📄 An Implemented Formalism for Computing Linguistic Presuppositions and Existential Commitments

Summary

Marcu and Hirst address a gap between two research traditions. Linguistic theories of presupposition explain things like factive complements but say little about why hearers assume that definite referents exist. Philosophical theories of nonexistence can describe dragons or Sherlock Holmes, but they do not explain that default commitment. The authors combine both traditions. They use Hirst's rich ontology, which separates physical, fictional and unactualized existence. They add Lejewski's unrestricted reading of quantifiers, under which quantifying over something does not claim it exists. They also add methodological principles drawn from Meinong and Grice. All of this sits inside stratified logic, where every fact is labelled either undefeasible (asserted) or defeasible (implied). Presuppositions are the defeasible facts of the "optimistic" models, meaning the preferred models that keep as much defeasible content as stays consistent. The system is implemented in Common Lisp as stratified Beth tableaux, using the nondeterminism of Screamer. It computes presuppositions uniformly, including existential ones, and it handles their cancellation even when the contradicting information arrives later in the discourse.

Key points

• Stratified logic splits relations by strength (undefeasible vs defeasible) and by polarity (positive vs negative), and it defines separate u-satisfiability and d-satisfiability.
• Existence is described with several predicates:
  • E! for physical existence;
  • F! for fictional objects, which implies ¬E!;
  • UE! for unactualized objects such as an averted strike, which also implies ¬E!.
• A general rule states that every definite reference defeasibly exists. Model ordering then keeps the optimistic models.
• In the worked examples:
  • "Pelé" receives a defeasible E!, while "Sherlock Holmes" receives F! and ¬E!.
  • "John does not regret that Mary came" presupposes that Mary came. A later "Mary did not come" removes that presupposition.
• The authors criticize earlier accounts:
  • Parsons builds existence into what is said, which leaves no room for cancellation.
  • Hobbs ties existential "transparency" to predicates rather than to objects, so the King of Buganda case cannot be handled.
  • Atlas, van der Sandt and Zeevat do not handle late cancellation or richer ontologies.

Interesting ideas

• I1. Mark every derived fact as either asserted (hard) or presupposed (soft), so that soft facts can be withdrawn when later discourse contradicts them. This avoids rebuilding the whole interpretation.
• I2. Existence is more than a yes/no property: objects can be real, fictional, unactualized (a cancelled party, an averted strike) or past.
• I3. Choose among candidate interpretations with a preference order: keep the most "optimistic" consistent model, the one holding the most defeasible content. This is a principled form of default reasoning rather than an ad hoc heuristic.
• I4. Whether an argument's referent exists should follow from knowledge about that object, not from a fixed property of the verb. The paper's Ross/Zeus and King of Buganda cases show why.
• I5. Express factive triggers as rules that survive negation: the negated main verb still yields its complement as a defeasible fact.

For Mova

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

• I1 (world): Store presupposed facts in the text world with a defeasible flag and retract them on contradiction, which keeps every change of belief explainable.
• I2 (world): Give each entity an existence-mode attribute so that fable characters, prevented events and historical people are not treated as present physical objects.
• I3 (answer): When a question depends on unstated defaults, the reader can choose the maximal consistent world and cite which defaults it relied on.
• I4 (frames): Do not hard-code existence entailments in VerbNet-based frames; let the world knowledge (for example, Wikidata or WordNet marking Zeus as mythological) decide.
• I5 (frames): Add presupposition rules for factives such as regret and know, and for verbs like stop, to the pragmatics crate, and test them on negated and later-cancelled examples as controls.