📄 Presuppositions and Default Reasoning: A Study in Lexical Pragmatics

Summary

Some words carry meaning that survives negation. Both "My cousin is a bachelor" and, in its usual reading, "My cousin is not a bachelor" suggest that the cousin is an adult male. These presuppositions can still disappear: an added remark about a three-year-old cancels them, and a disjunction with "spinster" blocks them. Explaining when they survive is the projection problem. Earlier solutions by Karttunen, Karttunen and Peters, Soames and Gazdar tagged parts of a word's meaning as presuppositional in advance. They then removed unwanted ones with special filtering or cancellation rules. Mercer instead treats presupposing as inference by the hearer. Following Gazdar's epistemic view and Grice's maxims, the hearer guesses what a cooperative speaker must know. Each trigger word contributes default rules in Reiter's Default Logic, an extension of Carnap's meaning postulates. These rules are evaluated inside the default theory built for the whole utterance, so the context decides what survives. The work offers no data or numbers. Its value is a clean division of labour: word knowledge sits in the lexicon and general reasoning sits in the inference engine. Mercer calls this lexical pragmatics.

Key points

• The identifying test for presupposition is the negation test: an inference follows from both a simple sentence and the preferred reading of its negation.
• There are two ways to cancel a presupposition: make it inconsistent with what follows, as in (2a), or use a disjunction that splits into cases each denying it, as in (2b) "bachelor or a spinster".
• The paper rejects three earlier families of solutions: filtering during composition (Karttunen 1973/1974, Karttunen and Peters 1979, Soames 1979), cancellation after interpretation (Gazdar 1979), and a hybrid (Soames 1982).
• Carnap's meaning postulate is strengthened from one-way implication to logical equivalence. The paper presents this as an agent-centred view of the definitions an agent holds at a given moment, not as a theory of correct definitions.
• Defaults are scoped to the sentence and guarded by an LF predicate. The guard stops them firing for logically equivalent paraphrases such as "not an unmarried adult male". Figure 1 shows an ISA hierarchy where negation targets only the last feature arc.

Interesting ideas

• I1. Treat a word's presuppositions as defaults that hold only if they stay consistent with the rest of the utterance, rather than as fixed facts filtered afterwards.
• I2. A disjunction can block presuppositions because each disjunct, read as a case, denies what the other would presuppose.
• I3. Limit the reach of defaults to one sentence, both to keep reasoning tractable and because defaults tend to act locally.
• I4. Attach defaults to the specific surface trigger through a guard, so a logically equivalent paraphrase does not fire the same presupposition.
• I5. In an ISA hierarchy, negating a concept flips only its last distinguishing feature, and everything else is inherited by default, as in "not a bachelor" or "toy dog".

For Mova

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

• I1 (frames): prag could emit "not a bachelor ⇒ adult male, married" as a defeasible inference that is retracted when a later clause, such as a stated age of three, contradicts it.
• I2 (world): when the text world holds an "A or B" claim, it could expand the claim into explicit cases and keep only inferences that survive in every case.
• I3 (world): default inferences from triggers could be checked against the current sentence's entities only, which keeps the derivation trace short and explainable.
• I4 (frames): key presupposition rules on the lemma and its node in the UD tree, not on the normalized logical form.
• I5 (world): the WordNet-based ontology could mark each concept's final differentiating feature, giving a principled reading for negated or modified nouns.