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Explaining presupposition projection with dynamic semantics

Paper · 2011 · Daniel Rothschild

Summary

The paper takes up an old complaint about Heim's dynamic semantics. The system predicts how presuppositions project through connectives, such as why "If John used to smoke, then he stopped smoking" does not presuppose that he smoked. Critics (Soames, Rooth via Heim 1990, Schlenker 2008a) object that it gets there only by giving each connective its own context-change rule, and nothing in the connective's truth conditions forces those rules. Rothschild makes the objection precise with the notion of a rewrite semantics. Complex dynamic formulas are restated using set operations on the context plus updates with simple sentences. He then proposes a looser dynamic semantics. A complex sentence is defined in a context if at least one rewrite exists that gives the correct truth conditions and never triggers a presupposition failure. With an added left-to-right order constraint, this matches Heim's predictions for negation, conjunction, disjunction, conditionals and quantifiers. Dropping the constraint yields a symmetric variant. The upshot is that dynamic semantics is not inherently unexplanatory, so the choice between projection theories must rest on other evidence.

Key points

  • Gazdar's (1979) conversational account handles the basic examples. It fails on Soames' (1982) variants with "heavily" ("If John used to smoke heavily, then he stopped smoking"), where the presupposition still does not surface.
  • Sentence meanings are modeled as partial context change potentials (CCPs), i.e. functions from sets of worlds to sets of worlds. A CCP is undefined when the context does not entail the presupposition.
  • Proposition 1 (unordered version) assumes CCPs with monotonic definedness and intersective meanings. Conjunction is then defined if either order of updating with the two conjuncts succeeds. Disjunction and the conditional are reduced to negation and conjunction.
  • Proposition 2 adds the order constraint, which recovers Heim's exact conditions:
    • α[φ∧ψ] and α[φ→ψ] require (α[φ])[ψ] to be defined.
    • α[φ∨ψ] requires (α[¬φ])[ψ] to be defined.
  • Proposition 3 covers quantifiers satisfying Conservativity and Non-Triviality. Definedness requires both α[φ] and (α[φ])[ψ] to be defined. Section 8 discusses empirical trouble with projection under quantification.

Interesting ideas

  • I1. Instead of hand-writing a projection rule per operator, the paper defines success as the existence of some evaluation route that keeps the truth conditions and never hits an undefined step, so behaviour follows from meaning plus a search.
  • I2. Presuppositions are encoded as partiality: an update simply fails unless the current context already entails the required fact, which makes infelicity a checkable condition rather than a label.
  • I3. A strict variant (left-to-right order) and a symmetric variant are built from the same machinery, which turns a theoretical choice into two concrete predictions that data can decide between.
  • I4. Minimal pairs like the "heavily" sentences break a superficially adequate theory while leaving the target behaviour intact, which makes them good stress tests.
  • I5. Disjunction and the conditional are reduced to negation and conjunction plus one constraint, so only a tiny core needs proving or implementing.

For Mova

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

  • I1 (frames): prag could compute presupposition filtering for "and/or/if" by searching over admissible update orders of clause frames, rather than keeping a separate table per connective.
  • I2 (world): before adding the state "John no longer smokes" to the world of the text, check that the world entails a prior smoking state, and otherwise flag accommodation explicitly so the step stays explainable.
  • I3 (learn): run both ordered and symmetric projection modes on the same texts and compare against teacher or annotated judgments to see which matches English usage.
  • I4 (learn): build paired probes where the conversational shortcut no longer applies, and use them as negative controls to confirm that presupposition handling is not just pattern-matching on repeated clauses.
  • I5 (answer): a reader answering "does the text assume X?" could normalise connectives to a negation/conjunction core first, keeping the inference chain short and auditable.

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 of OxfordOxford · United Kingdom104 works · 157,183 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

🧭 Topics 1Research subjects and languages the work is about.Implicature · 138 works

Cite

Cite as Daniel Rothschild. 2011. Explaining presupposition projection with dynamic semantics. Semantics and Pragmatics.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.3765/sp.4.3

@article{rothschild2011explaining,
  title = {{Explaining presupposition projection with dynamic semantics}},
  author = {Daniel Rothschild},
  journal = {Semantics and Pragmatics},
  year = {2011},
  doi = {10.3765/sp.4.3},
  url = {https://doi.org/10.3765/sp.4.3}
}

References

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