Anand & Hacquard (2013): Epistemics and Attitudes

@cite{anand-hacquard-2013}

Semantics & Pragmatics 6, Article 8: 1–59.

Summary

This paper investigates the distribution of epistemic modals (might, must) in the complements of attitude verbs across French, Italian, and Spanish. The central finding:

1. Epistemics are fully acceptable under attitudes of acceptance (doxastics, argumentatives, semifactives) but degraded under desideratives and directives.

2. Emotive doxastics (hope, fear) and dubitatives (doubt) show a mixed pattern: they license epistemic possibility (might) but not epistemic necessity (must).

Proposal

Two proposals are combined:

About epistemics (@cite{yalcin-2007}, @cite{hacquard-2006}): Epistemics quantify over an information state parameter S, obtained by anaphora to the embedding attitude.

About attitudes (@cite{bolinger-1968}, @cite{villalta-2008}):

• Representational attitudes (believe, say, know) provide an information state S = DOX(x,w) — epistemics are licensed.
• Non-representational attitudes (want, demand) use comparative semantics with S = ∅ — epistemics are trivial/contradictory.
• Hybrid attitudes (hope, fear, doubt) have both components: the representational component licenses possibility epistemics, but the uncertainty condition blocks necessity epistemics.

Connection to BToM

The hybrid structure of emotive doxastics maps directly onto BToM inference (@cite{baker-jara-ettinger-saxe-tenenbaum-2017}):

• Doxastic component = belief marginal P(b | a)
• Preference component = desire marginal P(d | a)
• Uncertainty condition = non-extreme credence

This bridges @cite{anand-hacquard-2013}'s attitude semantics with @cite{houlihan-kleiman-weiner-hewitt-tenenbaum-saxe-2023}'s emotion appraisal architecture: emotive doxastics ARE prospective emotions computed from BToM marginals.

Cross-Romance Survey Data

Seven-point acceptability ratings (1 = unacceptable, 7 = completely acceptable) for epistemic modals under attitude verbs, pooled across French (n=31), Italian (n=11), and Spanish (n=21).

Table 4: Pooled Descriptive Statistics (mean (sd) / median)

	des/direct	emo dox	dubitative	semifactive	accept	Mean
might	3.5/3	5.1/6	6.1/7	6.1/7	6.4/7	5.4 (1.8)/6
must	1.9/1	2.7/2	3.1/2	5.6/6	6.0/7	3.9 (1.7)/4
probable	2.4/3	4.2/5	4.8/6	5.6/7	6.2/7	5.0 (1.9)/5

The critical contrasts:

• Acceptance/semifactive: might ≈ must (both high)
• Des/directive: might ≈ must (both low)
• Emotive doxastic/dubitative: might >> must

We use AttitudeClass from Representationality.lean directly (7 classes) rather than defining a study-local enum. The survey collapses some classes (doxastics ≈ argumentatives, desideratives ≈ directives), but the theory predicts the same licensing for collapsed classes — which we verify.

inductive AnandHacquard2013.Acceptability : Type

Acceptability judgment: acceptable (median ≥ 5) or degraded.

• acceptable : Acceptability
• degraded : Acceptability

@[implicit_reducible]

instance AnandHacquard2013.instDecidableEqAcceptability : DecidableEq Acceptability

Equations

• AnandHacquard2013.instDecidableEqAcceptability x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance AnandHacquard2013.instReprAcceptability : Repr Acceptability

Equations

• AnandHacquard2013.instReprAcceptability = { reprPrec := AnandHacquard2013.instReprAcceptability.repr }

def AnandHacquard2013.instReprAcceptability.repr : Acceptability → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def AnandHacquard2013.observedAcceptability : Semantics.Attitudes.Representationality.AttitudeClass → Semantics.Attitudes.Representationality.EpistemicForce → Acceptability

Observed acceptability from the survey data, indexed by the full AttitudeClass from Representationality.lean. Argumentatives pattern with doxastics; directives pattern with desideratives.

Equations

• One or more equations did not get rendered due to their size.

def AnandHacquard2013.predictedAcceptability (att : Semantics.Attitudes.Representationality.AttitudeClass) (force : Semantics.Attitudes.Representationality.EpistemicForce) : Acceptability

Predicted licensing derived from AttitudeClass.licensesEpistemic (Representationality.lean). No stipulation — the prediction follows from the representationality classification.

