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Linglib.Phenomena.Modality.Studies.Narrog2012

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

@cite{narrog-2012}

Study file formalizing the core contributions of @cite{narrog-2012} beyond what is already captured in Semantics.Modality.Narrog (the 2D/3D semantic map) and Diachronic.ModalChange (Bybee et al. data + directionality).

New contributions formalized here #

  1. Category hierarchy (Tables 3.5–3.9): an empirically-derived scope hierarchy from Japanese data, finer-grained than @cite{cinque-1999}'s stipulated universal hierarchy. Categories at the bottom (voice, aspect) are event-oriented; categories at the top (mood, illocutionary modification) are speech-act-oriented.

  2. Source and target categories (Table 3.10): which grammatical categories serve as diachronic sources, targets, or both for modality.

  3. Category-climbing hypothesis (§3.3.1): semantic change involving grammatical categories proceeds from narrow-scope to wide-scope — i.e., from lower to higher in the hierarchy.

  4. Bridge: Narrog → Hacquard (our construction): the event-oriented / speech-act-oriented cut in Narrog's hierarchy aligns with @cite{hacquard-2006}'s AspP boundary. Categories below the boundary lack propositional content; categories above it have content. This unifies the diachronic (Narrog) and synchronic (Hacquard) perspectives. Narrog does not explicitly make this connection; we construct it here.

  5. Subjectification stages for English modals (Table 3.3): Langacker's three stages of modal development, mapped to SpeakerOrientationLevel.

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inductive Phenomena.Modality.Studies.Narrog2012.GramCategory :
Type

Grammatical categories relevant to the verbal clause, drawn from @cite{narrog-2012} Tables 3.5–3.9 and @cite{narrog-2009a}.

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.

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    instance Phenomena.Modality.Studies.Narrog2012.instDecidableEqGramCategory :
    DecidableEq GramCategory
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    def Phenomena.Modality.Studies.Narrog2012.instReprGramCategory.repr :
    GramCategory → ℕ → Std.Format
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      instance Phenomena.Modality.Studies.Narrog2012.instReprGramCategory :
      Repr GramCategory
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      instance Phenomena.Modality.Studies.Narrog2012.instBEqGramCategory :
      BEq GramCategory
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      def Phenomena.Modality.Studies.Narrog2012.instBEqGramCategory.beq :
      GramCategory → GramCategory → Bool
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        def Phenomena.Modality.Studies.Narrog2012.GramCategory.scopeLevel :
        GramCategory → ℕ

        Empirical scope level from Japanese data (@cite{narrog-2009a}, @cite{narrog-2012} 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 Phenomena.Modality.Studies.Narrog2012.instLEGramCategory :
          LE GramCategory
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          instance Phenomena.Modality.Studies.Narrog2012.instLTGramCategory :
          LT GramCategory
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          instance Phenomena.Modality.Studies.Narrog2012.instDecidableLeGramCategory (a b : GramCategory) :
          Decidable (a ≤ b)
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          instance Phenomena.Modality.Studies.Narrog2012.instDecidableLtGramCategory (a b : GramCategory) :
          Decidable (a < b)
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          theorem Phenomena.Modality.Studies.Narrog2012.epistemic_outscopes_deontic :
          GramCategory.deontic1 < GramCategory.epistemic1

          Epistemic modality outscopes deontic modality — the basic observation that all three frameworks (Cinque, Hacquard, Narrog) agree on.

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          theorem Phenomena.Modality.Studies.Narrog2012.dynamic_below_deontic :
          GramCategory.dynamicModality < GramCategory.deontic1

          Dynamic modality (ability) has narrower scope than deontic.

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          theorem Phenomena.Modality.Studies.Narrog2012.mood_outscopes_modality :
          GramCategory.epistemic3 ≤ GramCategory.volitiveMood ∧ GramCategory.deontic2 < GramCategory.volitiveMood

          Mood outscopes all levels of modality proper.

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          theorem Phenomena.Modality.Studies.Narrog2012.im_is_widest (c : GramCategory) :
          c ≤ GramCategory.illocutionaryMod

          Illocutionary modification is the widest-scope category.

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          def Phenomena.Modality.Studies.Narrog2012.GramCategory.toOrientation :
          GramCategory → Semantics.Modality.Narrog.SpeakerOrientationLevel

          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 IM are mood-level.

          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.

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            theorem Phenomena.Modality.Studies.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.

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            inductive Phenomena.Modality.Studies.Narrog2012.ChangeRole :
            Type

            Role of a grammatical category relative to modality in diachronic change.

            Based on @cite{narrog-2012} Table 3.10 (p. 113), which lists non-modal source, target, and bidirectional categories. Table 3.10 also includes categories not in our scope hierarchy: possession and directionals (sources), referent honorification (both), and politeness/addressee honorification (targets). Our changeRole function extends Table 3.10 to the full GramCategory type by classifying modal categories (deontic, epistemic, evidentiality) as .both.

