Gitksan Modal Inventory

@cite{matthewson-2013} @cite{matthewson-2016} @cite{peterson-2010}

Gitksan (Tsimshianic, ISO 639-3 git) modal system, spoken in northern British Columbia. The system shows two key typological properties:

1. Absolute epistemic/circumstantial split: epistemic modals cannot be used circumstantially and vice versa (@cite{matthewson-2016} Table 18.1).
2. Variable-force epistemic modals: ima('a) and gat are compatible with both necessity and possibility contexts, contrasting only in information source — not in force (@cite{peterson-2010}).
3. Prospective aspect dim: obligatorily marks future temporal orientation for modals; without it, epistemic ima('a) cannot be future-oriented (@cite{matthewson-2016} §18.4.3, examples 60–63).

@cite{matthewson-2013} Figure 1: Gitksan modal system

	Possibility	(Weak) Necessity
Circumstantial
Plain	da'akhlxw	sgi
Deontic	anook(xw)	sgi
Epistemic
Plain	ima('a)	ima('a)
Reportative	gat	gat

The (WEAK) annotation in the column header is load-bearing: Gitksan has no STRONG circumstantial necessity modal — pure-necessity cases like "I have to sneeze" use a plain future, not sgi (@cite{matthewson-2013} ex. 95–98). This asymmetry is the crux of Matthewson's "mixed system" typological claim: strength is encoded in the circumstantial domain, but only weakly.

Modal expressions

def Fragments.Gitksan.Modals.imaa : Semantics.Modality.Typology.ModalExpression

Variable-force plain epistemic modal. @cite{peterson-2010}: analysed as a possibility modal strengthened via ordering source, compatible with both necessity and possibility contexts. @cite{matthewson-2016} §18.3.2: not specialized for a particular force.

Equations

• Fragments.Gitksan.Modals.imaa = { form := "ima('a)", meaning := [Fragments.Gitksan.Modals.pe✝, Fragments.Gitksan.Modals.ne✝] }

def Fragments.Gitksan.Modals.gat : Semantics.Modality.Typology.ModalExpression

Variable-force reportative epistemic modal. Distinguished from ima('a) by information source: gat requires reportative evidence. Under @cite{kratzer-2012}'s reclassification, gat is content-evidential (the speaker can disbelieve the report), while ima('a) is factual-evidential.

Equations

• Fragments.Gitksan.Modals.gat = { form := "gat", meaning := [Fragments.Gitksan.Modals.pe✝, Fragments.Gitksan.Modals.ne✝] }

def Fragments.Gitksan.Modals.daakhlxw : Semantics.Modality.Typology.ModalExpression

General circumstantial possibility: pure circumstantial, ability, bouletic, teleological, and (in competition with anookxw) deontic permission. @cite{matthewson-2013} §4.1, ex. 63–65: da'akhlxw allows bouletic interpretations ('You could eat less cake'), teleological interpretations (subsumed under circumstantial in linglib's flavor inventory), and deontic permission ('My mother told me I could play'). Listed flavors: circumstantial (covering pure circumstantial, ability, teleological), deontic (permission overlap with anookxw), bouletic.

Equations

• Fragments.Gitksan.Modals.daakhlxw = { form := "da'akhlxw", meaning := [Fragments.Gitksan.Modals.pc✝, Fragments.Gitksan.Modals.pd✝, Fragments.Gitksan.Modals.pb✝] }

def Fragments.Gitksan.Modals.anookxw : Semantics.Modality.Typology.ModalExpression

Specialized deontic possibility ('allowed to'). @cite{matthewson-2013} §4.2: anook competes with da'akhlxw in permission contexts but is strictly deontic — infelicitous in pure circumstantial situations (ex. 79).

Equations

• Fragments.Gitksan.Modals.anookxw = { form := "anook(xw)", meaning := [Fragments.Gitksan.Modals.pd✝] }

def Fragments.Gitksan.Modals.sgi : Semantics.Modality.Typology.ModalExpression

Circumstantial weak necessity. @cite{matthewson-2013} §4.3 (and Figure 1: column header is "(WEAK) NECESSITY"): sgi expresses obligation, deontic 'should', and weak circumstantial necessity. The preferred English translation is 'should', a weak necessity modal.