Equations

• AnandHacquard2013.predictedAcceptability att force = if att.LicensesEpistemic force then AnandHacquard2013.Acceptability.acceptable else AnandHacquard2013.Acceptability.degraded

theorem AnandHacquard2013.theory_matches_data (att : Semantics.Attitudes.Representationality.AttitudeClass) (force : Semantics.Attitudes.Representationality.EpistemicForce) : predictedAcceptability att force = observedAcceptability att force

The representationality theory correctly predicts all 14 cells (7 attitude classes × 2 epistemic forces).

Epistemic Modals as Information-State Quantifiers

Following @cite{yalcin-2007} and @cite{veltman-1996}, epistemic modals quantify over an information state parameter S:

⟦might φ⟧^{c,w,S,g} = 1 iff ∃w' ∈ S: ⟦φ⟧^{c,w',S,g} = 1
⟦must φ⟧^{c,w,S,g} = 1 iff ∀w' ∈ S: ⟦φ⟧^{c,w',S,g} = 1

Attitude verbs update S with their quantificational domain:

⟦att φ⟧^{c,w,S,g} = λx. ∀w' ∈ S': ⟦φ⟧^{c,w',S',g} = 1
where S' = quantificational domain provided by att

For representational attitudes: S' = DOX(x,w) (non-trivial) For non-representational attitudes: S' = ∅ (trivial → tautology/contradiction)

@[reducible, inline]

abbrev AnandHacquard2013.InfoState (W : Type u_2) : Type u_2

Information state: a set of worlds (represented as a list).

Equations

• AnandHacquard2013.InfoState W = List W

def AnandHacquard2013.mightS {W : Type u_1} (S : InfoState W) (φ : W → Prop) : Prop

Epistemic possibility over information state S: ⟦might φ⟧_S = ∃w' ∈ S: φ(w')

Equations

• AnandHacquard2013.mightS S φ = ∃ w ∈ S, φ w

@[implicit_reducible]

instance AnandHacquard2013.instDecidableMightSOfDecidablePred {W : Type u_1} {S : InfoState W} {φ : W → Prop} [DecidablePred φ] : Decidable (mightS S φ)

Equations

• AnandHacquard2013.instDecidableMightSOfDecidablePred = id inferInstance

def AnandHacquard2013.mustS {W : Type u_1} (S : InfoState W) (φ : W → Prop) : Prop

Epistemic necessity over information state S: ⟦must φ⟧_S = ∀w' ∈ S: φ(w')

Equations

• AnandHacquard2013.mustS S φ = ∀ w ∈ S, φ w

@[implicit_reducible]

instance AnandHacquard2013.instDecidableMustSOfDecidablePred {W : Type u_1} {S : InfoState W} {φ : W → Prop} [DecidablePred φ] : Decidable (mustS S φ)

Equations

• AnandHacquard2013.instDecidableMustSOfDecidablePred = id inferInstance

def AnandHacquard2013.nonTrivial {W : Type u_1} (S : InfoState W) : Prop

Non-triviality presupposition (@cite{geurts-2005}): epistemics presuppose their modal base is non-trivial.

Equations

• AnandHacquard2013.nonTrivial S = (S ≠ [])

@[implicit_reducible]

instance AnandHacquard2013.instDecidableNonTrivial {W : Type u_1} {S : InfoState W} : Decidable (nonTrivial S)

Equations

• AnandHacquard2013.instDecidableNonTrivial = id inferInstance

theorem AnandHacquard2013.might_defined_iff_nontrivial {W : Type u_1} [DecidableEq W] (S : InfoState W) (φ : W → Prop) [DecidablePred φ] (_h : nonTrivial S) : mightS S φ ∨ ¬mightS S φ

Epistemic possibility is defined (non-trivial) whenever S ≠ ∅.

theorem AnandHacquard2013.might_empty {W : Type u_1} [DecidableEq W] (φ : W → Prop) : ¬mightS [] φ

With empty S, might is trivially false — yielding infelicity.

theorem AnandHacquard2013.must_empty {W : Type u_1} [DecidableEq W] (φ : W → Prop) : mustS [] φ

With empty S, must is trivially true — yielding infelicity.

def AnandHacquard2013.representationalS {W : Type u_1} {E : Type u_2} (R : Semantics.Attitudes.Doxastic.AccessRel W E) [(a : E) → (w w' : W) → Decidable (R a w w')] (agent : E) (w : W) (worlds : List W) : InfoState W

Representational attitude embedding: S' = DOX(x,w). The doxastic alternatives form the information state that embedded epistemics quantify over.

