Wang (2023): Honorifics without [HON]

Across Wang's survey the values recruited for honorific pronouns are plural number, third person and indefiniteness, never singular, first or second person, or definites (Table 1, (28)). These are the semantically unmarked values, the ones carrying the weakest presupposition (54)–(56), which the feature bundles order by specification. Recruitment follows from the Taboo of Directness (57), which in respect contexts demands the weakest presupposition, ranked above Heim's Maximize Presupposition! (59), which demands the strongest. Number systems with a dual (80) also need a weak taboo that avoids only the strongest presupposition (82), and the four attested patterns of honorific nonsingulars are the rankings of (83).

Main results

• tod_mp_general: Taboo » MP! selects the least specified cell alone, so no honorific singular, local person or definite arises.
• stod_mp_wtod, wtod_mp_stod, wtod_alone: the rankings of (83) give honorific plural only, dual only, and the non-escalating systems.

Implementation notes

The cells are the number bundles Number.Features, singular, dual and plural being the most, the intermediate and the least specified, the lower sets of the chain minimal < atomic; person and definiteness bundles have the same shape. The constraints count violations by the size of a bundle, the taboo as the size itself and MP! as its shortfall from the full bundle. The ternary tableaux are decided by the kernel. The paper's examples are the rows of Data.Examples.Wang2023.

TODO

• MP! (59) chooses the strongest presupposition compatible with what is assumed, a condition at the context, while mpConstraint counts a bundle's shortfall from the full bundle. On the lower sets of the chain the two agree when every stronger bundle is compatible, the shortfall being the number of strictly stronger competitors; deriving the constraint from Competition.unblocked over Number.dom waits on the dual's minimality domain, which Number.dom does not yet restrict.

References

• [Wan23]
• [Hei91]
• [Har16a]
• [Sau03]

The recruited values are the least specified cells (§4.1)

theorem Wang2023.plural_eq_bot : Number.pluralF = ⊥

The plural is the least specified number cell, the empty bundle (54).

theorem Wang2023.third_eq_bot : Person.third.toFeatures = ⊥

The third person is the least specified person cell, the empty bundle (55).

The Taboo of Directness and Maximize Presupposition! (§4.2)

def Wang2023.todConstraint : OptimalityTheory.Constraint Number.Features

The Taboo of Directness (57) asks in respect contexts for the form with the weakest presupposition; as a constraint it penalizes presuppositional strength.

Equations

• Wang2023.todConstraint = Finset.card

def Wang2023.mpConstraint : OptimalityTheory.Constraint Number.Features

Maximize Presupposition! (59) asks for the form with the strongest presupposition; as a constraint it penalizes the shortfall from the maximal strength.

Equations

• Wang2023.mpConstraint c = Fintype.card Number.Feature - Finset.card c

theorem Wang2023.todConstraint_lt_iff (c₁ c₂ : Number.Features) : todConstraint c₁ < todConstraint c₂ ↔ mpConstraint c₂ < mpConstraint c₁

The two maxims order well-formed cells oppositely.

theorem Wang2023.not_mem_optimal_of_top_pos {C : Type u_1} [DecidableEq C] {candidates : List C} {top : OptimalityTheory.Constraint C} {rest : List (OptimalityTheory.Constraint C)} {h : candidates ≠ []} {c c₀ : C} (hc₀ : c₀ ∈ candidates) (h0 : top c₀ = 0) (hc : 0 < top c) : c ∉ (OptimalityTheory.Tableau.ofRanking candidates (top :: rest) h).optimal

A candidate with violations of the top constraint loses to one without.

theorem Wang2023.tod_mp_only_minimal (candidates : List Number.Features) (hWF : ∀ c ∈ candidates, IsLowerSet ↑c) (hMin : Number.pluralF ∈ candidates) (hNE : candidates ≠ []) (c : Number.Features) : c ∈ (OptimalityTheory.Tableau.ofRanking candidates [todConstraint, mpConstraint] hNE).optimal → c = Number.pluralF

Under Taboo » MP! every optimal candidate is the least specified cell.

theorem Wang2023.tod_mp_minimal_mem_optimal (candidates : List Number.Features) (hMin : Number.pluralF ∈ candidates) (hNE : candidates ≠ []) : Number.pluralF ∈ (OptimalityTheory.Tableau.ofRanking candidates [todConstraint, mpConstraint] hNE).optimal

The least specified cell is optimal under Taboo » MP!, its profile being lexicographically least.

theorem Wang2023.tod_mp_general (candidates : List Number.Features) (hWF : ∀ c ∈ candidates, IsLowerSet ↑c) (hMin : Number.pluralF ∈ candidates) (hNE : candidates ≠ []) : (OptimalityTheory.Tableau.ofRanking candidates [todConstraint, mpConstraint] hNE).optimal = {Number.pluralF}

Taboo » MP! selects the least specified cell alone from any well-formed candidate set that contains it: the emergence of the semantically unmarked.

theorem Wang2023.maximal_not_optimal_of_tod_top (candidates : List Number.Features) (rest : List (OptimalityTheory.Constraint Number.Features)) (hNE : candidates ≠ []) (hMin : Number.pluralF ∈ candidates) : Number.singularF ∉ (OptimalityTheory.Tableau.ofRanking candidates (todConstraint :: rest) hNE).optimal

With the taboo on top, the most specified cell, singular, local person or definite, is never optimal beside a less specified competitor, so these honorifics are unattested (28).

Articulated number systems (§5)

def Wang2023.wtodConstraint : OptimalityTheory.Constraint Number.Features

The weak Taboo of Directness (82b) avoids the form with the strongest presupposition.

Equations

• Wang2023.wtodConstraint c = if Finset.card c = Fintype.card Number.Feature then 1 else 0

def Wang2023.number : List Number.Features

The singular, dual and plural of an articulated number system (80).

Equations

• Wang2023.number = [Number.singularF, Number.dualF, Number.pluralF]

theorem Wang2023.maximal_not_optimal_of_wtod_top (candidates : List Number.Features) (rest : List (OptimalityTheory.Constraint Number.Features)) (hNE : candidates ≠ []) (hMin : Number.pluralF ∈ candidates) : Number.singularF ∉ (OptimalityTheory.Tableau.ofRanking candidates (wtodConstraint :: rest) hNE).optimal

The weak taboo alone also excludes the most specified cell.

theorem Wang2023.stod_mp_wtod : (OptimalityTheory.Tableau.ofRanking number [todConstraint, mpConstraint, wtodConstraint] stod_mp_wtod._proof_1).optimal = {Number.pluralF}

Strong taboo » MP! » weak taboo recruits the plural only, as in Slovenian (83b).

theorem Wang2023.wtod_mp_stod : (OptimalityTheory.Tableau.ofRanking number [wtodConstraint, mpConstraint, todConstraint] stod_mp_wtod._proof_1).optimal = {Number.dualF}

Weak taboo » MP! » strong taboo recruits the dual only, as in Mwotlap and Kharia (83a).

theorem Wang2023.wtod_alone : (OptimalityTheory.Tableau.ofRanking number [wtodConstraint] stod_mp_wtod._proof_1).optimal = {Number.dualF, Number.pluralF}

The weak taboo alone leaves dual and plural, the non-escalating system of Imere (83d).

theorem Wang2023.mp_top : (OptimalityTheory.Tableau.ofRanking number [mpConstraint, todConstraint, wtodConstraint] stod_mp_wtod._proof_1).optimal = {Number.singularF}

Outside respect contexts MP! on top recruits the singular.