Contribution
Before this paper the quantum-cognition literature had tested concept combinations (“apple chip”, Bruza et al.) for contextuality, and Dzhafarov and colleagues had found none of them contextual once signalling was accounted for (LIT-264). This paper puts two-word ambiguous phrases of English into the sheaf-theoretic and Contextuality-by-Default frameworks, with meanings estimated from corpus frequencies. It shows that a non-signalling, possibilistically contextual language model can be written down. It shows that corpus estimates are signalling in every case examined. And it reports the first CbD-contextual systems from language data, which its own bootstrap does not secure.
Key insight
Treat each ambiguous word as a measurement and its selected meaning as the outcome; a phrase is a joint measurement. Then “context changes meaning” splits into two different things. The marginal for a word can shift between phrases (signalling, a direct influence of the partner word), or the joint selections can fail to come from any one global assignment beyond what those shifts allow (contextuality). Language data show plenty of the first. The second needs CbD to be asked at all.
Assumptions
- Two meanings per word, or three in the press/box model, chosen by the authors; other senses and metaphorical readings are ignored (§4 footnote 2, §9).
- Supports by judgement. The possibilistic models of §5 encode which readings the authors judge possible; they are not observed.
- Probabilities by hand annotation of corpus hits. In §6 each occurrence of a phrase in the BNC or ukWaC is assigned a reading by the authors. No annotator agreement is reported.
- A context is a word pair plus its grammatical relation. In §5.4 the verb–object and subject–verb readings of one noun–verb pair are two contexts sharing both contents, so the same word counts as the same measurement in both orders.
- Binary outcomes for the CbD cyclic criterion; the three-outcome model is handled by dichotomization.
Key results
- §5.1 {coach, boxer} × {lap, file} is possibilistically signalling: coach = bus is possible with lap and not with file. The sheaf criterion cannot be applied.
- §5.2 {tap, box} × {pitcher, cabinet} is possibilistically non-signalling and contextual. The constraints force tap = box = pitcher and cabinet the other value, so there are exactly two global assignments, and the locally possible (tap = touch, pitcher = baseball player) extends to neither. The paper’s phrasing, that “tap ↦ touch” cannot be extended, is loose: tap = touch extends; the pair does not. This is Hardy-type (possibilistic) contextuality, not strong.
- §5.3 {press, box} × {can, leaves} is possibilistically non-signalling and noncontextual; §5.4’s two noun–verb pairs are possibilistically signalling.
- §6 corpus versions. All are probabilistically signalling, e.g. P(box = put in boxes) is 2/3 in “box leaves” and 7/74 in “box can” (Eq. 1). The tap/box model’s corpus support also differs from §5.2’s.
- §8 CbD. press/box is noncontextual by a feasible linear program (105 constraints on 2¹⁶ events; the extraction prints “216”); coach/ boxer and tap/box are noncontextual by the Kujala–Dzhafarov cyclic inequality.
- §8.1 noun–verb pairs. adopt/boxer and throw/pitcher are CbD-contextual, with measures 1/30 and 7/30. Recomputed here from Fig. 12: for adopt/boxer the two contexts’ correlations are −1 and +1, so s_odd = 2, against Δ = 56/30; for throw/pitcher s_odd = 1.8 against Δ = 13/15. The excesses, 4/30 and 28/30, stand in the paper’s 1 : 7 ratio; its measure is a quarter of the excess.
- §8.1 reliability. Parametric bootstrap: the probability of a noncontextual system given these estimates is “larger than .56” for adopt/boxer and “larger than .08” for throw/pitcher.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | A two-word ambiguous-phrase scenario can be possibilistically non-signalling and contextual | strong, for the hand-set supports | §5.2, checked here |
| C2 | Corpus-estimated meaning-selection models are signalling | moderate | every model examined (§§6–7), a handful of phrases |
| C3 | Signalling models of ambiguous phrases can be CbD-contextual | weak | §8.1: two systems on small counts, both plausibly noncontextual by the paper’s own bootstrap |
| C4 | There is no reason for language to satisfy non-signalling | informal argument | §7, the coach/lap example |
| C5 | Contextuality frameworks let the effect of context on interpretation be studied formally | programme statement | §9 |
Concepts
- measurement / outcome: an ambiguous word / the meaning selected for it in a phrase.
- measurement context: the words of a phrase together with their grammatical relation (subject–verb, verb–object, adjective–noun).
- possibilistically contextual (logical contextuality): some locally possible joint outcome belongs to no consistent global assignment (after Abramsky and Hardy).
- signalling: a word’s meaning distribution differs between the contexts it occurs in; in CbD terms, inconsistent connectedness.
