Representationality and Epistemic Licensing

@cite{anand-hacquard-2013} @cite{bolinger-1968} @cite{stalnaker-1984}

Attitude verbs split into two fundamental semantic classes (@cite{bolinger-1968}):

• Representational attitudes convey a mental picture — a consistent set of propositions defining a non-trivial set of possible worlds (an information state). Doxastics (believe, think), argumentatives (say, argue), and semifactives (know, realize).

• Non-representational attitudes combine with their complement via a logic of preference, comparing the complement to contextual alternatives on a preference scale (@cite{villalta-2008}). Desideratives (want, wish) and directives (demand, order).

• Hybrid attitudes have both components: a representational (doxastic) component providing an information state, and a preference component ordering alternatives. Emotive doxastics (hope, fear) and dubitatives (doubt).

The central empirical generalization (@cite{anand-hacquard-2013}):

Epistemic Licensing Generalization: Epistemic modals are licensed only in the scope of attitudes that provide an information state — i.e., attitudes with a representational component.

Attitude class	Representational	Pref	might	must
Doxastics	✓	✗	✓	✓
Argumentatives	✓	✗	✓	✓
Semifactives	✓	✗	✓	✓
Desideratives	✗	✓	✗	✗
Directives	✗	✓	✗	✗
Emotive doxastics	✓	✓	✓	✗
Dubitatives	✓	✓	✓	✗

The might/must asymmetry under hybrids follows from the uncertainty condition: emotive doxastics require that the attitude holder is uncertain about the complement. This is compatible with epistemic possibility (∃w'∈DOX: φ(w')) but contradicts epistemic necessity (∀w'∈DOX: φ(w')), which would entail certainty.

Mood Correlation

Epistemic licensing correlates with mood selection in Romance, but they track different things:

• Epistemics track representationality (information state provision)
• Subjunctive mood tracks preferences (comparative semantics)

The overlap is large because most preference-based attitudes are non-representational. But hybrids (emotive doxastics) have both, explaining why they license possibility epistemics AND select subjunctive.

inductive Semantics.Attitudes.Representationality.Representationality : Type

Classification of attitude semantics by representationality.

An attitude is representational iff its semantics provides a non-trivial information state (a set of worlds) that embedded epistemics can be anaphoric to (@cite{anand-hacquard-2013}, §3).

• representational : Representationality

  Provides information state S = DOX(x,w). Doxastics, argumentatives, semifactives. Epistemics quantify over DOX directly.

• nonRepresentational : Representationality

  No information state: S = ∅. Desideratives, directives. Comparative semantics over alternatives (@cite{villalta-2008}). Embedded epistemics yield tautology (might) or contradiction (must).

• hybrid : Representationality

  Both components: representational (provides DOX for epistemic anaphora) + preference (orders alternatives). Emotive doxastics (hope, fear), dubitatives (doubt).

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidableEqRepresentationality : DecidableEq Representationality

Equations

• Semantics.Attitudes.Representationality.instDecidableEqRepresentationality x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Attitudes.Representationality.instReprRepresentationality.repr : Representationality → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instReprRepresentationality : Repr Representationality

Equations

• Semantics.Attitudes.Representationality.instReprRepresentationality = { reprPrec := Semantics.Attitudes.Representationality.instReprRepresentationality.repr }

def Semantics.Attitudes.Representationality.HasInformationState : Representationality → Prop

An attitude with a representational component provides an information state that epistemics can quantify over.

Equations

• Semantics.Attitudes.Representationality.HasInformationState Semantics.Attitudes.Representationality.Representationality.representational = True
• Semantics.Attitudes.Representationality.HasInformationState Semantics.Attitudes.Representationality.Representationality.nonRepresentational = False
• Semantics.Attitudes.Representationality.HasInformationState Semantics.Attitudes.Representationality.Representationality.hybrid = True

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidablePredRepresentationalityHasInformationState : DecidablePred HasInformationState

Equations

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

def Semantics.Attitudes.Representationality.HasPreferenceComponent : Representationality → Prop

An attitude with a preference component uses comparative semantics.

Equations

• Semantics.Attitudes.Representationality.HasPreferenceComponent Semantics.Attitudes.Representationality.Representationality.representational = False
• Semantics.Attitudes.Representationality.HasPreferenceComponent Semantics.Attitudes.Representationality.Representationality.nonRepresentational = True
• Semantics.Attitudes.Representationality.HasPreferenceComponent Semantics.Attitudes.Representationality.Representationality.hybrid = True

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidablePredRepresentationalityHasPreferenceComponent : DecidablePred HasPreferenceComponent

Equations

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

inductive Semantics.Attitudes.Representationality.EpistemicForce : Type

Epistemic modal force.