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              instance Phenomena.Modality.Studies.Narrog2012.instDecidableEqChangeRole :
              DecidableEq ChangeRole
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              instance Phenomena.Modality.Studies.Narrog2012.instBEqChangeRole :
              BEq ChangeRole
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              def Phenomena.Modality.Studies.Narrog2012.instBEqChangeRole.beq :
              ChangeRole → ChangeRole → Bool
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                def Phenomena.Modality.Studies.Narrog2012.instReprChangeRole.repr :
                ChangeRole → ℕ → Std.Format
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                  instance Phenomena.Modality.Studies.Narrog2012.instReprChangeRole :
                  Repr ChangeRole
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                  def Phenomena.Modality.Studies.Narrog2012.GramCategory.changeRole :
                  GramCategory → ChangeRole

                  Classification of categories by their diachronic role relative to modality. Extends @cite{narrog-2012} Table 3.10 to cover all GramCategory constructors (see ChangeRole docstring).

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                    theorem Phenomena.Modality.Studies.Narrog2012.source_below_target (c d : GramCategory) (hc : c.changeRole = ChangeRole.source) (hd : d.changeRole = ChangeRole.target) :
                    c < d

                    Every source category has strictly narrower scope than every target category. This is the structural precondition for category-climbing: semantic change from source to target always increases scope.

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                    theorem Phenomena.Modality.Studies.Narrog2012.source_is_event_oriented (c : GramCategory) (h : c.changeRole = ChangeRole.source) :
                    c.toOrientation = Semantics.Modality.Narrog.SpeakerOrientationLevel.eventOriented

                    All source categories are event-oriented; all target categories are at the mood level. The diachronic role aligns with the synchronic orientation: categories that give rise to modality sit at the event level, while categories that modality develops into sit at the speech-act level.

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                    theorem Phenomena.Modality.Studies.Narrog2012.target_is_mood (c : GramCategory) (h : c.changeRole = ChangeRole.target) :
                    c.toOrientation = Semantics.Modality.Narrog.SpeakerOrientationLevel.mood
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                    def Phenomena.Modality.Studies.Narrog2012.GramCategory.toHacquardPosition :
                    GramCategory → Semantics.Modality.EventRelativity.ModalPosition

                    Map Narrog's scope-based orientation to Hacquard's modal position.

                    Event-oriented categories (scope levels 0–2, up to perfective aspect) map to Hacquard's belowAsp; speaker-oriented and mood categories map to aboveAsp. The AspP boundary is the empirical cut-point that both frameworks independently identify.

                    NB: This bridge is our own construction. @cite{narrog-2012} compares his scope hierarchy to @cite{cinque-1999}'s in §3.2 but does not explicitly connect it to @cite{hacquard-2006}'s content licensing. The alignment is natural — both identify a boundary between event-level and propositional-level categories — but the formal mapping is ours.

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                      theorem Phenomena.Modality.Studies.Narrog2012.event_oriented_below_asp :
                      GramCategory.voice.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.belowAsp ∧ GramCategory.dynamicModality.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.belowAsp ∧ GramCategory.perfImperfAspect.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.belowAsp

                      Event-oriented categories map to belowAsp (VP events, no content).

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                      theorem Phenomena.Modality.Studies.Narrog2012.speaker_oriented_above_asp :
                      GramCategory.epistemic1.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.aboveAsp ∧ GramCategory.deontic1.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.aboveAsp ∧ GramCategory.evidentiality2.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.aboveAsp

                      Speaker-oriented categories map to aboveAsp (contentful events).

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                      theorem Phenomena.Modality.Studies.Narrog2012.hacquard_narrog_agree_on_epistemic :
                      GramCategory.epistemic1.toOrientation = Semantics.Modality.Narrog.SpeakerOrientationLevel.speakerOriented ∧ GramCategory.epistemic1.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.aboveAsp ∧ Semantics.Modality.EventRelativity.EventBinder.speechAct.canProjectEpistemic = true ∧ GramCategory.dynamicModality.toOrientation = Semantics.Modality.Narrog.SpeakerOrientationLevel.eventOriented ∧ GramCategory.dynamicModality.toHacquardPosition = Semantics.Modality.EventRelativity.ModalPosition.belowAsp ∧ Semantics.Modality.EventRelativity.EventBinder.vpEvent.canProjectEpistemic = false

                      The Hacquard bridge preserves the epistemic/root prediction: epistemic categories map to aboveAsp (where Hacquard licenses epistemic), and dynamic/ability categories map to belowAsp (where Hacquard blocks epistemic). This is the key unification of the diachronic and synchronic perspectives.

