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Resolving symmetry without constraining alternatives

Paper · 2026 · Bernhard Schwarz and Michael Wagner

Summary

The paper addresses the symmetry problem, first noted by Kroch (1972). "Some players responded" can be enriched to mean "not all responded" but never "all responded", although both enrichments are formally mirror images: one negates a proposition, the other negates its negation. The standard fix, from Katzir (2007) and Fox & Katzir (2011), filters the exclusion set so that only alternatives no more syntactically complex than the utterance may be negated. Schwarz and Wagner use constructed examples and speaker judgments, not corpora or experiments. They argue the filter fails in two ways. Simple antonyms still let it derive unattested readings, and it forbids alternatives that some attested readings actually require. Their replacement is a blocking constraint on the output: an enriched reading is unavailable when an equally simple or simpler sentence already says that meaning literally. Alternatives can then be freely chosen meanings, and context can also rule readings out through the question under discussion and recoverability. This moves sensitivity to form from the input of pragmatic strengthening to its result.

Key points

  • Strengthening is modelled as the basic meaning conjoined with the negations of an exclusion set (Excl). The rival account is the complexity filter (CF): excluded propositions must be meanings of sentences no more complex than the utterance.
  • The proposed Blocking Constraint (BC) rules out an enriched meaning of φ if some ψ, no more complex than φ, has exactly that meaning as its literal content. Here "same meaning" means mutual entailment, with presuppositions taken into account.
  • Worked contrast: "All players responded" blocks the unattested reading of "some". "Some but not all players responded" is longer, so the attested reading survives as a useful abbreviation.
  • Two cases resist explanation by the question under discussion and, the authors argue, need BC:
    • a card game where "some cards are red" cannot mean all are red, even though "black" is an equally simple antonym;
    • "going to confession is permitted", which conveys "not required" rather than "required".
  • The authors reject the auxiliary assumption that context can never resolve symmetry. They admit BC does not explain every missing implicature, and they suggest it may follow from Grice's Manner maxims (brevity, avoiding ambiguity) or from RSA.

Interesting ideas

  • I1. Check the candidate output, not the candidate alternatives: a reading is discarded if a cheaper literal phrasing of it exists, so the set of alternatives never needs a syntactic definition.
  • I2. Treat enrichment as abbreviation: an implicature is licensed only when it saves words compared with the explicit paraphrase.
  • I3. Probe a reading by asking whether a speaker could reject it with "No, …" (or "Are you saying that…"). Attested readings can be denied this way, while unattested ones sound odd.
  • I4. Antonym pairs like red/black and permitted/optional are cheap stress tests, because they create symmetric alternatives without extra complexity.
  • I5. Compare meanings by mutual entailment, with presuppositional items like "again" counted as part of the meaning.

For Mova

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

  • I1 (frames): crate prag could compute scalar implicatures from freely chosen negated propositions, then drop any result that matches the literal meaning of an equally short sentence built from the lexicon.
  • I2 (frames): the "some → not all" rule could store an explainable trace in the frame, such as "allowed because the explicit form 'some but not all' is longer".
  • I3 (learn): this denial test could serve as a negative control when an LLM teacher labels implicatures, by checking that the teacher refuses denials of blocked readings.
  • I4 (answer): fable and test QA sets could include such pairs, to verify that the reader does not infer "all red" from "some red".
  • I5 (world): when two text-world states are tested for equivalence, presupposed facts should be part of the state, so that extra presuppositional words are not mistaken for redundancy.

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

🎓McGill UniversityMontreal · Canada87 works · 11,027 citations

 Fields, topics and concepts

📚 Shelves 5The 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 worksPhilosophy · 284 works

Cite

Cite as Bernhard Schwarz and Michael Wagner. 2026. Resolving symmetry without constraining alternatives. Semantics and Pragmatics.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.3765/sp.19.8

@article{schwarz2026resolving,
  title = {{Resolving symmetry without constraining alternatives}},
  author = {Bernhard Schwarz and Michael Wagner},
  journal = {Semantics and Pragmatics},
  year = {2026},
  doi = {10.3765/sp.19.8},
  url = {https://doi.org/10.3765/sp.19.8}
}

References

28 references, 1 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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