Documentation

Linglib.Theories.Semantics.Modality.Narrog

Narrog's Semantic Map of Modality and Mood #

@cite{narrog-2010} @cite{narrog-2012} @cite{heine-1995}

@cite{narrog-2010}'s two-dimensional semantic map classifies modal meanings along two orthogonal axes:

Volitivity (horizontal): whether a modal meaning involves the speaker's or subject's will. Deontic obligation/permission and boulomaic wish/desire are volitive; epistemic possibility, ability, and evidentiality are non-volitive.
Speaker-orientation (vertical): the degree to which the modal meaning is anchored in the speech situation. Event-oriented modality (ability, circumstantial) is at the bottom; speaker-oriented modality (epistemic assessment, deontic imposition) is in the middle; mood and illocutionary force modulation (imperative, hortative) are at the top.

The central diachronic claim: modal meanings always shift upward — toward increased speaker-orientation — independently of the volitive/non-volitive dimension. The well-known deontic → epistemic shift is just one instance.

@cite{narrog-2012} adds a third dimension: performativity — whether the utterance constitutes the modal act or merely describes it. This dimension is orthogonal to speaker-orientation and is precisely what Traugott's subjectivity cline fails to distinguish (§2.4, ch. 3).

Bridges #

toVolitivity classifies ModalFlavor into Narrog's volitivity dimension: deontic = volitive; epistemic, circumstantial = non-volitive.
NarrogRegion → ModalFlavor: reverse bridge from the 2D map back to Kratzer's flavor classification (partial — mood regions have no Kratzer analog).
SpeakerOrientationLevel → SubjectivityLevel: event-oriented = nonSubjective; speaker-oriented = subjective; mood = intersubjective. Note: @cite{narrog-2012} argues this bridge is an oversimplification — see performativity_invisible_to_traugott.
Core.Modality.DeonticNecessity: cross-linguistic data on obligation markers from the same 200-language sample.

inductive Semantics.Modality.Narrog.Volitivity :

Whether a modal meaning involves the will of the speaker or subject.

@cite{narrog-2010} §3.1, building on Jespersen ([1924] 1992) and @cite{heine-1995}: "the element of will" is the most fundamental distinguishing element between different kinds of mood.

volitive : Volitivity
nonVolitive : Volitivity

Instances For

@[implicit_reducible]

instance Semantics.Modality.Narrog.instDecidableEqVolitivity :

DecidableEq Volitivity

Equations

Semantics.Modality.Narrog.instDecidableEqVolitivity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Modality.Narrog.instReprVolitivity.repr :

Volitivity → ℕ → Std.Format

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instReprVolitivity :

Repr Volitivity

Equations

Semantics.Modality.Narrog.instReprVolitivity = { reprPrec := Semantics.Modality.Narrog.instReprVolitivity.repr }

def Semantics.Modality.Narrog.instInhabitedVolitivity.default :

Equations

Semantics.Modality.Narrog.instInhabitedVolitivity.default = Semantics.Modality.Narrog.Volitivity.volitive

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instInhabitedVolitivity :

Inhabited Volitivity

Equations

Semantics.Modality.Narrog.instInhabitedVolitivity = { default := Semantics.Modality.Narrog.instInhabitedVolitivity.default }

def Semantics.Modality.Narrog.toVolitivity :

Core.Modality.ModalFlavor → Volitivity

Classify ModalFlavor into Narrog's volitivity dimension.

Deontic modality (obligation, permission) is volitive because it involves the speaker's or some authority's will. Epistemic and circumstantial modality are non-volitive — they describe the world independently of anyone's will.

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inductive Semantics.Modality.Narrog.SpeakerOrientationLevel :

Degree of anchoring to the speech situation.

@cite{narrog-2010} Figure 1: the vertical axis ranges from event-oriented (bottom) through speaker-oriented modality (middle) to mood / illocutionary force modulation (top).

eventOriented : SpeakerOrientationLevel
speakerOriented : SpeakerOrientationLevel
mood : SpeakerOrientationLevel

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instDecidableEqSpeakerOrientationLevel :

DecidableEq SpeakerOrientationLevel

Equations

Semantics.Modality.Narrog.instDecidableEqSpeakerOrientationLevel x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Modality.Narrog.instReprSpeakerOrientationLevel.repr :

SpeakerOrientationLevel → ℕ → Std.Format

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instReprSpeakerOrientationLevel :

Repr SpeakerOrientationLevel

Equations

Semantics.Modality.Narrog.instReprSpeakerOrientationLevel = { reprPrec := Semantics.Modality.Narrog.instReprSpeakerOrientationLevel.repr }

def Semantics.Modality.Narrog.instInhabitedSpeakerOrientationLevel.default :

