📄 Presupposition Accommodation as Exception Handling

Summary

The paper asks whether van der Sandt's view that presuppositions behave like anaphora can be moved out of DRT and into de Groote's (2006) type-theoretic dynamic semantics. That framework extends Montague's simple type theory with an environment type γ and continuations. The authors show this works for presuppositions triggered by definite descriptions: proper names, pronouns, possessive noun phrases, and referents introduced only implicitly.

The environment is enriched so that it stores individuals together with their properties. Each trigger calls a selection function, sel, which looks up a reference marker matching a given property. The framework does not commit to any particular resolution algorithm behind sel. If no suitable marker exists, sel raises an exception that carries the missing property. The discourse update operator catches it, introduces a fresh existentially bound referent with that property, adds it to the environment, and retries the update.

Accommodation thus becomes ordinary exception handling. The result is a fully compositional, Montague-style account that also absorbs Geurts' binding theory. The paper is purely formal and contains no empirical evaluation.

Key points

• Types used: ι (individuals), o (propositions), and γ (environment). A dynamic proposition is Ω = γ → (γ → o) → o. NPs have type ((γ → ι) → Ω) → Ω, so individuals are always parameterized by the environment.
• The selection function has type sel : (ι → o) → γ → ι. Following the quotation theory of names (Kneale), "John" is interpreted as λP.P(sel(named "John")). The pronoun "he" selects an individual that is human ∧ masculine, which also covers cataphora ("When he woke up, Tom felt better").
• Possessives ("John's car") are handled by nesting selections. A higher-order SEL, defined via sel, works on dynamic propositions. Together with a dynamic conjunction, it builds the 's term compositionally from the possessor NP and the possessed noun.
• Implicit referents are handled in the lexicon. The entry for "is married" already selects a wife or husband of x, so "His wife" in the next sentence can bind to that referent.
• Discourse update is recursive. On a failure carrying property Q, the handler adds ∃x.(Qx) and pushes the pair (x, Qx) onto the environment, which implements global accommodation. A worked example shows the derivation for "This story is about John. John loves Mary."

Interesting ideas

• I1. When a definite finds no antecedent, this is treated as a typed failure that carries the missing description, and a handler creates the entity and retries instead of silently guessing.
• I2. All anaphora resolution sits behind one interface, select(property, environment), so the semantics does not depend on any particular resolver.
• I3. The environment stores each referent together with what has been said about it, much like file cards, rather than as a bare list of IDs.
• I4. Lexical entries can presuppose related participants, as when "married" brings in a spouse, which lets later possessives bind to referents nobody mentioned explicitly.
• I5. Proper names are treated as definite descriptions ("the individual named X"), so names, pronouns and descriptions all share one resolve-or-accommodate mechanism.

For Mova

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

• I1 (world): Unresolved definites in the world of the text could raise a "missing entity with property Q" event, and the handler would add the entity and record the accommodation step in the explanation trace.
• I2 (frames): The coreference module could expose exactly this API, so rule-based and learned resolvers can be swapped and compared without touching frame construction.
• I3 (world): Each entity in the text world could carry its accumulated descriptive properties, so later descriptions ("the old man", "his car") can be matched against them.
• I4 (frames): Frames built from VerbNet/FrameNet could declare implicit participants, which become bindable targets for "his wife"-style NPs in fables and tales.
• I5 (world): Names, pronouns and descriptions could share one lookup-or-create path in the entity store, which removes special-case code for first mentions.