📄 Conflicting presuppositions in disjunction

Summary

The squib examines disjunctions whose two disjuncts carry presuppositions that cannot both hold, such as a sentence reporting that Suzan met either Bessarabia's king or its president. Speakers judge such sentences to presuppose only that one of the two presuppositions holds. They count as false when that background holds but neither disjunct is true, and their negations can then be true. Yagi tests four established accounts against these two observations: Strong Kleene trivalent logic, Karttunen & Peters two-dimensional semantics (with symmetric filtering), propositional update semantics, and Schlenker's local-context calculus. Through short formal derivations he shows that all four make such disjunctions impossible to be both defined and false. In the dynamic versions, the sentence is defined only when the context already settles its truth. He then weighs two repairs. One is Beaver & Krahmer's meta-assertion operator. The other is a looser disjunction rule that lets each disjunct be evaluated against a restricted sub-context. The second captures both observations, but only through underspecification. The contribution is a sharp test case that any future explanatory theory of presupposition projection must handle.

Key points

• The data are three classic examples: the fermenting liquid (Hausser 1976), the king or president of Bessarabia (Landman 1986), and the King or President of Buganda (Beaver 2001). For the last two, world knowledge rules out a nation having both a king and a president.
• Strong Kleene: if a disjunction is defined, it must be true. Being false would require both presuppositions to hold, which is impossible here.
• Two-dimensional semantics: the symmetric presupposition formula is satisfied only in cases that already make the assertion true. Replacing it with a plain disjunction of presuppositions fixes these examples but becomes too weak for Karttunen's "bald children" sentence.
• Update semantics and Schlenker (2009): an update is defined only when the input state already guarantees one disjunct. The disjunction therefore never removes any worlds.
• Flexible accommodation: by default, both disjuncts are updated against the full context. When that fails a genuineness requirement, each disjunct's context is restricted to the worlds where the other disjunct's presupposition fails. Applied to a four-world state, this keeps the two "true" worlds, and negation keeps the other two. Two problems remain: accommodation is forced under negation, and the factive "realize" example (18) is mispredicted.

Interesting ideas

• I1. The paper judges each theory against a tiny fixed set of desiderata: it should presuppose p-or-q, and it should be falsifiable. A theory fails if it misses either one.
• I2. Truth claims are checked through the negated sentence. If an analysis says a sentence can never be false, it cannot explain why the "neither…nor" version sounds true.
• I3. Contexts are modeled as small explicit world sets, such as one world per combination of "disjunct holds" and "presupposition holds," and every update rule is traced by hand on them.
• I4. Disjuncts get their own local contexts. A clause is evaluated only against the part of the context compatible with its own presupposition, and the default full-context evaluation is abandoned only when it would make a disjunct impossible.
• I5. The definedness check is a uniform failure value that spreads through set operations, so any undefined part makes the whole update undefined.

For Mova

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

• I1 (learn): Build small hand-made test suites for each phenomenon, with explicit pass/fail conditions such as "can be false" and "negation is true here," and use them as negative controls for prag rules.
• I2 (answer): When a reader answers yes/no questions, also check that it gets the negated question right, which catches analyses that are vacuously true.
• I3 (world): Represent uncertain facts like "the head of state is a king or a president" as a few explicit alternative worlds, and verify that each update actually removes some, so every step stays explainable.
• I4 (frames): Presupposition triggers inside "either…or" (definite descriptions, aspectual verbs like "stop") should not be projected globally when they conflict; prag can instead attach each one locally to its own branch.
• I5 (world): A dedicated "undefined" state that propagates through world updates gives a clear, explainable signal that a presupposition failed, instead of silently producing an empty world.