SpeakerOrientationLevel

Equations

Semantics.Modality.Narrog.instInhabitedSpeakerOrientationLevel.default = Semantics.Modality.Narrog.SpeakerOrientationLevel.eventOriented

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instInhabitedSpeakerOrientationLevel :

Inhabited SpeakerOrientationLevel

Equations

Semantics.Modality.Narrog.instInhabitedSpeakerOrientationLevel = { default := Semantics.Modality.Narrog.instInhabitedSpeakerOrientationLevel.default }

def Semantics.Modality.Narrog.SpeakerOrientationLevel.toNat :

SpeakerOrientationLevel → ℕ

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instLinearOrderSpeakerOrientationLevel :

LinearOrder SpeakerOrientationLevel

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def Semantics.Modality.Narrog.SpeakerOrientationLevel.toSubjectivityLevel :

SpeakerOrientationLevel → Features.Subjectivity.SubjectivityLevel

Bridge to Traugott's subjectivity cline.

The vertical axis of Narrog's map aligns with Traugott's cline: event-oriented = nonSubjective, speaker-oriented = subjective, mood = intersubjective (imperatives direct the addressee).

Caveat: @cite{narrog-2012} ch. 3 argues this bridge is an oversimplification. Traugott's cline conflates speaker-orientation with performativity: deontic obligation (performative, face-threatening) and epistemic assessment (descriptive, not face-threatening) both map to subjective, but they differ fundamentally in their pragmatic effects. See performativity_invisible_to_traugott.

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theorem Semantics.Modality.Narrog.speakerOrientation_toSubjectivity_monotone (a b : SpeakerOrientationLevel) (h : a ≤ b) :

a.toSubjectivityLevel ≤ b.toSubjectivityLevel

The bridge preserves ordering.

structure Semantics.Modality.Narrog.NarrogRegion :

A region in Narrog's 2D semantic map of modality and mood.

volitivity : Volitivity
orientation : SpeakerOrientationLevel

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def Semantics.Modality.Narrog.instReprNarrogRegion.repr :

NarrogRegion → ℕ → Std.Format

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instReprNarrogRegion :

Repr NarrogRegion

Equations

Semantics.Modality.Narrog.instReprNarrogRegion = { reprPrec := Semantics.Modality.Narrog.instReprNarrogRegion.repr }

@[implicit_reducible]

instance Semantics.Modality.Narrog.instDecidableEqNarrogRegion :

DecidableEq NarrogRegion

Equations

Semantics.Modality.Narrog.instDecidableEqNarrogRegion = Semantics.Modality.Narrog.instDecidableEqNarrogRegion.decEq

def Semantics.Modality.Narrog.instDecidableEqNarrogRegion.decEq (x✝ x✝¹ : NarrogRegion) :

Decidable (x✝ = x✝¹)

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structure Semantics.Modality.Narrog.NarrogPosition :

A position in Narrog's full 3D space: volitivity × orientation × performativity.

@cite{narrog-2012} §2.4: "subjectivity" decomposes into speaker-orientation (who is the modal source) and performativity (whether the utterance constitutes the modal act). The 2D map captures the first two dimensions; the full 3D space adds the third.

volitivity : Volitivity
orientation : SpeakerOrientationLevel
performativity : Features.Subjectivity.Performativity

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def Semantics.Modality.Narrog.instReprNarrogPosition.repr :

NarrogPosition → ℕ → Std.Format

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@[implicit_reducible]

instance Semantics.Modality.Narrog.instReprNarrogPosition :

Repr NarrogPosition

Equations

Semantics.Modality.Narrog.instReprNarrogPosition = { reprPrec := Semantics.Modality.Narrog.instReprNarrogPosition.repr }

@[implicit_reducible]

instance Semantics.Modality.Narrog.instDecidableEqNarrogPosition :

DecidableEq NarrogPosition

Equations

Semantics.Modality.Narrog.instDecidableEqNarrogPosition = Semantics.Modality.Narrog.instDecidableEqNarrogPosition.decEq

def Semantics.Modality.Narrog.instDecidableEqNarrogPosition.decEq (x✝ x✝¹ : NarrogPosition) :

Decidable (x✝ = x✝¹)

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def Semantics.Modality.Narrog.NarrogPosition.toRegion (r : NarrogPosition) :

Project to the 2D semantic map (dropping performativity).

Equations

r.toRegion = { volitivity := r.volitivity, orientation := r.orientation }

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def Semantics.Modality.Narrog.NarrogRegion.toModalFlavor :

NarrogRegion → Option Core.Modality.ModalFlavor

Map Narrog's 2D region to Kratzer's modal flavor classification.

