Documentation

Studies.Narrog2012

Narrog (2012): Modality, Subjectivity, and Semantic Change #

This file formalizes the category hierarchy and the category-climbing hypothesis of [Nar12]. Scope data from Japanese order the grammatical categories of the verbal clause from voice and benefactives at the bottom through aspect, dynamic and deontic modality, negation and epistemic modality, and tense to mood and illocutionary modification at the top (GramCategory, GramCategory.scopeLevel), an empirical hierarchy finer than the stipulated universal one of [Cin99]; epistemic modality outscopes deontic and dynamic modality, and mood outscopes modality proper (epistemic_outscopes_deontic, mood_outscopes_modality). Scope level determines speaker orientation (scope_implies_orientation), and the non-modal categories that are only diachronic sources of modality lie strictly below those that are only its targets (GramCategory.IsSource, GramCategory.IsTarget, source_below_target), the structural precondition of the hypothesis that semantic change involving grammatical categories climbs from narrower to wider scope.

Implementation notes #

The scope levels follow the combined hierarchy of the book's third chapter, categories on a shared level being unordered. Possession, directionals, and the two kinds of honorification, which the book's table of source and target categories also lists, are not in the scope hierarchy and are left out. The most frequent attested changes of modal meaning are tabulated in Studies/Narrog2010, and the last section checks them against the scale.

TODO #

The book derives a category's role as source or target from its scope level relative to the modal categories. IsSource and IsTarget transcribe the table; deriving them turns on whether the speculative category on the level of volitive mood counts as modality or as mood.

References #

inductive Narrog2012.SpeechActOrientation :

Speech act orientation at the three positions labelled on the vertical axis of the book's semantic map. The book treats the dimension as gradual and open-ended, a property of a use that follows from performativity, and gives most modal categories a broad range of positions.

eventOriented : SpeechActOrientation
The modal judgment concerns conditions on the described event and its participants.
speakerOriented : SpeechActOrientation
The modal judgment is the speaker's own at the time of speech.
speechActOriented : SpeechActOrientation
The use is tied to the speech act itself, including the hearer and the discourse. Clausal mood and illocutionary modification lie here.

Instances For

@[instance_reducible]

instance Narrog2012.instDecidableEqSpeechActOrientation :

DecidableEq SpeechActOrientation

Equations

Narrog2012.instDecidableEqSpeechActOrientation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance Narrog2012.instFintypeSpeechActOrientation :

Fintype SpeechActOrientation

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

@[instance_reducible]

instance Narrog2012.instReprSpeechActOrientation :

Repr SpeechActOrientation

Equations

Narrog2012.instReprSpeechActOrientation = { reprPrec := Narrog2012.instReprSpeechActOrientation.repr }

def Narrog2012.instReprSpeechActOrientation.repr :

SpeechActOrientation → ℕ → Std.Format

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

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@[instance_reducible]

instance Narrog2012.SpeechActOrientation.instLinearOrder :

LinearOrder SpeechActOrientation

The positions are ordered as they are listed, from the event-oriented pole upwards. A change of use from o to o' conforms to the directionality hypothesis when o ≤ o'.

Equations

Narrog2012.SpeechActOrientation.instLinearOrder = LinearOrder.lift' Narrog2012.SpeechActOrientation.ctorIdx Narrog2012.SpeechActOrientation.instLinearOrder._proof_1

@[instance_reducible]

instance Narrog2012.SpeechActOrientation.instBoundedOrder :

BoundedOrder SpeechActOrientation

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theorem Narrog2012.SpeechActOrientation.top_def :

⊤ = speechActOriented

inductive Narrog2012.GramCategory :

Grammatical categories relevant to the verbal clause, drawn from [Nar12] Tables 3.5–3.9 and [Nar09].

The categories are ordered by empirical scope from Japanese data: lower scope (event-oriented) to wider scope (speech-act-oriented). Categories at the same scope level are grouped into a shared scopeLevel.

voice : GramCategory
benefactive : GramCategory
phasalAspect : GramCategory
dynamicModality : GramCategory
perfImperfAspect : GramCategory
deontic1 : GramCategory
evidentiality1 : GramCategory
negation : GramCategory
epistemic1 : GramCategory
evidentiality2 : GramCategory
tense : GramCategory
deontic2 : GramCategory
epistemic2 : GramCategory
evidentiality3 : GramCategory
epistemic3 : GramCategory
volitiveMood : GramCategory
illocutionaryMod : GramCategory

Instances For

@[instance_reducible]

instance Narrog2012.instDecidableEqGramCategory :

DecidableEq GramCategory

Equations

Narrog2012.instDecidableEqGramCategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance Narrog2012.instReprGramCategory :

Repr GramCategory

Equations

Narrog2012.instReprGramCategory = { reprPrec := Narrog2012.instReprGramCategory.repr }

def Narrog2012.instReprGramCategory.repr :

GramCategory → ℕ → Std.Format

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

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def Narrog2012.GramCategory.scopeLevel :

GramCategory → ℕ

Empirical scope level from Japanese data ([Nar09], [Nar12] Tables 3.5–3.7, 3.9). Lower number = narrower scope.

Multiple categories can share a level; the ordering between categories at the same level is not empirically established.

Level assignments follow the groupings established in the text (p. 97): "Evidentiality 3 and Epistemic modality 2... are located on the same level as Tense"; "Epistemic modality 1 and Evidentiality 2... are located at the same level as (Internal) negation." Non-modal anchors (Tense, Negation, Perf/Imperf, Phasal aspect) and the modal categories listed alongside them share the same level.