• possibility : EpistemicForce
• necessity : EpistemicForce

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidableEqEpistemicForce : DecidableEq EpistemicForce

Equations

• Semantics.Attitudes.Representationality.instDecidableEqEpistemicForce x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instReprEpistemicForce : Repr EpistemicForce

Equations

• Semantics.Attitudes.Representationality.instReprEpistemicForce = { reprPrec := Semantics.Attitudes.Representationality.instReprEpistemicForce.repr }

def Semantics.Attitudes.Representationality.instReprEpistemicForce.repr : EpistemicForce → ℕ → Std.Format

Equations

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

def Semantics.Attitudes.Representationality.LicensesEpistemic : Representationality → EpistemicForce → Prop

Whether an attitude class licenses an embedded epistemic of given force. This is the central prediction of @cite{anand-hacquard-2013}.

• Representational: licenses both might and must (S = DOX, non-trivial)
• Non-representational: licenses neither (S = ∅, trivial modal base)
• Hybrid: licenses might but not must (S = DOX, but uncertainty condition contradicts universal quantification)

Equations

• One or more equations did not get rendered due to their size.
• Semantics.Attitudes.Representationality.LicensesEpistemic Semantics.Attitudes.Representationality.Representationality.representational x✝ = True
• Semantics.Attitudes.Representationality.LicensesEpistemic Semantics.Attitudes.Representationality.Representationality.nonRepresentational x✝ = False

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidableLicensesEpistemic (r : Representationality) (f : EpistemicForce) : Decidable (LicensesEpistemic r f)

Equations

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

theorem Semantics.Attitudes.Representationality.representational_licenses_all (f : EpistemicForce) : LicensesEpistemic Representationality.representational f

Representational attitudes license all epistemics.

theorem Semantics.Attitudes.Representationality.nonRepresentational_blocks_all (f : EpistemicForce) : ¬LicensesEpistemic Representationality.nonRepresentational f

Non-representational attitudes block all epistemics.

theorem Semantics.Attitudes.Representationality.hybrid_possibility_only : LicensesEpistemic Representationality.hybrid EpistemicForce.possibility ∧ ¬LicensesEpistemic Representationality.hybrid EpistemicForce.necessity

Hybrids license possibility but not necessity.

theorem Semantics.Attitudes.Representationality.licensing_requires_information_state (r : Representationality) (f : EpistemicForce) (h : LicensesEpistemic r f) : HasInformationState r

Epistemic licensing requires an information state.

def Semantics.Attitudes.Representationality.fromMoodSelector : Mood.MoodSelector → Representationality

Map mood selector to expected representationality.

This captures the strong (but imperfect) correlation between mood selection and representationality across Romance. The correlation is imperfect because subjunctive tracks preferences, not representationality directly (@cite{anand-hacquard-2013}, §6).

Equations

• Semantics.Attitudes.Representationality.fromMoodSelector Semantics.Mood.MoodSelector.indicativeSelecting = Semantics.Attitudes.Representationality.Representationality.representational
• Semantics.Attitudes.Representationality.fromMoodSelector Semantics.Mood.MoodSelector.subjunctiveSelecting = Semantics.Attitudes.Representationality.Representationality.nonRepresentational
• Semantics.Attitudes.Representationality.fromMoodSelector Semantics.Mood.MoodSelector.crossLinguisticallyVariable = Semantics.Attitudes.Representationality.Representationality.hybrid
• Semantics.Attitudes.Representationality.fromMoodSelector Semantics.Mood.MoodSelector.moodNeutral = Semantics.Attitudes.Representationality.Representationality.representational

theorem Semantics.Attitudes.Representationality.indicative_representational : fromMoodSelector Mood.MoodSelector.indicativeSelecting = Representationality.representational

Indicative-selecting attitudes are representational: they provide an information state and license epistemics.

theorem Semantics.Attitudes.Representationality.subjunctive_nonRepresentational : fromMoodSelector Mood.MoodSelector.subjunctiveSelecting = Representationality.nonRepresentational

Subjunctive-selecting attitudes are non-representational: they use comparative semantics and block epistemics.

theorem Semantics.Attitudes.Representationality.variable_hybrid : fromMoodSelector Mood.MoodSelector.crossLinguisticallyVariable = Representationality.hybrid

Cross-linguistically variable attitudes are hybrid: they have both representational and preference components.

inductive Semantics.Attitudes.Representationality.AttitudeClass : Type

Classification of specific attitude verbs. Each verb maps to a representationality class, which determines its epistemic licensing behavior.

