Van der Sandt & Maier (2003) — Denials in Discourse #
@cite{van-der-sandt-maier-2003}
Denials in Discourse. Michigan Linguistics and Philosophy Workshop, 2003.
Formalization of directed reverse anaphora (RA*) applied to the paper's worked examples. Connects three linglib modules:
Core.Semantics.ContentLayer—Off(which layers are offensive)Theories.Semantics.Dynamic.DRT.Basic— LDRT types and RA*Phenomena.Negation.Denial— empirical denial data
Layer Naming Convention #
The paper's layer labels map to ContentLayer constructors as follows:
| Paper | Code | Meaning |
|---|---|---|
pr | .presupposition | Backgrounded precondition |
fr (Frege) | .atIssue | Assertoric/at-issue content |
imp | .implicature | Scalar implicature or connotation |
Core Mechanism #
Denial is a non-monotonic discourse operation that selectively retracts content. The RA* algorithm (§4.3):
- Identifies offensive layers via
Off— those inconsistent with the correction - Moves conditions at offensive layers under negation
- Preserves conditions at non-offensive layers
Verified Examples #
| Example | Denial type | Off | RA* result |
|---|---|---|---|
| King of France (49) | Presuppositional | {pr, fr} | 1 cond: ¬[pr+fr] |
| Possible/necessary (68) | Implicature | {imp} | 3 conds: pr, fr + ¬[imp] |
| Lady/wife (69) | Connotation | {imp} | 4 conds: pr, fr, fr + ¬[imp] |
σ₁: "The King of France walks in the park." σ₂: "No, he doesn't," σ₃: "France doesn't have a king."
The correction targets the existence presupposition of the definite. Off = {pr, fr}: both layers conflict with "no king."
Note: the Denial.lean datum kingBald_presuppositional uses a different
sentence (ex. 30b: "The king of France is not bald") but the same denial
type — presuppositional. The bridge theorem below connects the Off
computation to that datum's target layer.
Equations
- VanDerSandtMaier2003.instDecidableEqKFW x✝ y✝ = if h : VanDerSandtMaier2003.KFW.ctorIdx✝ x✝ = VanDerSandtMaier2003.KFW.ctorIdx✝ y✝ then isTrue ⋯ else isFalse ⋯
Equations
- One or more equations did not get rendered due to their size.
Instances For
Equations
- VanDerSandtMaier2003.instReprKFW = { reprPrec := VanDerSandtMaier2003.instReprKFW.repr }
Off: "no king" conflicts with both pr (king exists) and fr (king walks).
After RA* with Off = {pr, fr}: no conditions survive (both are offensive). All material moves under a single negation wrapper.
The sole surviving condition is at fr level (the negation wrapper is assertoric content: "it is not the case that ...").
σ₁: "It is possible the Pope is right." σ₂: "No, it's not POssible," σ₃: "it's NECessary that he's right."
The correction targets the scalar implicature ¬□p. Off = {imp}: only the implicature conflicts with correction □p. At-issue content ◇p survives (□p entails ◇p).
Equations
- VanDerSandtMaier2003.instDecidableEqModalW x✝ y✝ = if h : VanDerSandtMaier2003.ModalW.ctorIdx✝ x✝ = VanDerSandtMaier2003.ModalW.ctorIdx✝ y✝ then isTrue ⋯ else isFalse ⋯
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Instances For
Equations
- VanDerSandtMaier2003.instReprModalW = { reprPrec := VanDerSandtMaier2003.instReprModalW.repr }
Off: correction "necessary" (□p) conflicts only with imp (¬□p).
After RA* with Off = {imp}: pr and fr survive; imp moves under negation. Result: 2 surviving + 1 negation wrapper = 3 conditions.
Surviving layers: pr, fr at top level; negated imp tagged fr.
σ₁: "Now, THAT's a nice lady." σ₂: "Yes, she is," σ₃: "but she's not a LAdy," σ₄: "she's my WIfe."
The correction targets the connotation of "a lady" (implicature: the person is a stranger, not a close relative). The literal predication (lady, nice) and presupposition (pointing) survive; only the stranger implicature is retracted. Off = {imp}.
The paper's derivation has 4 utterances; σ₂ (affirmation "yes, she is") is treated as monotonic merge and omitted here. The Off computation depends only on σ₁ + σ₄.
Note: the Denial.lean datum lady_wife uses a related sentence
(ex. 13: "That wasn't a lady I kissed last night") but the same denial
type — implicature targeting the connotation of "lady."
Equations
- VanDerSandtMaier2003.instDecidableEqLadyW x✝ y✝ = if h : VanDerSandtMaier2003.LadyW.ctorIdx✝ x✝ = VanDerSandtMaier2003.LadyW.ctorIdx✝ y✝ then isTrue ⋯ else isFalse ⋯
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- One or more equations did not get rendered due to their size.
Instances For
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- VanDerSandtMaier2003.instReprLadyW = { reprPrec := VanDerSandtMaier2003.instReprLadyW.repr }
Off: correction "wife" conflicts only with imp (stranger). Crucially, lady (fr) is consistent with wife — Off does NOT retract the literal predication "lady."
After RA*: pr, fr (lady), fr (nice) survive. imp (stranger) moves under negation. Result: 3 surviving + 1 negated = 4.
Surviving layers: pr, fr, fr at top level; negated imp as fr.
Full pipeline for the modal example: assertion adds content (monotonic merge), denial selectively retracts (non-monotonic RA*).
This demonstrates the paper's central architectural claim: assertion and denial are dual discourse operations, one monotonic and one not.
Denial update: 4 conditions = 2 surviving (pr + ◇right) + 1 correction (□right) + 1 negated wrapper (¬[¬□right]).
All surviving content is at pr or fr level. No imp content remains at the top level.
The imp layer has been fully retracted from the top level.
The Off computations from §§ 1–3 agree with the denial-type
classification in Phenomena.Negation.Denial. Each Off result
contains the target layer of the corresponding DenialDatum.
This is the end-to-end chain: a semantic computation over layered propositions (Off) yields offensive layers that match the empirical denial-type taxonomy.
The Off result for the modal example includes the datum's target layer. The semantic Off computation (checking proposition consistency) agrees with the empirical classification (implicature denial).
The Off result for the KF example includes the datum's target layer.
The Off result for the lady/wife example includes the datum's target layer.
@cite{van-der-sandt-maier-2003} §2.1: denial and negation are orthogonal concepts. Denial is a discourse operation (non-monotonic correction); negation is a semantic operator (truth-functional connective). A denial can use a positive sentence (ex. 6), and a negative sentence can be a plain assertion, not a denial (ex. 2).
Positive denial exists: the denial utterance IS the correction, with no negation involved. Denial is a discourse function, not a syntactic form.
Positive denial is propositional — it targets fr (at-issue content), just like negative propositional denials. The mechanism is the same regardless of surface polarity.
The same surface negation can correspond to different denial types, disambiguated by the correction (§2.3: "still" denials, ex. 19–20).