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LIT-842: On the Quantum-like Contextuality of Ambiguous Phrases

4 min read

Properties7
StatusActive — read in full 2026-10-09 (NOTE-645); worth reading as the first paper to test natural-language data for contextuality in the formal sense rather than the loose one, and as the paper that names the obstacle the test meets: corpus estimates of meaning selection are almost always signalling. In the sheaf-theoretic framework one hand-specified support model ({tap, box} × {pitcher, cabinet}) is possibilistically contextual (a Hardy-type failure), but its corpus probabilities are signalling, so the framework cannot judge them. Under Contextuality-by-Default the Bell-type corpus systems are noncontextual, and two noun–verb pairs read as subject–verb and verb–object (adopt/boxer, throw/pitcher) are CbD-contextual, by 1/30 and 7/30. Its own parametric bootstrap then gives those two a probability above .56 and above .08 of being noncontextual, on fractions with denominators between 3 and 30, so the contextual verdicts are not statistically secured.
Tagscontextuality, linguistics, quantum-foundations, probabilistic-modeling, cognition, compositionality
ExtendsLIT-016 — The sheaf-theoretic structure of non-locality and contextuality, LIT-777 — Context–content systems of random variables: The Contextuality-by-Default theory
Extended byLIT-844 — Quantum-Like Contextuality in Large Language Models, LIT-851 — Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools
SupportsCLAIM-037 — Formal contextuality is a failure of global extension, distinct from ordinary context dependence, and needs Contextuality-by-Default when marginals shift with context
Cited as “paper” byNOTE-645 — On the Quantum-like Contextuality of Ambiguous Phrases
Cited as “source” byTHEORY-623 — In the two tests of contextuality in language data that the record has read, the contextuality is put there by the experimenter or not secured: meaning-selection models of ambiguous phrases estimated from corpora are all signalling and their two Contextuality-by-Default verdicts are plausibly noncontextual by their own bootstrap, while BERT's 52 million anaphora models have a support fixed by the sentence schema, so whether each counts as contextual depends only on how uncertain the model's three referent choices are

Graph View

Daphne Wang, Mehrnoosh Sadrzadeh, Samson Abramsky and Víctor H. Cervantes (2021), in Proceedings of the 2021 Workshop on Semantic Spaces at the Intersection of NLP, Physics, and Cognitive Science (SemSpace), ACL Anthology 2021.semspace-1.5, pp. 42–52 — ARXIV-2107.14589

Key takeaways

  • The set-up. A phrase of two ambiguous words is a bipartite measurement: each word is a measurement, its outcome the meaning selected, and a context is a pair of words in a fixed grammatical relation. Four words in a 2 × 2 Bell-type arrangement give a cyclic scenario. Supports in §5 are set by the authors’ judgement; probabilities in §6 are relative frequencies of hand-annotated readings in the BNC and ukWaC.
  • Possibilistic contextuality, once, and only on hand-set supports. {tap, box} × {pitcher, cabinet} is possibilistically non-signalling and contextual: its only global assignments are tap = box = pitcher, cabinet the other value, so the locally possible (tap = touch, pitcher = baseball player) does not extend. {coach, boxer} × {lap, file} is possibilistically signalling; {press, box} × {can, leaves} is non-signalling and noncontextual.
  • Corpus data are signalling. Every corpus-estimated model is signalling, including the probabilistic version of the tap/box model, so the sheaf-theoretic criterion does not apply to any of them (§§6–7). The authors argue that non-signalling has no reason to hold for language: a word’s selected meaning constrains its partner’s.
  • Contextuality-by-Default verdicts. The Bell-type corpus systems are CbD-noncontextual (a 105-constraint linear program over 2¹⁶ events for press/box, the Kujala–Dzhafarov cyclic inequality for the others). Two rank-2 systems, the same noun–verb pair read as verb–object and as subject–verb, are CbD-contextual: adopt/boxer by 1/30 and throw/pitcher by 7/30 (Dzhafarov, Kujala and Cervantes’s measure).
  • The verdicts are not secured. By parametric bootstrap the probability of a noncontextual system given these estimates is above .56 for adopt/boxer and above .08 for throw/pitcher (§8.1). The counts behind them are small: the printed fractions have denominators 30 and 4 for the two adopt/boxer contexts and 10 and 3 for throw/pitcher, so one context may rest on as few as three or four occurrences.

Standing in the record

Filed on 2026-10-09 at the owner’s direct request, as the work by Sadrzadeh and collaborators that tests ambiguous phrases for formal contextuality, following Abramsky and Sadrzadeh’s Semantic Unification (LIT-841). It is not from the manuscript bibliography: the owner asked for it directly on 2026-10-09. It is the first data test of the record’s contextuality line (LIT-016, THEORY-012) on language, and the first language case for Contextuality-by-Default (LIT-777, LIT-264, THEORY-013). NOTE-645 says how it bears on the manuscript’s argument on line pragmatic-transport.

The same programme’s other papers, named here and not filed:

  • The journal follow-up. Wang, Sadrzadeh, Abramsky and Cervantes, “Analysing Ambiguous Nouns and Verbs with Quantum Contextuality Tools”, Journal of Cognitive Science 22(3):391–420 (2021), DOI 10.17791/jcs.2021.22.3.391, author copy at UCL Discovery (eprint 10146180). It was read in full for this filing. It does not test contextuality again. It builds 90 rank-2 noun–verb systems from the same corpora and measures their direct influences (signalling) instead, through Jones’s canonical models, finding verbs with several meanings carry about 70% of a phrase’s direct influence against about 50% for verbs with several senses. It carries a different result, not half of this one, so it was not filed separately at first. The owner asked for it on 2026-10-09, and it is now LIT-851, with its own reading.
  • Later work. Lo, Sadrzadeh and Mansfield on anaphora: a BERT-based sheaf model of anaphoric ambiguity (EPTCS 366, 2022, arXiv 2208.05720); a generalised Winograd schema with crowdsourced judgements violating Bell–CHSH by 0.192 (EPTCS 384, 2023, arXiv 2308.16498); further developments with a contextual fraction of 0.096 (EPTCS 408, 2024, arXiv 2402.04505); and a large-scale BERT study reporting 77,118 sheaf-contextual and 36,938,948 CbD-contextual instances (Proc. R. Soc. A, 2025, DOI 10.1098/rspa.2024.0399, arXiv 2412.16806). Wang and Sadrzadeh’s causal analysis of the same phrases is EPTCS 394 (2023, arXiv 2206.06807), and Wang’s thesis covers the line (arXiv 2408.07402). None of these was read.

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