Caveat: Matthewson herself hedges. sgi is INFELICITOUS in some pure strong-necessity contexts (sneeze case, ex. 96–98), but IS felicitous in others (ex. 100, "k'ap sgi dim gwalga daxw-'m" 'We must all die'). The §4.3 conclusion (p. 384) suggests the infelicity may be a modality-TYPE issue (perhaps sgi requires a non-empty priority ordering source) rather than a strict weak-necessity restriction. The Fig. 1 parenthesization of "(WEAK)" reflects this uncertainty.

Equations

• Fragments.Gitksan.Modals.sgi = { form := "sgi", meaning := [Fragments.Gitksan.Modals.wnd✝, Fragments.Gitksan.Modals.wnc✝] }

def Fragments.Gitksan.Modals.allExpressions : List Semantics.Modality.Typology.ModalExpression

Equations

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

Force analysis

The Gitksan epistemic modals are variable-force: they do not lexically specify necessity or possibility, but are compatible with both. The circumstantial modals have fixed force.

def Fragments.Gitksan.Modals.forceAnalysis : Semantics.Modality.Typology.ModalExpression → Core.Modality.ForceAnalysis

Force analysis for each Gitksan modal.

Equations

• Fragments.Gitksan.Modals.forceAnalysis { form := "ima('a)", meaning := meaning } = Core.Modality.ForceAnalysis.variableForce
• Fragments.Gitksan.Modals.forceAnalysis { form := "gat", meaning := meaning } = Core.Modality.ForceAnalysis.variableForce
• Fragments.Gitksan.Modals.forceAnalysis { form := "da'akhlxw", meaning := meaning } = Core.Modality.ForceAnalysis.fixed Core.Modality.ModalForce.possibility
• Fragments.Gitksan.Modals.forceAnalysis { form := "anook(xw)", meaning := meaning } = Core.Modality.ForceAnalysis.fixed Core.Modality.ModalForce.possibility
• Fragments.Gitksan.Modals.forceAnalysis { form := "sgi", meaning := meaning } = Core.Modality.ForceAnalysis.fixed Core.Modality.ModalForce.weakNecessity
• Fragments.Gitksan.Modals.forceAnalysis x✝ = Core.Modality.ForceAnalysis.fixed Core.Modality.ModalForce.possibility

Three-way background classification (@cite{matthewson-2016} Table 18.3)

Gitksan lexicalizes all three background classes:

• factual-circumstantial: da'akhlxw, anookxw, sgi
• factual-evidential: ima('a) (inferential, speaker cannot disbelieve)
• content-evidential: gat (reportative, speaker can disbelieve)

def Fragments.Gitksan.Modals.backgroundClass : Semantics.Modality.Typology.ModalExpression → Core.Modality.BackgroundClass

Equations

• Fragments.Gitksan.Modals.backgroundClass { form := "ima('a)", meaning := meaning } = Core.Modality.BackgroundClass.factualEvidential
• Fragments.Gitksan.Modals.backgroundClass { form := "gat", meaning := meaning } = Core.Modality.BackgroundClass.contentEvidential
• Fragments.Gitksan.Modals.backgroundClass x✝ = Core.Modality.BackgroundClass.factualCircumstantial

Absolute epistemic/circumstantial split

The epistemic and circumstantial domains are strictly separated: epistemic modals cannot be used circumstantially and vice versa. @cite{matthewson-2016} §18.2.3, example 20.

def Fragments.Gitksan.Modals.epistemicModals : List Semantics.Modality.Typology.ModalExpression

Epistemic modals.

Equations

• Fragments.Gitksan.Modals.epistemicModals = [Fragments.Gitksan.Modals.imaa, Fragments.Gitksan.Modals.gat]

def Fragments.Gitksan.Modals.circumstantialModals : List Semantics.Modality.Typology.ModalExpression

Circumstantial modals.