Mood-level regions (imperative, hortative) are illocutionary rather than truth-conditional, so they have no clean Kratzer flavor.

@cite{narrog-2012} §2.4: this bridge makes explicit Narrog's claim that his 2D map classifies the Kratzer parameterization space — the combination of volitivity and orientation determines whether the conversational background is epistemic, deontic, or circumstantial.

Equations

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{ volitivity := volitivity, orientation := Semantics.Modality.Narrog.SpeakerOrientationLevel.mood }.toModalFlavor = none

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theorem Semantics.Modality.Narrog.toModalFlavor_consistent_volitivity (r : NarrogRegion) (f : Core.Modality.ModalFlavor) (h : r.toModalFlavor = some f) :

toVolitivity f = r.volitivity

The flavor bridge is consistent with the volitivity bridge: if a region maps to a flavor, that flavor's volitivity matches.

theorem Semantics.Modality.Narrog.modalFlavor_roundtrip (f : Core.Modality.ModalFlavor) (hf : f ≠ Core.Modality.ModalFlavor.bouletic) :

{ volitivity := toVolitivity f, orientation := match f, hf with | Core.Modality.ModalFlavor.deontic, hf => SpeakerOrientationLevel.speakerOriented | Core.Modality.ModalFlavor.bouletic, hf => SpeakerOrientationLevel.speakerOriented | Core.Modality.ModalFlavor.epistemic, hf => SpeakerOrientationLevel.speakerOriented | Core.Modality.ModalFlavor.circumstantial, hf => SpeakerOrientationLevel.eventOriented }.toModalFlavor = some f

Every non-mood ModalFlavor round-trips through the Narrog map: flavor → (volitivity, canonical orientation) → flavor.

theorem Semantics.Modality.Narrog.performativity_invisible_to_traugott :

{ volitivity := Volitivity.volitive, orientation := SpeakerOrientationLevel.speakerOriented }.orientation.toSubjectivityLevel = { volitivity := Volitivity.nonVolitive, orientation := SpeakerOrientationLevel.speakerOriented }.orientation.toSubjectivityLevel

Performativity is invisible to the Traugott bridge: deontic obligation (volitive, speaker-oriented, performative) and epistemic assessment (non-volitive, speaker-oriented, descriptive) both map to the same SubjectivityLevel.subjective, even though they differ radically in face-threatening potential and pragmatic effects.

This is @cite{narrog-2012}'s central critique of Traugott's unidirectional subjectification: the cline conflates two independent dimensions (speaker-orientation and performativity), collapsing distinctions that matter for understanding both synchronic typology and diachronic change.

def Semantics.Modality.Narrog.NarrogPosition.isFaceThreatening (r : NarrogPosition) :

Bool

Derive face-threatening potential from the 3D position.

An utterance is face-threatening when it is performative (creates rather than describes the modal state), volitive (involves the will), and speaker-oriented or higher (directed at the addressee).

@cite{narrog-2010} §4.2: strong obligation is cross-linguistically avoided with 2nd-person subjects precisely because it occupies this region — performative + volitive + speaker-oriented.

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def Semantics.Modality.Narrog.strongObligation :

Canonical positions for major modal types.

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def Semantics.Modality.Narrog.weakObligation :

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def Semantics.Modality.Narrog.epistemicAssessment :

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def Semantics.Modality.Narrog.dynamicAbility :

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def Semantics.Modality.Narrog.imperative :

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theorem Semantics.Modality.Narrog.strong_obligation_face_threatening :

strongObligation.isFaceThreatening = true

Strong obligation is face-threatening.

theorem Semantics.Modality.Narrog.weak_obligation_not_face_threatening :

weakObligation.isFaceThreatening = false

Weak obligation is NOT face-threatening (descriptive, not performative).

theorem Semantics.Modality.Narrog.epistemic_not_face_threatening :

epistemicAssessment.isFaceThreatening = false

Epistemic assessment is NOT face-threatening.

theorem Semantics.Modality.Narrog.imperative_face_threatening :

imperative.isFaceThreatening = true

Imperatives are face-threatening (performative + volitive + mood > eventOriented).

theorem Semantics.Modality.Narrog.strong_weak_differ_only_in_performativity :

strongObligation.toRegion = weakObligation.toRegion

Strong and weak obligation differ ONLY in performativity — they share volitivity and orientation. The Traugott bridge cannot distinguish them because it drops performativity.

Diachronic modal change data and directionality theorems are now in Theories.Diachronic.ModalChange, which imports this file and uses NarrogRegion and SpeakerOrientationLevel to formalize the claim that modal meanings always shift upward in the semantic map.