Dekier (2021): Morphosyntax of specific and non-specific indefinite markers

This file formalizes Dekier's nanosyntactic analysis of the markers of the non-specific, specific unknown and specific known functions of Haspelmath's map. Across a sample of 45 languages the three markers show the syncretism patterns AAA, ABB, AAB and ABC and never ABA, Table 7, the generalization of Bobaljik, so they spell out a hierarchy of structural containment, (4): the non-specific layer inside the specific unknown one inside the specific known one, the direction fixed by functional complexity, (37). A language's lexicon stores for each marker the largest layer it spells out; the Superset Principle of Starke and Caha, (42), lets an entry spell out any layer it contains and the Elsewhere Principle, (47), picks the smallest match, so the lexicon read off the coverage Haspelmath draws for each paradigm reproduces that coverage by spellout, the absence of ABA is the contiguity of spellout, (48), and a paradigm gap, Table 6, sits above every filled layer, since an entry spelling out a layer spells out every layer below it. An interrogative pronoun can be spelled out as a subset of an indefinite entry, (78) and (79), and suffixes arise by spellout-driven movement where prefixes arise by subderivation, (57).

Implementation notes

Layers are the grades Fin 3 of the containment substrate and entries its context-free span rules, with spellout the exponent of the Superset-and-Elsewhere winner. The paradigms are those of Studies/Haspelmath1997.lean, a series covering a layer when the layer's function lies in the region the book draws for it. A layer's form is the marker of the one series covering its function, none at a gap or where series overlap. The markers are named as the book names them, which departs from the paper's notation in places (-nibud' against -nibud, kaut against kaut-), so the theorems over them compare coverage patterns and the paper's marker tables are rows. The paper's Russian row has the three series that divide the hierarchy and not -libo, which the book draws over the non-specific function beside -nibud'; the book draws -to over that function too, so Russian's coverage has no single non-specific form and its ABC pattern is the work of the Elsewhere Principle (russian_elsewhere). The derivations of prefixes and suffixes in §4.2 are not modelled.

References

• [Dek21]
• [Has97]
• [Bob12]
• [Sta09a]
• [Cah09]

The hierarchy

def Dekier2021.layer : Indefinite.SpecificityFunction ≃ Fin 3

layer sends a specificity function to the layer of the hierarchy (4) its marker spells out, the non-specific function to the lowest and the specific known to the highest.

Equations

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

def Dekier2021.function (g : Fin 3) : Indefinite.HaspelmathFunction

The function of the map each layer spells out.

Equations

• Dekier2021.function g = (Dekier2021.layer.symm g).toFunction

def Dekier2021.formAt (p : List Haspelmath1997.Series) (f : Indefinite.HaspelmathFunction) : Option String

The form of a paradigm at a function is the form of the one series covering it, and none at a gap or where series overlap.

Equations

• Dekier2021.formAt p f = match List.filter (fun (x : Haspelmath1997.Series) => decide (f ∈ x.functions)) p with | [e] => some e.name | x => none

def Dekier2021.pattern (p : List Haspelmath1997.Series) : Morphology.Paradigm 3 (Option String)

A paradigm's forms over the three layers, the triple the syncretism patterns classify.

Equations

• Dekier2021.pattern p g = Dekier2021.formAt p (Dekier2021.function g)

def Dekier2021.layers (e : Haspelmath1997.Series) : Finset (Fin 3)

The layers a series covers.

Equations

• Dekier2021.layers e = {x : Fin 3 | Dekier2021.function x ∈ e.functions}

def Dekier2021.lexicon (p : List Haspelmath1997.Series) : Morphology.Exponence.RuleSet (Morphology.Containment.SupersetRule 3 String)

In the nanosyntactic lexicon of a paradigm each form stores the largest layer it covers, the Superset and Elsewhere Principles deriving the rest of its coverage.

Equations

• Dekier2021.lexicon p = List.filterMap (fun (e : Haspelmath1997.Series) => WithBot.map (fun (x : Fin 3) => { exponent := e.name, spans := x }) (Dekier2021.layers e).max) p

def Dekier2021.russian : List Haspelmath1997.Series

The Russian series of the paper's row are koe-, -to and -nibud'.