Equations

• Fragments.Gitksan.Modals.circumstantialModals = [Fragments.Gitksan.Modals.daakhlxw, Fragments.Gitksan.Modals.anookxw, Fragments.Gitksan.Modals.sgi]

theorem Fragments.Gitksan.Modals.epistemic_no_circumstantial : (epistemicModals.all fun (e : Semantics.Modality.Typology.ModalExpression) => e.meaning.all fun (ff : Core.Modality.ForceFlavor) => ff.flavor == Core.Modality.ModalFlavor.epistemic) = true

No epistemic modal has a circumstantial reading.

theorem Fragments.Gitksan.Modals.circumstantial_no_epistemic : (circumstantialModals.all fun (e : Semantics.Modality.Typology.ModalExpression) => e.meaning.all fun (ff : Core.Modality.ForceFlavor) => ff.flavor != Core.Modality.ModalFlavor.epistemic) = true

No circumstantial modal has an epistemic reading.

Prospective aspect marker dim

@cite{matthewson-2013} §3–4: prospective aspect marking with dim is required asymmetrically. Circumstantial modals (da'akhlxw, anookxw, sgi) require dim regardless of temporal orientation — past, present, or future, dim must always co-occur (§4.1 ex. 51–58, §4.2 ex. 73–78, §4.3 ex. 82–88). Epistemic modals (imaa, gat) require dim only when the temporal orientation is future (§3.3 ex. 38–42); past and present orientations are felicitous without dim.

The contrast with English is the central typological mirror @cite{matthewson-2013} §3.3 draws: English obligatorily marks past orientation (via have), Gitksan obligatorily marks future orientation (via dim) — but for Gitksan epistemics only. Circumstantials uniformly demand the marker.

def Fragments.Gitksan.Modals.requiresDim (e : Semantics.Modality.Typology.ModalExpression) (orient : Core.Modality.TemporalOrientation) : Bool

Whether prospective dim is required, given a modal expression and the temporal orientation of its prejacent. The asymmetry follows the modal's flavor: circumstantials always require dim; epistemics only require dim when oriented to the future.

Equations

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

Per-modal dim requirements

@cite{matthewson-2013} §3.3 ex. 38–42 (imaa), §3.3 (gat): epistemic modals are felicitous without dim for past/present orientations and require dim for future.

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_imaa_past : requiresDim imaa Core.Modality.TemporalOrientation.past = false

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_imaa_present : requiresDim imaa Core.Modality.TemporalOrientation.present = false

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_imaa_future : requiresDim imaa Core.Modality.TemporalOrientation.future = true

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_gat_past : requiresDim gat Core.Modality.TemporalOrientation.past = false

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_gat_present : requiresDim gat Core.Modality.TemporalOrientation.present = false

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_gat_future : requiresDim gat Core.Modality.TemporalOrientation.future = true

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_daakhlxw (o : Core.Modality.TemporalOrientation) : requiresDim daakhlxw o = true

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_anookxw (o : Core.Modality.TemporalOrientation) : requiresDim anookxw o = true

@[simp]

theorem Fragments.Gitksan.Modals.requiresDim_sgi (o : Core.Modality.TemporalOrientation) : requiresDim sgi o = true

theorem Fragments.Gitksan.Modals.requiresDim_circumstantial : (circumstantialModals.all fun (e : Semantics.Modality.Typology.ModalExpression) => [Core.Modality.TemporalOrientation.past, Core.Modality.TemporalOrientation.present, Core.Modality.TemporalOrientation.future].all fun (o : Core.Modality.TemporalOrientation) => requiresDim e o) = true

Circumstantial modals require dim for any orientation (§4.1 ex. 51–58, §4.2 ex. 73–78, §4.3 ex. 82–88).

theorem Fragments.Gitksan.Modals.epistemics_nonuniform_dim : (epistemicModals.any fun (e : Semantics.Modality.Typology.ModalExpression) => [Core.Modality.TemporalOrientation.past, Core.Modality.TemporalOrientation.present].any fun (o : Core.Modality.TemporalOrientation) => !requiresDim e o) = true

Epistemic modals do not uniformly require dim: at least one epistemic / past-or-present pair is felicitous without it.