Qin (2025): Canonical and Non-Canonical Roots: The Diversity of Roots in Mandarin Chinese

This file formalizes [qin-2025]'s canonical typology of roots. The base definition, a morphologically unanalyzable form that serves as a morphological core of word formation, is the substrate's Morphology.Morph.IsCoreIn, and the paper's -fer shows that the judgment is formal rather than semantic: -fer is a core of the primary word refer though it has no meaning of its own (fer_core). Four criteria (Table 1), boundness, positional flexibility, phonological richness, and meaning lexicality, span a space of sixteen cells anchored by the canonical root that meets all four, and Fig. 1's one way of being canonical against fifteen of being non-canonical is the binomial count of the tiers (tier_card). The case study classifies 122 Mandarin morphemes (Appendix A): the forms carry the appendix's codes on the four criteria, its five groups are the number of criteria a form fails (forms_group), and the property of the distribution the paper singles out holds of every form, that a phonologically deficient morpheme, toneless in a tone language, is maximally non-canonical (deficient_maximal). The tiers run from the canonical 厂 chǎng of Table 3 through 不 bù, 霸 bà, and 性 xìng to the toneless 边 -bian and 个 -ge (mandarin_tiers).

Implementation notes

The appendix is a CLDF FormTable whose custom columns are the paper's codes: F or B for boundness, FLEX, SL, or SR for position, 1 or TL for phonology, and L or NL for meaning. A row reads the codes as a Boolean judgment on each criterion, the canonical value being true; the two fixed positions SL and SR both count as fixed. The counts of Tables 2 and 4 are the distribution of the forms and are not restated.

TODO

The paper says that six of the unattested cells of the space require phonological deficiency; the appendix leaves seven such cells unattested, since only the maximally non-canonical cell contains a toneless morpheme, and the cell of free, fixed, toned, lexical morphemes is unattested as well.

References

• [qin-2025]
• [Blo33]

The base definition and -fer (§3.1)

def Qin2025.re : Morphology.Morph

The bound prefix of refer.

Equations

• Qin2025.re = Morphology.Morph.pref "re"

def Qin2025.fer : Morphology.Morph

-fer, a bound root with no identifiable meaning.

Equations

• Qin2025.fer = Morphology.Morph.root "fer"

def Qin2025.con : Morphology.Morph

The bound prefix of confer.

Equations

• Qin2025.con = Morphology.Morph.pref "con"

def Qin2025.ferWords : List (List Morphology.Morph)

The mini-fragment refer and confer, both free forms and both primary, since neither re-, con-, nor -fer is free.

Equations

• Qin2025.ferWords = [[Qin2025.re, Qin2025.fer], [Qin2025.con, Qin2025.fer]]

theorem Qin2025.fer_core : fer.IsCoreIn ferWords ferWords

-fer is a morphological core: it occurs in the primary word refer.

The four criteria and the theoretical space (§3.2, §3.3)

structure Qin2025.Row : Type

A morpheme's judgment on the four criteria of Table 1: free, positionally flexible, phonologically rich, and lexical in meaning.

• c1 : Bool

  C1: free rather than bound.

• c2 : Bool

  C2: positionally flexible rather than fixed.

• c3 : Bool

  C3: phonologically rich rather than deficient.

• c4 : Bool

  C4: lexical rather than less lexical in meaning.

def Qin2025.instDecidableEqRow.decEq (x✝ x✝¹ : Row) : Decidable (x✝ = x✝¹)

Equations

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

@[instance_reducible]

instance Qin2025.instDecidableEqRow : DecidableEq Row

Equations

• Qin2025.instDecidableEqRow = Qin2025.instDecidableEqRow.decEq

def Qin2025.instReprRow.repr : Row → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance Qin2025.instReprRow : Repr Row

Equations

• Qin2025.instReprRow = { reprPrec := Qin2025.instReprRow.repr }

@[instance_reducible]

instance Qin2025.instFintypeRow : Fintype Row

Equations

• Qin2025.instFintypeRow = Fintype.ofEquiv ((_ : Bool) × (_ : Bool) × (_ : Bool) × Bool) Qin2025.Row.proxyTypeEquiv

def Qin2025.Row.violations (r : Row) : ℕ

The number of criteria a row fails, its distance from the canonical root.

Equations

• r.violations = (((if r.c1 = true then 0 else 1) + if r.c2 = true then 0 else 1) + if r.c3 = true then 0 else 1) + if r.c4 = true then 0 else 1

def Qin2025.Row.IsCanonical (r : Row) : Prop

A canonical root satisfies all four criteria.

Equations

• r.IsCanonical = (r.violations = 0)

@[instance_reducible]

instance Qin2025.instDecidableIsCanonical (r : Row) : Decidable r.IsCanonical

Equations

• Qin2025.instDecidableIsCanonical r = Qin2025.instDecidableIsCanonical._aux_1 r

theorem Qin2025.space_card : Fintype.card Row = 16

The theoretical space of roots has sixteen cells (Fig. 1).

theorem Qin2025.tier_card (k : Fin 5) : {r : Row | r.violations = ↑k}.card = Nat.choose 4 ↑k

Fig. 1's tiers: 4.choose k ways to fail exactly k criteria, so fifteen ways of being non-canonical against one of being canonical.

The Mandarin case study (§4, Appendix A)

def Qin2025.interpret (f : Data.Forms.Form) : Option Row

A form's judgments, read from the appendix's codes.

Equations

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

def Qin2025.violations? (f : Data.Forms.Form) : Option ℕ

The number of criteria a form fails.

Equations

• Qin2025.violations? f = Option.map Qin2025.Row.violations (Qin2025.interpret f)

def Qin2025.group? : String → Option ℕ

The appendix's group of a form: canonical roots, then non-canonical roots by the number of criteria violated.

Equations

• Qin2025.group? "1" = some 0
• Qin2025.group? "2" = some 1
• Qin2025.group? "3" = some 2
• Qin2025.group? "4" = some 3
• Qin2025.group? "5" = some 4
• Qin2025.group? x✝ = none

theorem Qin2025.forms_group (f : Data.Forms.Form) : f ∈ Forms.all → (f.column? "Group").bind group? = violations? f ∧ (violations? f).isSome = true

Every form is classified on all four criteria, and its group is the number it fails.

theorem Qin2025.deficient_maximal (f : Data.Forms.Form) : f ∈ Forms.all → ∀ row ∈ interpret f, row.c3 = false → row.violations = 4

A phonologically deficient morpheme is maximally non-canonical: only the bottom cell of the space holds a toneless morpheme.

theorem Qin2025.mandarin_tiers : violations? Forms.chang = some 0 ∧ violations? Forms.bu_2 = some 1 ∧ violations? Forms.ba_2 = some 2 ∧ violations? Forms.xing_4 = some 3 ∧ violations? Forms.bian = some 4 ∧ violations? Forms.ge_2 = some 4

The five tiers: canonical 厂 chǎng (Table 3), 不 bù deviating on meaning alone, bound and fixed 霸 bà, schematic 性 xìng, and the toneless 边 -bian and 个 -ge meeting no criterion.