Diachronic Modal Change

@cite{narrog-2010} @cite{bybee-perkins-pagliuca-1994}

Cross-linguistic patterns of diachronic change in modal and mood meanings, formalized using Narrog's 2D semantic map (Semantics.Modality.Narrog).

The central claim: modal meanings always shift upward in the semantic map — toward increased speaker-orientation — regardless of volitivity. The well-known deontic → epistemic shift is just one instance of this general pattern.

Main definitions

• ModalChange: an attested cross-linguistic modal meaning change
• commonChanges: the 8 most frequent changes from Bybee et al. (1994)
• directionality: every attested change increases speaker-orientation

Data source

Bybee, Perkins & Pagliuca (1994) The Evolution of Grammar, ch. 6, tabulated in @cite{narrog-2010} Table 2.

structure Diachronic.ModalChange.Change : Type

An attested cross-linguistic modal meaning change. gramCount = number of "grams" (markers) in Bybee et al.'s sample exhibiting this change.

• label : String
• source : Semantics.Modality.Narrog.NarrogRegion
• target : Semantics.Modality.Narrog.NarrogRegion
• gramCount : ℕ

instance Diachronic.ModalChange.instReprChange : Repr Change

Equations

• Diachronic.ModalChange.instReprChange = { reprPrec := Diachronic.ModalChange.instReprChange.repr }

def Diachronic.ModalChange.instReprChange.repr : Change → ℕ → Std.Format

Equations

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

def Diachronic.ModalChange.commonChanges : List Change

The 8 most common cross-linguistic changes in modal meanings. Source: @cite{bybee-perkins-pagliuca-1994} ch. 6, tabulated in @cite{narrog-2010} Table 2.

Equations

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

theorem Diachronic.ModalChange.directionality : (commonChanges.all fun (c : Change) => decide (c.source.orientation ≤ c.target.orientation)) = true

Directionality of change: every attested change increases (or maintains) speaker-orientation. This is Narrog's central diachronic claim.

@cite{narrog-2010} §3.1: "modal meanings always shift in the direction of increased speaker-orientation."

theorem Diachronic.ModalChange.no_decrease : (commonChanges.all fun (c : Change) => !decide (c.target.orientation.toNat < c.source.orientation.toNat)) = true

No attested change decreases speaker-orientation.

theorem Diachronic.ModalChange.volitivity_crossing : (List.filter (fun (c : Change) => c.source.volitivity != c.target.volitivity && c.source.orientation == c.target.orientation) commonChanges).length = 2

Changes #6 and #7 cross the volitivity boundary (volitive → non-volitive) while maintaining speaker-orientation level. This shows volitivity is orthogonal to the directionality of change.

theorem Diachronic.ModalChange.nonvolitive_to_volitive_changes : (List.filter (fun (c : Change) => c.source.volitivity == Semantics.Modality.Narrog.Volitivity.nonVolitive && c.target.volitivity == Semantics.Modality.Narrog.Volitivity.volitive) commonChanges).length = 3

Changes #1, #2, #3 go from non-volitive to volitive: the "unexpected" direction per @cite{narrog-2010} p. 397. These are the three most frequent cross-linguistic changes (13, 9, 5 grams respectively).

theorem Diachronic.ModalChange.directionality_via_subjectivity : (commonChanges.all fun (c : Change) => decide (c.source.orientation.toSubjectivityLevel ≤ c.target.orientation.toSubjectivityLevel)) = true

End-to-end: the speaker-orientation → subjectivity bridge preserves the directionality claim. Every attested change that increases speaker-orientation also increases (or maintains) subjectivity level.