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 (
Features/Prominence): 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/): 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.
Map a PersonLevel to Just's IndexingPersonLevel. 1st/2nd → SAP, 3rd → third.
Equations
- Aissen2003.personToLevel Features.Prominence.PersonLevel.first = Phenomena.Agreement.DifferentialIndexing.IndexingPersonLevel.sap
- Aissen2003.personToLevel Features.Prominence.PersonLevel.second = Phenomena.Agreement.DifferentialIndexing.IndexingPersonLevel.sap
- Aissen2003.personToLevel Features.Prominence.PersonLevel.third = Phenomena.Agreement.DifferentialIndexing.IndexingPersonLevel.third
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.
Kaqchikel indexes all three argument positions (agent, patient, intranS). This makes it non-differential: no prominence condition gates indexing.
Both A (agent) and P (patient) are indexed in Kaqchikel: agent via Set A on Voice/v, patient via Set B on Infl/T.
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).
Map Kaqchikel argument positions to Just's A/P roles. The absolutive collapse: S patterns with P, A stays distinct; ditransitive R/T default to P (consistent with absolutive grouping).
Equations
- Aissen2003.kaqArgToRole Features.Prominence.ArgumentRole.A = Features.Prominence.ArgumentRole.A
- Aissen2003.kaqArgToRole Features.Prominence.ArgumentRole.S = Features.Prominence.ArgumentRole.P
- Aissen2003.kaqArgToRole Features.Prominence.ArgumentRole.P = Features.Prominence.ArgumentRole.P
- Aissen2003.kaqArgToRole Features.Prominence.ArgumentRole.R = Features.Prominence.ArgumentRole.P
- Aissen2003.kaqArgToRole Features.Prominence.ArgumentRole.T = Features.Prominence.ArgumentRole.P
Instances For
Identity on A and P; the load-bearing structure is the S → P
collapse encoded in kaqArgToRole.
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. The structural correlate is that the [participant]
probe (π⁰) takes priority over the [plural] probe (#⁰) under the
two-probe relativized-probing system @cite{bejar-rezac-2003} —
NOT a salience hierarchy. @cite{preminger-2014} Ch. 7 explicitly
argues against direct salience-scale primitives; the rank
ordering below is a surface effect of probe priority, not a
hierarchy-as-grammatical-primitive. See
Phenomena/Agreement/Studies/Preminger2014.lean for the
anti-hierarchy theorems.
Person dominates for both P and A indexing (derived from fragments).
Two-probe surface ranking @cite{bejar-rezac-2003}: [+participant] cells outrank [+plural,−participant] cells, which outrank 3SG. The typological frequency hierarchy (person > animacy > definiteness) parallels this — person features are both structurally privileged at the probe level and typologically dominant in indexing systems.
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.
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.
Georgian Fragment's P indexing matches the Just survey.
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`.
Hungarian verbs have distinct definite vs indefinite conjugation forms. This IS the morphological reflex of differential P indexing by definiteness.
Hungarian is definiteness-conditioned (derived from the marking predicate), confirming the Fragment's conjugation split.
Hungarian is NOT person-conditioned — all persons can trigger both conjugation types.