Equations

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

Syncretism and its absence

theorem Dekier2021.map_syncretism : Setoid.ker (pattern Haspelmath1997.english) = Setoid.ker Morphology.Paradigm.aaa ∧ Setoid.ker (pattern Haspelmath1997.yakut) = Setoid.ker Morphology.Paradigm.abb ∧ Setoid.ker (pattern Haspelmath1997.latin) = Setoid.ker Morphology.Paradigm.aab

The paradigms' coverage of the map gives the syncretism patterns of Table 1, English AAA, Yakut ABB and Latin AAB.

theorem Dekier2021.russian_elsewhere : pattern russian 0 = none ∧ Morphology.Containment.spellout (lexicon russian) = ![some "-nibud'", some "-to", some "koe-"] ∧ Setoid.ker (Morphology.Containment.spellout (lexicon russian)) = Setoid.ker Morphology.Paradigm.abc

Russian's ABC is the Elsewhere Principle at work, since -to covers the non-specific function beside -nibud', so coverage gives that layer no single form, and the lexicon, storing -to at the specific unknown layer, gives it to the smaller match -nibud'.

theorem Dekier2021.kannada_gap : pattern Haspelmath1997.kannada 2 = none

Kannada's paradigm has a gap at the specific known layer.

theorem Dekier2021.spellout_lexicon (p : List Haspelmath1997.Series) : p ∈ [Haspelmath1997.english, Haspelmath1997.yakut, Haspelmath1997.latin, Haspelmath1997.kannada] → Morphology.Containment.spellout (lexicon p) = pattern p

The lexicon read off each paradigm reproduces its coverage of the three functions by spellout, for English (59), Yakut (67), Latin (70), and Kannada with its gap.

theorem Dekier2021.not_aba {v : Morphology.Exponence.RuleSet (Morphology.Containment.SupersetRule 3 String)} (hv : v.Antihomophonous) (h : Morphology.Containment.spellout v 0 = Morphology.Containment.spellout v 2) : Morphology.Containment.spellout v 0 = Morphology.Containment.spellout v 1

The Elsewhere Principle rules out ABA, (48), since spellout is contiguous, so that a marker spelling out both the non-specific and the specific known layer spells out the specific unknown one.

theorem Dekier2021.ne_none_of_le {v : Morphology.Exponence.RuleSet (Morphology.Containment.SupersetRule 3 String)} {g g' : Fin 3} (h : g ≤ g') (hg' : Morphology.Containment.spellout v g' ≠ none) : Morphology.Containment.spellout v g ≠ none

A paradigm gap sits above every filled layer, §6.3, since an entry spelling out a layer spells out every layer it contains; a lone gap is thus the specific known type and two gaps are the specific types.

theorem Dekier2021.interrogative_subset : Morphology.Containment.spellout [{ exponent := "shénme", spans := 1 }] = ![some "shénme", some "shénme", none, none] ∧ Morphology.Containment.spellout [{ exponent := "wat", spans := 3 }] = fun (x : Fin 4) => some "wat"

With the interrogative pronoun as a layer below the hierarchy, (78) and (79), Mandarin shénme spells out the interrogative and the non-specific layer and Dutch wat all four.

The sample

def Dekier2021.rowPattern (e : Datum) : Morphology.Paradigm 3 (Option String)

A row's markers over the three layers, a gap read as none.

Equations

• Dekier2021.rowPattern e = ![e.feature? "nonSpecific", e.feature? "specificUnknown", e.feature? "specificKnown"]

theorem Dekier2021.rows_contiguous (e : Datum) : e ∈ Examples.all → Morphology.IsContiguous (rowPattern e)

Every paradigm of the sample in Table 7 is contiguous, so none is ABA.

theorem Dekier2021.rows_gap_above (e : Datum) : e ∈ Examples.all → ∀ (g g' : Fin 3), g ≤ g' → rowPattern e g' ≠ none → rowPattern e g ≠ none

Every gap of the sample in Table 6 sits above the filled layers.