• doxastic : AttitudeClass
• argumentative : AttitudeClass
• semifactive : AttitudeClass
• desiderative : AttitudeClass
• directive : AttitudeClass
• emotiveDoxastic : AttitudeClass
• dubitative : AttitudeClass

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidableEqAttitudeClass : DecidableEq AttitudeClass

Equations

• Semantics.Attitudes.Representationality.instDecidableEqAttitudeClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Attitudes.Representationality.instReprAttitudeClass.repr : AttitudeClass → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instReprAttitudeClass : Repr AttitudeClass

Equations

• Semantics.Attitudes.Representationality.instReprAttitudeClass = { reprPrec := Semantics.Attitudes.Representationality.instReprAttitudeClass.repr }

def Semantics.Attitudes.Representationality.AttitudeClass.representationality : AttitudeClass → Representationality

Each attitude class maps to a representationality value.

Equations

• Semantics.Attitudes.Representationality.AttitudeClass.doxastic.representationality = Semantics.Attitudes.Representationality.Representationality.representational
• Semantics.Attitudes.Representationality.AttitudeClass.argumentative.representationality = Semantics.Attitudes.Representationality.Representationality.representational
• Semantics.Attitudes.Representationality.AttitudeClass.semifactive.representationality = Semantics.Attitudes.Representationality.Representationality.representational
• Semantics.Attitudes.Representationality.AttitudeClass.desiderative.representationality = Semantics.Attitudes.Representationality.Representationality.nonRepresentational
• Semantics.Attitudes.Representationality.AttitudeClass.directive.representationality = Semantics.Attitudes.Representationality.Representationality.nonRepresentational
• Semantics.Attitudes.Representationality.AttitudeClass.emotiveDoxastic.representationality = Semantics.Attitudes.Representationality.Representationality.hybrid
• Semantics.Attitudes.Representationality.AttitudeClass.dubitative.representationality = Semantics.Attitudes.Representationality.Representationality.hybrid

def Semantics.Attitudes.Representationality.AttitudeClass.LicensesEpistemic (c : AttitudeClass) (f : EpistemicForce) : Prop

Derived epistemic licensing for attitude classes.

Equations

• c.LicensesEpistemic f = Semantics.Attitudes.Representationality.LicensesEpistemic c.representationality f

@[implicit_reducible]

instance Semantics.Attitudes.Representationality.instDecidableLicensesEpistemic_1 (c : AttitudeClass) (f : EpistemicForce) : Decidable (c.LicensesEpistemic f)

Equations

• Semantics.Attitudes.Representationality.instDecidableLicensesEpistemic_1 c f = id inferInstance

Per-cell verification of @cite{anand-hacquard-2013} Table 3.

theorem Semantics.Attitudes.Representationality.doxastic_might : AttitudeClass.doxastic.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.doxastic_must : AttitudeClass.doxastic.LicensesEpistemic EpistemicForce.necessity

theorem Semantics.Attitudes.Representationality.argumentative_might : AttitudeClass.argumentative.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.argumentative_must : AttitudeClass.argumentative.LicensesEpistemic EpistemicForce.necessity

theorem Semantics.Attitudes.Representationality.semifactive_might : AttitudeClass.semifactive.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.semifactive_must : AttitudeClass.semifactive.LicensesEpistemic EpistemicForce.necessity

theorem Semantics.Attitudes.Representationality.desiderative_might : ¬AttitudeClass.desiderative.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.desiderative_must : ¬AttitudeClass.desiderative.LicensesEpistemic EpistemicForce.necessity

theorem Semantics.Attitudes.Representationality.directive_might : ¬AttitudeClass.directive.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.directive_must : ¬AttitudeClass.directive.LicensesEpistemic EpistemicForce.necessity

theorem Semantics.Attitudes.Representationality.emotiveDoxastic_might : AttitudeClass.emotiveDoxastic.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.emotiveDoxastic_must : ¬AttitudeClass.emotiveDoxastic.LicensesEpistemic EpistemicForce.necessity

theorem Semantics.Attitudes.Representationality.dubitative_might : AttitudeClass.dubitative.LicensesEpistemic EpistemicForce.possibility

theorem Semantics.Attitudes.Representationality.dubitative_must : ¬AttitudeClass.dubitative.LicensesEpistemic EpistemicForce.necessity