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Linglib.Theories.Syntax.Case.Alignment

Alignment Case-Assignment Functions #

@cite{dixon-1994} @cite{comrie-1989} @cite{marantz-1991}

The SAP-indexed counterpart to Theories/Syntax/Case/Dependent.lean's configural algorithm. Each Alignment.X.assignCase is a function from Features.Prominence.ArgumentRole to Core.Case capturing the canonical case pattern of alignment type X. The configural derivations in Dependent.lean (Marantz/Baker) and the typology classifier in Linglib/Typology/Alignment.lean (WALS-style observation) are checked against the functions here as ground truth.

Coverage #

Alignment.nominativeAccusative.assignCase — accusative alignment (S = A, P distinct). The default for Indo-European, Niger-Congo, much of Eurasia.
Alignment.ergative.assignCase — canonical ergative-absolutive (S = P, A distinct). Found in Mayan perfective, Basque, Inuit, Australian languages.
Alignment.extendedErgative.assignCase — Mayan non-perfective pattern: S/A both bear genitive (Set A), P bears absolutive. Per @cite{coon-2013}
- @cite{imanishi-2020}, this arises when a nominalized clause embeds the external argument so the subject receives genitive from D rather than ergative from v. The "extended ergative" label is from @cite{dixon-1994}.

Ditransitive defaults (R, T) #

ArgumentRole has 5 constructors covering ditransitives. Ditransitive case alignment (indirective vs secundative vs neutral, per @cite{haspelmath-2005}'s typology) is its own dimension orthogonal to monotransitive alignment. The R/T cases below pick conservative defaults intended to support monotransitive reasoning at zero cost; they have no published audit trail and no current consumers in linglib (no call site applies .assignCase .R or .T). Treat them as scaffolding subject to revision when ditransitive consumers arrive:

ergative.{R, T} → ABS: most ergative languages neutralize ditransitive R/T with monotransitive P, but secundative languages (some Bantu) override.
nominativeAccusative.R → DAT: typical for Indo-European and Uralic ditransitive paradigms; English/many Bantu/Tagalog have R → ACC instead ("double-object" / secundative). The DAT default is IE-biased.
nominativeAccusative.T → ACC: standard.
extendedErgative.{R, T} → ABS: UNVERIFIED — Cholan ditransitives in non-perfective aspect aren't well-documented in the published literature; this default may not survive empirical validation. Flagged for future audit when Mateo-Toledo 2008 / Pascual 2007 (Q'anjob'al) or detailed Cholan ditransitive data become available.

def Alignment.ergative.assignCase :

Features.Prominence.ArgumentRole → Core.Case

Ergative-absolutive case assignment. Monotransitive: A → ERG, S | P → ABS. R/T default to ABS.

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def Alignment.nominativeAccusative.assignCase :

Features.Prominence.ArgumentRole → Core.Case

Nominative-accusative case assignment. Monotransitive: S | A → NOM, P → ACC. R defaults to DAT (the recipient case found in Indo-European and Uralic ditransitive paradigms); T to ACC. R → DAT is IE-biased — secundative and double-accusative languages (English, many Bantu, Tagalog) assign R → ACC instead and would override this default.

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def Alignment.extendedErgative.assignCase :

Features.Prominence.ArgumentRole → Core.Case

Cholan/Q'anjob'alan non-perfective: S | A → GEN (from D under nominalization), P → ABS (from Voice). Per @cite{coon-2013}; @cite{imanishi-2020} parameterizes the same surface pattern via inherent vs structural Case. R/T default to ABS.

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def Alignment.tripartite.assignCase :

Features.Prominence.ArgumentRole → Core.Case

Tripartite case assignment: A → ERG, P → ACC, S → ABS — three distinct cases, one per argument. Found in San Juan Atitán Mam (Mayan, K'ichean-Mamean) per @cite{scott-2023} ch. 3, and (per @cite{dixon-1994} §2.1.5) attested in Pitta-Pitta, Wangkumara, and several other Australian languages. Mam lacks independent DP case morphology — the tripartite analysis is recoverable only from agreement patterns (Set A on A, no agreement on P, Set B on S). R/T default to ACC (consistent with P) since Mam ditransitives aren't documented in the analyzed corpus.

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def Alignment.invertedErgative.assignCase :

Features.Prominence.ArgumentRole → Core.Case

Kaqchikel-type non-perfective (specifically PROG sentences with the ajin matrix predicate): S | A → ABS, P → GEN. The OBJECT receives ergative/genitive case rather than the subject — opposite of the canonical extended-ergative pattern.

Per @cite{imanishi-2014} §3.3.1 ("Kaqchikel: ERG=OBJ", p. 122): "Kaqchikel exhibits a cross-linguistically rare alignment pattern in the nominative-accusative system found in the progressives and in the complement position of certain embedding verbs – the object of a transitive verb is aligned with an ergative or genitive agreement morpheme."