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@[instance_reducible]

instance Narrog2012.instPreorderGramCategory :

Preorder GramCategory

Categories are compared by scope level, categories on one level lying below each other.

Equations

Narrog2012.instPreorderGramCategory = Preorder.lift Narrog2012.GramCategory.scopeLevel

@[instance_reducible]

instance Narrog2012.instDecidableLEGramCategory :

DecidableLE GramCategory

Equations

Narrog2012.instDecidableLEGramCategory a b = { decide := a.scopeLevel.ble b.scopeLevel, reflects_decide := ⋯ }

@[instance_reducible]

instance Narrog2012.instDecidableLTGramCategory :

DecidableLT GramCategory

Equations

Narrog2012.instDecidableLTGramCategory a b = { decide := a.scopeLevel.succ.ble b.scopeLevel, reflects_decide := ⋯ }

theorem Narrog2012.epistemic_outscopes_deontic :

GramCategory.deontic1 < GramCategory.epistemic1

Epistemic modality outscopes deontic modality.

theorem Narrog2012.dynamic_below_deontic :

GramCategory.dynamicModality < GramCategory.deontic1

Dynamic modality (ability) has narrower scope than deontic.

theorem Narrog2012.mood_outscopes_modality :

GramCategory.epistemic3 ≤ GramCategory.volitiveMood ∧ GramCategory.deontic2 < GramCategory.volitiveMood

Mood outscopes all levels of modality proper.

theorem Narrog2012.im_is_widest (c : GramCategory) :

c ≤ GramCategory.illocutionaryMod

Illocutionary modification is the widest-scope category.

def Narrog2012.GramCategory.toOrientation :

GramCategory → SpeechActOrientation

Map a category to its speaker-orientation level in Narrog's 2D map.

Categories below the aspect boundary are event-oriented; categories at the modal level are speaker-oriented; mood and illocutionary modification are speech act-oriented.

At scope level 2, event-oriented (perfective aspect) and speaker-oriented (deontic 1, evidentiality 1) categories coexist, reflecting Narrog's observation (p. 97, point 4) that volitive modalities rank low due to descriptive use. The mapping is therefore approximate at the event/speaker boundary; see scope_implies_orientation for the precise (strict <) relationship.

Equations

Instances For

theorem Narrog2012.scope_implies_orientation (a b : GramCategory) (h : a < b) :

a.toOrientation ≤ b.toOrientation

Strict scope increase implies non-decreasing orientation.

If category a is strictly narrower in scope than b, then a's orientation is no higher than b's. This is the formal link between Narrog's Hypothesis I (category climbing: narrow → wide scope) and Hypothesis II (event-oriented → speech-act-oriented).

The theorem requires strict < rather than ≤ because at the boundary between event-oriented and speaker-oriented categories (scope level 2), perfective/imperfective aspect (event-oriented) and deontic modality 1 (speaker-oriented) share the same scope level. Narrog (p. 97, point 4) notes this: volitive categories rank low in the scope hierarchy due to their descriptive use, even though their performative use is high.

def Narrog2012.GramCategory.IsSource (c : GramCategory) :

The non-modal categories from which modal markers may derive, in the book's table of potential source and target categories for modality: voice and benefactives, and aspect, tense, and negation, which the table lists as both source and target.

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def Narrog2012.GramCategory.IsTarget (c : GramCategory) :

The non-modal categories into which modal markers may develop: mood and illocutionary modification, and aspect, tense, and negation.

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@[instance_reducible]

instance Narrog2012.GramCategory.instDecidablePredIsSource :

DecidablePred IsSource

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@[instance_reducible]

instance Narrog2012.GramCategory.instDecidablePredIsTarget :

DecidablePred IsTarget

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theorem Narrog2012.source_below_target (c d : GramCategory) (hc : c.IsSource) (hc' : ¬c.IsTarget) (hd : d.IsTarget) (hd' : ¬d.IsSource) :

c < d

Every category that is only a source has strictly narrower scope than every category that is only a target, the structural precondition for category climbing.

theorem Narrog2012.source_is_event_oriented (c : GramCategory) (hc : c.IsSource) (hc' : ¬c.IsTarget) :

c.toOrientation = SpeechActOrientation.eventOriented

The categories that are only sources are event-oriented.

theorem Narrog2012.target_is_speech_act_oriented (c : GramCategory) (hc : c.IsTarget) (hc' : ¬c.IsSource) :

c.toOrientation = SpeechActOrientation.speechActOriented

The categories that are only targets are speech act-oriented.

The changes of [Nar10a] #

def Narrog2012.minOrientation (m : Narrog2010.Meaning) :

SpeechActOrientation

The lowest position a use of a meaning tabulated in [Nar10a] can take: the directive moods lie at the speech act-oriented end, and modality proper and the future reach down to the event-oriented pole.

Equations

Narrog2012.minOrientation m = if m.IsMood then ⊤ else ⊥

Instances For

theorem Narrog2012.le_minOrientation_of_isMood (c : Narrog2010.Change) :

c ∈ Narrog2010.commonChanges → c.target.IsMood → ∀ (o : SpeechActOrientation), o ≤ minOrientation c.target

Every tabulated change into mood conforms to the directionality hypothesis wherever the source use lay.

theorem Narrog2012.not_minOrientation_le {m : Narrog2010.Meaning} (hm : m.IsMood) {o : SpeechActOrientation} (ho : o < ⊤) :

¬minOrientation m ≤ o

A change out of mood would not conform unless its target were again speech act-oriented; none is tabulated (Narrog2010.source_not_isMood).