- CbD-contextual: no coupling of all contexts makes each word’s copies agree with the maximal probability their marginals allow.
Connections
The scenario and the possibilistic criterion are Abramsky and Brandenburger’s (LIT-016), with bundle diagrams from Abramsky et al. (LIT-278). The probabilistic criterion is Contextuality-by-Default (LIT-777) through the cyclic-system results of Kujala and Dzhafarov (2016) and the measures of Dzhafarov, Kujala and Cervantes (2020), neither held. The rank-2 noun–verb design is modelled on question-order effects (Wang and Busemeyer, LIT-834), which CbD had already found noncontextual (LIT-264). The paper does not cite Abramsky and Sadrzadeh’s Semantic Unification (LIT-841); the journal follow-up names it only as a future direction. The two works share an author and a framework, not a construction: LIT-841 glues discourse sections, this paper tests distributions over word meanings.
The journal follow-up (Wang et al., Journal of Cognitive Science 2021, read in full) changes the question. Across 90 rank-2 noun–verb systems it measures direct influence, Δ, which by its Proposition 1 is twice the sum over contents of Jones’s minimal direct influences. Verbs with several meanings carry about 70% of Δ (0.70, on 14 systems from six verbs), verbs with several senses about 50% (0.48, on 55), and nouns about 50% either way. The paper calls the difference significant with “more than 95% confidence” but names no test; recomputed, it holds only one-sided (Welch p ≈ 0.03; two-sided ≈ 0.06), and over all 69 signalling systems the verb share is 0.52 ± 0.04 (NOTE-654). It notes that Δ > 2 rules out contextuality in rank-2 systems, and it reports no new contextual system. Its conclusion prints the earlier measures garbled in extraction; they are the 1/30 and 7/30 here.
Bearing on the record
- THEORY-013 (behavioural, social and word-meaning data published as
contextual show none once signalling is separated). This paper is the
first claim of CbD contextuality in language data. It does not meet
THEORY-013’s
promote_whenthe other way: its own bootstrap gives noncontextuality a probability above .56 and .08. The record should not cite it as a robust counterexample. The candidate that might be is the 2025 BERT study by Lo, Sadrzadeh and Mansfield (not held), whose distributions come from a language model, not from people or corpora. - CLAIM-044 (ambiguity admits several global assignments, contextuality none). Here ambiguity is the outcome set and is never by itself contextual: press/box has several readings and global assignments for all of them. But the one contextual model, tap/box, is possibilistically contextual and still has two global assignments. What fails is that one locally possible reading extends to none. So “a contextual one admits none” holds only for strong contextuality. Possibilistic and probabilistic contextuality are compatible with global assignments existing.
- CLAIM-037 (formal contextuality needs Contextuality-by-Default when marginals shift). Supported directly: every corpus model was signalling, and the sheaf criterion could not be applied to any.
- CLAIM-038 (a communicative object is a compatible family over a cover). The data here are not compatible families: meaning marginals disagree on overlaps. Applied to language, the claim’s premise of compatibility needs either CbD or a signalling-corrected sheaf treatment, as in Lo et al.’s later work.
- CLAIM-009 (pragmatic judgements may be formally contextual). The paper tests lexical meaning selection, not pragmatic judgement. Its contextual systems are not secured. It shows the test can be run on language data; it is not evidence that the supposition holds.
- CLAIM-041 (context sensitivity does not by itself establish contextuality). Consistent: the bulk of what the data show is signalling.
- No instruction for machine-learning practice; nothing for the anthology.
Limitations
- A handful of phrases, chosen by hand, with two meanings each.
- Supports in §5 are the authors’ judgements, and the corpus readings are their annotations, with no agreement measure.
- Small counts throughout: the contextual systems rest on fractions with denominators of 3 to 30, and the bootstrap leaves both plausibly noncontextual.
- British corpora: the bus sense of coach was nearly absent (§9).
- Possibilistic contextuality appears only in a model whose supports are stipulated; once estimated from the corpus it is signalling.
- One printed error: in Fig. 10a the tap/pitcher row reads 17/22 and 15/22, which sum to 32/22; one entry is wrong, probably 7/22.
Open questions
- Whether CbD contextuality in ambiguous phrases survives with human plausibility judgements and adequate sample sizes. The authors propose this (§9). Wang and Sadrzadeh’s 2023 human-judgement data, and Lo et al.’s crowdsourced Winograd schemas, would answer it in part.
- Whether treating “adopt” in “adopt boxer” and “boxer adopts” as one content is right. If the grammatical role changes what is measured, the rank-2 systems are not about one property in two contexts.
- Whether any non-signalling language system exists outside stipulated supports.