Documentation

Linglib.Phenomena.Agreement.Studies.Aissen2003

Differential Indexing ↔ DOM, PersonGeometry, Kaqchikel @cite{aissen-2003} @cite{just-2024} @cite{preminger-2014}

Connects @cite{just-2024} differential indexing to three existing formalizations:

@cite{aissen-2003} DOM profiles (Phenomena/Case/Typology): DOM is the P-flagging specialization of the general differential marking framework. This bridge proves that DOM profiles and P-indexing profiles share the same monotonicity constraint over the same scales.
@cite{preminger-2014} PersonGeometry (Theories/Syntax/Minimalism/Core/): Just's binary person split (SAP vs 3rd) is precisely Preminger's [±participant] feature. This bridge makes the connection explicit.
Kaqchikel Agreement (Fragments/Kaqchikel/): Kaqchikel indexes both A and P arguments (Set A for agent, Set B for patient). This is a non-differential system — all person-number combinations are indexed — which serves as the baseline against which differential systems are defined.

DOMProfile is an abbreviation for DifferentialMarkingProfile (specialized to role P + channel flagging), and IndexingFragment extends DifferentialMarkingProfile (with channel = .indexing). Both DOM profiles and indexing fragments inherit all DMP infrastructure (monotonicity, dimensionality, cutoff constructors, mirror image) directly — no conversion or bridge theorems needed.

Just's binary person split (SAP vs 3rd) is exactly Preminger's [±participant] feature decomposition.

def Phenomena.Agreement.Studies.Aissen2003.personToLevel :

Core.Prominence.PersonLevel → DifferentialIndexing.IndexingPersonLevel

Map a PersonLevel to Just's IndexingPersonLevel. 1st/2nd → SAP, 3rd → third.

Equations

Instances For

personToLevel agrees with decomposePerson on the participant split: SAP ↔ [+participant], third ↔ [−participant].

SAP has higher prominence rank than 3rd, just as [+participant] gives higher probe resolution rank.

Kaqchikel indexes both A and P arguments uniformly across all person-number combinations. This is a NON-differential system: there is no prominence-based asymmetry in which arguments get indexed.

@cite{just-2024} defines differential indexing against this kind of
baseline: a differential system is one where indexing depends on
prominence properties.

theorem Phenomena.Agreement.Studies.Aissen2003.kaqchikel_indexes_all :

(Fragments.Mayan.Kaqchikel.kaqArgPositions.all fun (p : Fragments.Mayan.Kaqchikel.KaqArgPosition) => p.isPhiAgreed) = true

Kaqchikel indexes all three argument positions (agent, patient, intranS). This makes it non-differential: no prominence condition gates indexing.

theorem Phenomena.Agreement.Studies.Aissen2003.kaqchikel_A_and_P_indexed :

Fragments.Mayan.Kaqchikel.KaqArgPosition.agent.isPhiAgreed = true ∧ Fragments.Mayan.Kaqchikel.KaqArgPosition.patient.isPhiAgreed = true

Both A (agent) and P (patient) are indexed in Kaqchikel: agent via Set A on Voice/v, patient via Set B on Infl/T.

theorem Phenomena.Agreement.Studies.Aissen2003.kaqchikel_dual_paradigms :

Fragments.Mayan.Kaqchikel.setAExponent Fragments.Mayan.Kaqchikel.PersonNumber.p1sg ≠ Fragments.Mayan.Kaqchikel.setBExponent Fragments.Mayan.Kaqchikel.PersonNumber.p1sg ∧ Fragments.Mayan.Kaqchikel.setAExponent Fragments.Mayan.Kaqchikel.PersonNumber.p2sg ≠ Fragments.Mayan.Kaqchikel.setBExponent Fragments.Mayan.Kaqchikel.PersonNumber.p2sg

The A marker paradigm (Set A) and P marker paradigm (Set B) are distinct: every person-number combination gets a unique marker in each set (except 3SG which is ∅ in Set B).

def Phenomena.Agreement.Studies.Aissen2003.kaqArgToRole :

Fragments.Mayan.Kaqchikel.KaqArgPosition → Core.Prominence.ArgumentRole

Map Kaqchikel argument positions to Just's A/P roles.

