rank 2 (34 systems have Δ ≥ 2, which already suffices), and it repeats LIT-842’s two contextual systems.

Standing in the record

Filed on 2026-10-09 at the owner’s request, as the journal follow-up to LIT-842 (Wang et al., “On the Quantum-like Contextuality of Ambiguous Phrases”). That entry named it and did not file it. It is not from the manuscript bibliography. It was read on its own terms (NOTE-654); NOTE-645 compares the two papers from LIT-842’s side.

It is the record’s only quantification of signalling in natural-language data, as opposed to a verdict on contextuality. Its proved identity is the source of THEORY-177. Its data bear on THEORY-013 only indirectly: they show that corpus meaning selection is heavily signalling (mean Δ 1.35 out of a maximum of 4), which is the condition under which THEORY-013 says published contextuality claims dissolve.

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