Imanishi's mechanism: the Unaccusative Requirement on Nominalization (eq. 90, p. 123) forces nominalized transitive verbs in Kaqchikel to passivize, removing the external argument. The object becomes the only Case-less DP in the nominalized clause and receives ergative Case from D as phase head ("phase head ergative Case", his central thesis). The subject is base-generated in the matrix (Spec-PredP headed by ajin) and gets absolutive from Infl.

Construction-specific: this pattern arises specifically in progressive ajin constructions and certain embedding-verb constructions (e.g., chäp 'begin' in (117), p. 137 — though that construction has a slightly different sub-pattern with all subjects getting ERG too). The chäp variant is not encoded here.

Dialectal variation (per @cite{imanishi-2014} fn. 26, p. 141): "My Kaqchikel consultants do not accept nominalized patterns as in (120). This is presumably because of dialectal differences." Some Kaqchikel varieties may not show the inverted pattern even in PROG sentences; @cite{garcia-matzar-rodriguez-guajan-1997} document broader patterns that Imanishi's consultants don't accept. R/T default to ABS.

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theorem Alignment.ergative_distinguishes_A :

ergative.assignCase Features.Prominence.ArgumentRole.A ≠ ergative.assignCase Features.Prominence.ArgumentRole.S

theorem Alignment.ergative_groups_S_with_P :

ergative.assignCase Features.Prominence.ArgumentRole.S = ergative.assignCase Features.Prominence.ArgumentRole.P

theorem Alignment.accusative_distinguishes_P :

nominativeAccusative.assignCase Features.Prominence.ArgumentRole.P ≠ nominativeAccusative.assignCase Features.Prominence.ArgumentRole.S

theorem Alignment.accusative_groups_S_with_A :

nominativeAccusative.assignCase Features.Prominence.ArgumentRole.S = nominativeAccusative.assignCase Features.Prominence.ArgumentRole.A

theorem Alignment.extendedErgative_groups_S_with_A :

extendedErgative.assignCase Features.Prominence.ArgumentRole.S = extendedErgative.assignCase Features.Prominence.ArgumentRole.A

theorem Alignment.extendedErgative_distinguishes_P :

extendedErgative.assignCase Features.Prominence.ArgumentRole.P ≠ extendedErgative.assignCase Features.Prominence.ArgumentRole.A

theorem Alignment.invertedErgative_groups_S_with_A :

invertedErgative.assignCase Features.Prominence.ArgumentRole.S = invertedErgative.assignCase Features.Prominence.ArgumentRole.A

theorem Alignment.invertedErgative_distinguishes_P :

invertedErgative.assignCase Features.Prominence.ArgumentRole.P ≠ invertedErgative.assignCase Features.Prominence.ArgumentRole.A

theorem Alignment.invertedErgative_swaps_extendedErgative_on_AP :

invertedErgative.assignCase Features.Prominence.ArgumentRole.A = extendedErgative.assignCase Features.Prominence.ArgumentRole.P ∧ invertedErgative.assignCase Features.Prominence.ArgumentRole.P = extendedErgative.assignCase Features.Prominence.ArgumentRole.A

Inverted ergative is the mirror image of extended ergative on the A/P axis: where extended-ergative gives A → GEN and P → ABS, inverted gives A → ABS and P → GEN. The S/A grouping is the same in both.

theorem Alignment.tripartite_distinguishes_all :

tripartite.assignCase Features.Prominence.ArgumentRole.A ≠ tripartite.assignCase Features.Prominence.ArgumentRole.P ∧ tripartite.assignCase Features.Prominence.ArgumentRole.A ≠ tripartite.assignCase Features.Prominence.ArgumentRole.S ∧ tripartite.assignCase Features.Prominence.ArgumentRole.P ≠ tripartite.assignCase Features.Prominence.ArgumentRole.S

Tripartite distinguishes all three SAP arguments — the distinguishing property of tripartite alignment vs the others (which all collapse at least one pair).

theorem Alignment.alignments_distinct_on_A :

ergative.assignCase Features.Prominence.ArgumentRole.A = UD.Case.erg ∧ nominativeAccusative.assignCase Features.Prominence.ArgumentRole.A = UD.Case.nom ∧ extendedErgative.assignCase Features.Prominence.ArgumentRole.A = UD.Case.gen ∧ invertedErgative.assignCase Features.Prominence.ArgumentRole.A = UD.Case.abs ∧ tripartite.assignCase Features.Prominence.ArgumentRole.A = UD.Case.erg

The five alignments are pairwise distinct on the agent: each picks a different case for A (erg, nom, gen, abs, erg). Tripartite shares A → ERG with canonical ergative — they differ on P (acc vs abs).

theorem Alignment.tripartite_differs_from_ergative_on_P :

tripartite.assignCase Features.Prominence.ArgumentRole.P ≠ ergative.assignCase Features.Prominence.ArgumentRole.P

Tripartite is distinguished from canonical ergative by P: tripartite gives P → ACC, canonical gives P → ABS (grouping with S).