Demonstration Semantics for Quotative Complements #

@cite{rudin-2025b} @cite{davidson-2015} @cite{eckardt-2014} @cite{maier-2017}

A double-Davidsonian analysis of quotative complements to verbs of speech, following @cite{rudin-2025b}'s "Embedded Intonation and Quotative Complements to Verbs of Speech" (Linguistic Inquiry).

The Core Shift #

Standard analysis of Sara said "Aaron likes apples":

say is a 2-place predicate of events and propositions
The quote denotes a proposition (or content individual)
say introduces a CONTENT relation between the event and the proposition

@cite{rudin-2025b}'s proposal: verbs of speech are uniformly 1-place event predicates. The complementizer — overt that or covert QUOTE — supplies the relation:

⟦say⟧ = λe. SAY(e) ⟦that⟧ introduces CONTENT(e, p) for propositional δ ⟦QUOTE⟧ introduces REENACT(e, u) for a paratactic performance u

A quotative complement is a covert demonstrative pthat whose referent is the cotemporaneous performance u itself. Composition is via predicate modification, not function application.

Architecture #

We split the formalization in two layers:

PerformanceOntology Perf — properties of utterance-events (LINGMAT, Loud, Whispered, RisingDecl, Commits, RaisesIssue) and the cross-property axioms that drive verb-class postulates.
SpeechVerbs Time SemObj Perf [Ω] — verb predicates (SAY, ASK, ASSERT, YELL, WHISPER), event relations (CONTENT, REENACT), and meaning postulates that connect verbs to performances via the ontology.

This split mirrors mathlib practice: a small "data" structure exposing properties + axioms, separated from the larger structure that consumes them. It also makes the Farkas-Bruce bridge possible: a discourse-state adapter can supply a PerformanceOntology instance whose Commits and RaisesIssue are derived from F&B dcS / table operations rather than stipulated (see Theories/Pragmatics/Assertion/QuotationFBOntology.lean).

Meaning Postulates #

The verb-class differences are captured by meaning postulates constraining the relation between verbal predicates and properties of performances:

SAY(e) ↔ ∀u. REENACT(e,u) → LINGMAT(u) (Rudin §3.3.4) ASK(e) ↔ ∀u. REENACT(e,u) → RESP(u) (Rudin §4.4.1) ASSERT(e) ↔ SAY(e) ∧ ∀u. REENACT(e,u) → Commits(u) [extrapolation] YELL(e) ↔ SAY(e) ∧ ∀u. REENACT(e,u) → Loud(u) [extrapolation] WHISPER(e) ↔ SAY(e) ∧ ∀u. REENACT(e,u) → Whispered(u) [extrapolation]

where RESP(u) := RaisesIssue(u) ∧ ¬ Commits(u) is the "response-eliciting" property characterized by @cite{rudin-2025b}.

These postulates derive @cite{rudin-2025b}'s empirical generalizations:

yell is consistent with quotative complements requiring loud performances; whisper is not (incompatible with loud quotation).
assert requires the speaker to commit to the content; rising declaratives don't commit; therefore assert "p?" is infelicitous while say "p?" is fine.
ask requires the absence of commitment AND issue-raising; rising declaratives are exactly that; therefore ask "p?" is fine even though propositional ask that p is not.

The ASSERT/YELL/WHISPER postulates are formal extrapolations of the informal generalizations in @cite{rudin-2025b} (the paper states the empirical generalization but does not provide a formal postulate for each verb). The SAY and ASK postulates are explicit in the paper.

Anchoring #

Performances are events in their own right — utterance-events paratactically associated with the speech-event. We model Performance as a type synonym Event Time, following @cite{rudin-2025b}'s remark that performances are special-purpose events. But the SpeechVerbs structure is parameterized over an arbitrary Perf type, so alternative ontologies (e.g., a Farkas-Bruce-derived discourse adapter) can supply their own performance type.