Equations

• AnandHacquard2013.representationalS R agent w worlds = List.filter (fun (w' : W) => decide (R agent w w')) worlds

def AnandHacquard2013.nonRepresentationalS {W : Type u_1} : InfoState W

Non-representational attitude embedding: S' = ∅. Comparative semantics provides no information state.

Equations

• AnandHacquard2013.nonRepresentationalS = []

theorem AnandHacquard2013.representational_nontrivial {W : Type u_1} [DecidableEq W] {E : Type u_2} (R : Semantics.Attitudes.Doxastic.AccessRel W E) [(a : E) → (w w' : W) → Decidable (R a w w')] (agent : E) (w : W) (worlds : List W) (h : ∃ w' ∈ worlds, R agent w w') : nonTrivial (representationalS R agent w worlds)

Representational attitudes yield non-trivial information states (when there is at least one accessible world).

theorem AnandHacquard2013.nonRepresentational_trivial {W : Type u_1} [DecidableEq W] : ¬nonTrivial nonRepresentationalS

Non-representational attitudes yield trivial information states.

theorem AnandHacquard2013.believe_must {W : Type u_1} [DecidableEq W] {E : Type u_2} (R : Semantics.Attitudes.Doxastic.AccessRel W E) [(a : E) → (w w' : W) → Decidable (R a w w')] (agent : E) (w : W) (worlds : List W) (p : W → Prop) [DecidablePred p] : mustS (representationalS R agent w worlds) p ↔ Semantics.Attitudes.Doxastic.boxAt R agent w worlds p

Under a representational attitude, embedded must p holds iff all doxastic alternatives satisfy p — a non-trivial claim.

theorem AnandHacquard2013.want_must_trivial {W : Type u_1} [DecidableEq W] (p : W → Prop) : mustS nonRepresentationalS p

Under a non-representational attitude, must p is trivially true.

theorem AnandHacquard2013.want_might_trivial {W : Type u_1} [DecidableEq W] (p : W → Prop) : ¬mightS nonRepresentationalS p

Under a non-representational attitude, might p is trivially false.

Concrete Demonstration

We instantiate the abstract theory with a finite model demonstrating the must/might asymmetry under emotive doxastics.

World model: 3 worlds {w₁, w₂, w₃}

• w₁: it is raining
• w₂: it is not raining
• w₃: it is raining (backup)

John's beliefs (DOX): {w₁, w₂} — uncertain whether it's raining. John's preference: raining worlds preferred to non-raining.

Predictions:

• "John hopes it is raining": ✓ (uncertainty + doxastic + preference)
• "John hopes it might be raining": ✓ (same doxastic assertion)
• "John hopes it must be raining": ✗ (contradicts uncertainty)

inductive AnandHacquard2013.RainWorld : Type

• raining₁ : RainWorld
• notRaining : RainWorld
• raining₂ : RainWorld

@[implicit_reducible]

instance AnandHacquard2013.instDecidableEqRainWorld : DecidableEq RainWorld

Equations

• AnandHacquard2013.instDecidableEqRainWorld x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance AnandHacquard2013.instReprRainWorld : Repr RainWorld

Equations

• AnandHacquard2013.instReprRainWorld = { reprPrec := AnandHacquard2013.instReprRainWorld.repr }

def AnandHacquard2013.instReprRainWorld.repr : RainWorld → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def AnandHacquard2013.isRaining : RainWorld → Prop

Equations

• AnandHacquard2013.isRaining AnandHacquard2013.RainWorld.raining₁ = True
• AnandHacquard2013.isRaining AnandHacquard2013.RainWorld.notRaining = False
• AnandHacquard2013.isRaining AnandHacquard2013.RainWorld.raining₂ = True

@[implicit_reducible]

instance AnandHacquard2013.instDecidablePredRainWorldIsRaining : DecidablePred isRaining

Equations

• One or more equations did not get rendered due to their size.

def AnandHacquard2013.johnDox : RainWorld → Bool

John's doxastic accessibility: worlds w₁ and w₂ are doxastically accessible (he's uncertain), w₃ is not.

