📄 Solving Some Persistent Presupposition Problems

Summary

The paper tackles a set of counterexamples that Soames (1979, 1982) raised against Gazdar's 1979 account of how presuppositions project from complex sentences. The troublesome cases are conditionals ('if … then') where a sentential adverb such as too or again sits in the antecedent or the consequent. Earlier fixes were Landman's extra clausal implicatures and Soames' own hybrid of the Gazdar and Karttunen–Peters approaches. Both had been argued against, so these examples were left unexplained. Mercer reuses his default-logic theory of presupposition (Mercer 1987, 1988). In that theory, presuppositions are default inferences drawn from a first-order S4 modal representation of the utterance, with operators Ks and Ps. Clausal implicatures decide how the theory is split into cases. The new step is a claim about the conditional: the logically or conversationally prior clause fixes how negation scopes over an adverb in the other clause. With that representation, the presupposition is correctly blocked in most of Soames' examples and correctly kept in one. The paper argues that presupposition depends on semantic representation and negation scope, not only on surface triggers.

Key points

• Presuppositions are encoded as normal default rules. The paper reinterprets them as follows: if the speaker says α and β is consistent with the hearer's knowledge base KBH, the hearer may conjecture β. An utterance u adds Ks u to KBH.
• Following Gazdar's version of Grice, the speaker becomes committed to PsA, Ps¬A, PsB and Ps¬B whenever they utter a disjunction ('A or B') or a conditional ('if A then B'). These implicatures license a case analysis. For 'A or B' the two cases are A∧¬B and ¬A∧B.
• Default logic has no law of the excluded middle, so case analysis is needed. The cases must be chosen carefully:
  • too few cases let unwanted statements through;
  • too many cases can block valid ones, because the logic is non-monotonic.
• For 'if a then b', the material a⊃b is derived from Stalnaker's conditional a>b. The resulting cases are a∧b and ¬a∧¬b. Default rules for too (kick-subject-too) and again (call-subject-again) generate the presuppositions.
• In the analyses (33), (34) and (36), negation does not take the adverb in its scope, so the presupposition is not derived. In (35), the adverb is in the prior antecedent, normal wide scope applies, and the presupposition appears.

Interesting ideas

• I1. The negation test (an inference survives both a sentence and its plain negation) works as an operational filter that separates presuppositions from ordinary entailments.
• I2. Disjunctions and conditionals are split into cases that fully fix every clause's truth value, and an inference is accepted only if it holds in every case.
• I3. A trigger fires only if its default stays consistent with what the hearer already knows, so context can cancel it without any special rule.
• I4. The scope of negation over an adverb like too or again in one clause is inherited from the logically or conversationally prior clause.
• I5. Separating the speaker's knowledge (Ks) from mere possibility (Ps) lets clausal implicatures be stated precisely.

For Mova

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

• I1 (frames): prag could tag a candidate inference as presupposed only if it also holds under the negated frame, which keeps the decision explainable.
• I2 (world): when a text says "X or Y" or "if X then Y", the world builder could keep parallel case-worlds and promote to the main world only facts that are true in all of them.
• I3 (world): presupposed facts could be stored as defeasible entries that are withdrawn automatically when they contradict existing world state.
• I4 (frames): when negating a consequent clause containing a focus adverb, prag could copy the scope decision made for the antecedent instead of always using wide scope.
• I5 (answer): QA readers could use this to distinguish "the narrator asserts X" from "X is left open" when answering questions about conditional statements in fables.