                      The category-climbing hypothesis — that cross-linguistic modal change always proceeds from narrow-scope (event-oriented) to wide-scope (speech-act-oriented) — is proved as Diachronic.ModalChange.directionality over the Bybee et al. (1994) dataset. The source_below_target theorem above establishes the structural precondition for this in our hierarchy: every source category is strictly below every target category.

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                      structure Phenomena.Modality.Studies.Narrog2012.ModalDevelopmentStage :
                      Type

                      A stage in the diachronic development of English modals. @cite{narrog-2012} Table 3.3, following Langacker (1990; 1998; 1999).

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                        instance Phenomena.Modality.Studies.Narrog2012.instReprModalDevelopmentStage :
                        Repr ModalDevelopmentStage
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                        def Phenomena.Modality.Studies.Narrog2012.instReprModalDevelopmentStage.repr :
                        ModalDevelopmentStage → ℕ → Std.Format
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                          def Phenomena.Modality.Studies.Narrog2012.langackerStages :
                          List ModalDevelopmentStage

                          Langacker's stages for English modal verbs (@cite{narrog-2012} Table 3.3).

                          Stage I>II: Physical → social force (main verb → modal verb). Stage I>II: Potency source/target diffuse (main verb → modal verb). Stage II: Maximal diffusion = deontic → epistemic meaning. Stage II,III: Potency → speaker's knowledge (present-oriented epistemic). Stage II>III: Directed potency lost → grounding predications.

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                            theorem Phenomena.Modality.Studies.Narrog2012.langacker_stages_monotone :
                            List.Pairwise (fun (a b : ModalDevelopmentStage) => a.orientation ≤ b.orientation) langackerStages

                            The stages are monotonically non-decreasing in orientation — consistent with Narrog's directionality hypothesis.

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                            theorem Phenomena.Modality.Studies.Narrog2012.three_way_agreement_epistemic_above_root :
                            ComparePosition.CinqueModHead.modEpistemic.isHigh = true ∧ Semantics.Modality.EventRelativity.ModalPosition.aboveAsp.defaultBinder.canProjectEpistemic = true ∧ GramCategory.dynamicModality < GramCategory.epistemic1

                            All three frameworks agree that epistemic is "higher" than root/dynamic, but for different reasons:

                            • @cite{cinque-1999}: stipulated functional heads place epistemic above TP.
                            • @cite{hacquard-2006}: content licensing blocks epistemic below AspP.
                            • @cite{narrog-2012}: empirical scope data from Japanese places epistemic at scope levels 3–5 vs. dynamic at level 1.

                            This theorem states the common prediction, which each framework derives differently.

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                            def Phenomena.Modality.Studies.Narrog2012.orientationOfFlavor :
                            Core.Modality.ModalFlavor → Semantics.Modality.Narrog.SpeakerOrientationLevel

                            Derive a default speaker-orientation from a ModalFlavor.

                            Epistemic modality is speaker-oriented (the speaker assesses likelihood). Deontic modality is speaker-oriented (the speaker imposes norms). Circumstantial modality is event-oriented (describes abilities/facts).

                            This bridges the existing ModalItem.meaning (List ForceFlavor) data that fragment entries already carry to Narrog's orientation axis, without requiring changes to the ModalItem structure.

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                              theorem Phenomena.Modality.Studies.Narrog2012.circumstantial_is_event_oriented :
                              orientationOfFlavor Core.Modality.ModalFlavor.circumstantial = Semantics.Modality.Narrog.SpeakerOrientationLevel.eventOriented

                              Circumstantial-only modals are event-oriented.

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                              theorem Phenomena.Modality.Studies.Narrog2012.epistemic_is_speaker_oriented :
                              orientationOfFlavor Core.Modality.ModalFlavor.epistemic = Semantics.Modality.Narrog.SpeakerOrientationLevel.speakerOriented

                              Epistemic modals are speaker-oriented.

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                              theorem Phenomena.Modality.Studies.Narrog2012.orientationOfFlavor_consistent (f : Core.Modality.ModalFlavor) :
                              ∃ (r : Semantics.Modality.Narrog.NarrogRegion), r.toModalFlavor = some f ∧ r.orientation = orientationOfFlavor f

                              The orientationOfFlavor bridge is consistent with NarrogRegion.toModalFlavor: for each flavor, there exists a Narrog region that maps to that flavor and whose orientation matches what orientationOfFlavor assigns.

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                              theorem Phenomena.Modality.Studies.Narrog2012.toHacquardPosition_factors (c : GramCategory) :
                              c.toHacquardPosition = ComparePosition.narrogOrientationToPosition c.toOrientation

                              toHacquardPosition factors through toOrientation and ComparePosition.narrogOrientationToPosition. This links the category-level bridge (§4) to the orientation-level bridge in ComparePosition.