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On the source of distributive inferences

Paper · 2026 · Paul Marty, Sonia Ramotowska, Richard Breheny et al.

Summary

The paper examines how two inferences relate when a disjunction sits under a universal operator. For "every box contains A or B", hearers infer that some box has A and some box has B. These are distributive (D) inferences. Hearers may also infer that not every box has A, and likewise for B. These are negated universal (NU) inferences. Standard implicature theory derives the D-inferences from the NU-inferences. Earlier work (Crnič et al. 2015) found that this dependence fails for every, but claimed it holds for modals like must. The authors ran two online sentence–picture acceptability experiments with box-and-ball scenes. Experiment 1 compared every with epistemic must, and Experiment 2 compared every with deontic must. Sentences were accepted when an NU-inference was false but the D-inferences were true, and accepted less often when a D-inference was also false. This held for both quantifier types. The finding contradicts the claimed nominal/modal asymmetry. It favours theories that derive D-inferences without NU-inferences, such as Bar-Lev & Fox (2023) recursive exhaustification and Aloni's (2022) neglect-zero account in BSML.

Key points

  • Each experiment had 100 native English speakers (UK/US) recruited on Prolific. Each person took part in only one experiment, was paid £2, and spent about 13 minutes.
  • Materials were adapted from Marty et al. (2024b, Experiments 4–6):
    • each item showed a sentence over a row of boxes plus a character (Mia or Sam);
    • colours were drawn from yellow, blue, green and gray.
  • There were two critical conditions:
    • target-1: one NU-inference false, D-inferences true;
    • target-2: one NU-inference false and one D-inference false.
  • Control sentences C1–C4 covered plain universal, conjunctive and negative ("No…", "cannot…") variants.
  • Results:
    • the every results replicate Crnič et al. 2015;
    • for both epistemic and deontic must, D-inferences also arose without NU-inferences, which is the new finding.
  • Two accounts fit the data:
    • Bar-Lev & Fox (2023), in which pruning conjunctive alternatives keeps D-inferences but drops exclusivity and NU-like inferences;
    • Aloni (2022) neglect-zero, extended to first-order quantifiers by Aloni & van Ormondt (2023).

Interesting ideas

  • I1. The design breaks one inference while keeping another true, then compares acceptance, so each inference's contribution is isolated rather than assumed.
  • I2. Unambiguous control sentences (plain universal, conjunction, negation) run alongside the critical items to check that judges are attending and behaving logically.
  • I3. The distributive reading ("each disjunct is a live option") is treated as its own inference, not a consequence of "not all A", and it holds for both nominal and modal universals.
  • I4. Neglect-zero says hearers ignore situations that satisfy a sentence only vacuously, such as an empty substate verifying a disjunct.
  • I5. In the recursive exhaustification account, the reading depends on which alternatives stay in the set; pruning the conjunctive one changes the output.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

  • I1 (learn): Build minimal-pair test worlds where exactly one candidate implicature is false, as negative controls showing which inference our pipeline actually relies on.
  • I2 (answer): Pair every tricky QA probe with trivially decidable control questions over the same picture/world, so failures can be split into reasoning errors and pragmatic disagreements.
  • I3 (frames): In crate prag, generate the D-inference for "every/must … A or B" as an independent, defeasible implicature, with the NU-inference as a separate, context-dependent one.
  • I4 (world): When the world of a text checks a disjunction or universal, flag verifications that succeed only through an empty set or empty substate, and treat them as unlikely intended readings.
  • I5 (frames): Keep implicature alternatives as an explicit, logged set, so each enrichment can be explained by naming which alternatives were negated or pruned.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University College LondonLondon · United Kingdom88 works · 19,432 citations🎓Heinrich Heine University DüsseldorfDüsseldorf · Germany33 works · 1,487 citations🎓University of MaltaMsida · Malta29 works · 894 citations🎓University College LahoreLahore · Pakistan2 works

 Fields, topics and concepts

📚 Shelves 6The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksPsychology · 1,552 worksExperimental and Cognitive Psychology · 870 works

Cite

Cite as Paul Marty, Sonia Ramotowska, Richard Breheny, Jacopo Romoli and Yasutada Sudo. 2026. On the source of distributive inferences. Semantics and Pragmatics.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.3765/sp.19.12

@article{marty2026source,
  title = {{On the source of distributive inferences}},
  author = {Paul Marty, Sonia Ramotowska, Richard Breheny, Jacopo Romoli and Yasutada Sudo},
  journal = {Semantics and Pragmatics},
  year = {2026},
  doi = {10.3765/sp.19.12},
  url = {https://doi.org/10.3765/sp.19.12}
}

References

37 references, 4 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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