Equations

Instances For

theorem Phenomena.Agreement.Studies.Aissen2003.kaqArg_role_mapping :

kaqArgToRole Fragments.Mayan.Kaqchikel.KaqArgPosition.agent = Core.Prominence.ArgumentRole.A ∧ kaqArgToRole Fragments.Mayan.Kaqchikel.KaqArgPosition.patient = Core.Prominence.ArgumentRole.P

Agent maps to A, patient maps to P.

theorem Phenomena.Agreement.Studies.Aissen2003.erg_abs_matches_AP :

Fragments.Mayan.Kaqchikel.KaqArgPosition.agent.case ≠ Fragments.Mayan.Kaqchikel.KaqArgPosition.patient.case ∧ Fragments.Mayan.Kaqchikel.KaqArgPosition.patient.case = Fragments.Mayan.Kaqchikel.KaqArgPosition.intranS.case

Ergative-absolutive alignment: A is distinguished (ERG) while P and S pattern together (ABS). This parallels Just's A/P split.

Person is the dominant conditioning factor for both P indexing and A indexing. This connects to @cite{preminger-2014}'s observation that person features are structurally more prominent in the φ-geometry ([participant] outranks [plural]).

Person dominates for both P and A indexing (derived from fragments).

theorem Phenomena.Agreement.Studies.Aissen2003.preminger_participant_outranks :

Minimalism.probeResolutionRank Core.Prominence.PersonLevel.first false > Minimalism.probeResolutionRank Core.Prominence.PersonLevel.third true ∧ Minimalism.probeResolutionRank Core.Prominence.PersonLevel.third true > Minimalism.probeResolutionRank Core.Prominence.PersonLevel.third false

Preminger's participant > plural hierarchy mirrors the person > animacy > definiteness frequency hierarchy: person features are both structurally and typologically dominant.

The Basque agreement fragment (Fragments.Basque.Agreement) encodes the same person-conditioned P indexing that @cite{just-2024} reports. We prove that the Fragment's pIsIndexed matches the survey data.

Basque Fragment's P indexing matches the Just survey: SAP → indexed, 3rd → not indexed, exactly as basque.personIndexed.

theorem Phenomena.Agreement.Studies.Aissen2003.basque_fragment_is_differential :

Fragments.Basque.Agreement.allPersonNumbers.any Fragments.Basque.Agreement.pIsIndexed = true ∧ (!decide (Fragments.Basque.Agreement.allPersonNumbers.all Fragments.Basque.Agreement.pIsIndexed = true)) = true

Basque Fragment confirms differential P indexing: some indexed, some not.

The Georgian agreement fragment (Fragments.Georgian.Agreement) derives P indexing from the presence of object agreement prefixes (m-, g-, gv-). The indexed/not-indexed split aligns with SAP vs 3rd — same as the Just survey data.

theorem Phenomena.Agreement.Studies.Aissen2003.georgian_indexing_grounded :

(Fragments.Georgian.Agreement.allPersonNumbers.all fun (pn : Fragments.Georgian.Agreement.PersonNumber) => Fragments.Georgian.Agreement.pIsIndexed pn == (Fragments.Georgian.Agreement.objectPrefix pn).isSome) = true

Georgian Fragment's P indexing is grounded in object prefix morphology: indexed iff has overt prefix. Not stipulated — follows from the data.

The Hungarian predicate fragment (Fragments.Hungarian.Predicates) models the definite/indefinite conjugation split. This IS Just's differential P indexing by definiteness: the verb's agreement paradigm changes depending on whether the object is definite.

The fragment's `formPastDef ≠ formPastIndef` encodes the same claim
as the Just survey entry `hungarian.definitenessConditioned`.

theorem Phenomena.Agreement.Studies.Aissen2003.hungarian_conjugation_split :

Fragments.Hungarian.Predicates.tud.formPastDef ≠ Fragments.Hungarian.Predicates.tud.formPastIndef ∧ Fragments.Hungarian.Predicates.mond.formPastDef ≠ Fragments.Hungarian.Predicates.mond.formPastIndef ∧ Fragments.Hungarian.Predicates.hisz.formPastDef ≠ Fragments.Hungarian.Predicates.hisz.formPastIndef

Hungarian verbs have distinct definite vs indefinite conjugation forms. This IS the morphological reflex of differential P indexing by definiteness.

theorem Phenomena.Agreement.Studies.Aissen2003.hungarian_definiteness_conditioned :

DifferentialIndexing.hungarian.definitenessConditioned = true

Hungarian is definiteness-conditioned (derived from the marking predicate), confirming the Fragment's conjugation split.

theorem Phenomena.Agreement.Studies.Aissen2003.hungarian_not_person_conditioned :

DifferentialIndexing.hungarian.personConditioned = false

Hungarian is NOT person-conditioned — all persons can trigger both conjugation types.