Equations

• AnandHacquard2013.johnDox AnandHacquard2013.RainWorld.raining₁ = true
• AnandHacquard2013.johnDox AnandHacquard2013.RainWorld.notRaining = true
• AnandHacquard2013.johnDox AnandHacquard2013.RainWorld.raining₂ = false

def AnandHacquard2013.allRainWorlds : List RainWorld

Equations

• AnandHacquard2013.allRainWorlds = [AnandHacquard2013.RainWorld.raining₁, AnandHacquard2013.RainWorld.notRaining, AnandHacquard2013.RainWorld.raining₂]

def AnandHacquard2013.johnS : InfoState RainWorld

John's doxastic information state

Equations

• AnandHacquard2013.johnS = List.filter AnandHacquard2013.johnDox AnandHacquard2013.allRainWorlds

theorem AnandHacquard2013.johnS_eq : johnS = [RainWorld.raining₁, RainWorld.notRaining]

theorem AnandHacquard2013.john_nontrivial : nonTrivial johnS

John's DOX is non-trivial (he has beliefs).

theorem AnandHacquard2013.john_might_rain : mightS johnS isRaining

"might be raining" is true in John's DOX — there's a raining world.

theorem AnandHacquard2013.john_must_rain : ¬mustS johnS isRaining

"must be raining" is false in John's DOX — there's a non-raining world.

theorem AnandHacquard2013.john_uncertain : mightS johnS isRaining ∧ mightS johnS fun (w : RainWorld) => ¬isRaining w

Uncertainty: both raining and non-raining worlds in DOX.

The BToM–Emotive Doxastic Bridge

@cite{houlihan-kleiman-weiner-hewitt-tenenbaum-saxe-2023}'s emotion model computes retrospective appraisals from BToM marginals. We show that @cite{anand-hacquard-2013}'s emotive doxastic semantics gives the formal content of prospective emotions computed from the same marginals.

The mapping:

A&H component	BToM computation
Doxastic assertion	beliefMarginal: Pr(b | a) > 0 for b ⊨ φ
Uncertainty condition	0 < Σ_b Pr(b|a)·⟦φ⟧_b < 1
Preference assertion	desireMarginal: Σ_d Pr(d|a)·U(φ,d) > Σ_d Pr(d|a)·U(¬φ,d)

This unification means:

• hope is a prospective emotion with positive AU (prefers φ-resolution)
• fear is a prospective emotion with negative AU (prefers ¬φ-resolution)
• Both require the same BToM inference (belief + desire marginals)
• The emotive doxastic lexical semantics IS the readout function for prospective emotions, just as the 8-dimensional β vector is the readout for retrospective emotions

theorem AnandHacquard2013.hope_from_uncertainty_and_preference (cred u_true u_false : ℚ) (h_pos : 0 < cred) (h_lt_one : cred < 1) (h_pref : u_false < u_true) : { beliefCredence := cred, utilityIfTrue := u_true, utilityIfFalse := u_false }.isHope = true

Hope holds from uncertainty + positive preference over resolutions.

theorem AnandHacquard2013.fear_from_uncertainty_and_dispreference (cred u_true u_false : ℚ) (h_pos : 0 < cred) (h_lt_one : cred < 1) (h_pref : u_true < u_false) : { beliefCredence := cred, utilityIfTrue := u_true, utilityIfFalse := u_false }.isFear = true

Fear holds from uncertainty + negative preference over resolutions.

theorem AnandHacquard2013.necessity_contradicts_uncertainty (cred : ℚ) (h_high : cred ≥ 1) (h_lt : cred < 1) : False

The uncertainty condition in the emotive doxastic semantics is the same as requiring non-extreme credence in the BToM framework: Pr(φ) > 0 ∧ Pr(φ) < 1 ↔ ∃w' ∈ DOX: φ(w') ∧ ∃w' ∈ DOX: ¬φ(w').

This is the formal content of why necessity epistemics are blocked: Pr(φ) ≥ θ_must (≈ 1) contradicts Pr(φ) < 1.