Person Feature Geometry @cite{harley-ritter-2002} @cite{bejar-rezac-2003}

@cite{bejar-rezac-2009} @cite{preminger-2014} @cite{pancheva-zubizarreta-2018}

The privative-feature geometry @cite{harley-ritter-2002} decomposes person into a containment hierarchy where each sub-feature implies the next:

[φ] → [PERSON] → [participant] → [author]
[φ] → [NUMBER] → [plural]

This decomposition drives relativized probing (@cite{bejar-rezac-2003}): a probe seeking [participant] skips DPs that lack it (3rd person), targeting only 1st/2nd person DPs. A separate probe seeking [plural] skips DPs that lack it (singulars), targeting only plurals.

@cite{bejar-rezac-2003} apply this two-probe mechanism to derive the Person Case Constraint; @cite{bejar-rezac-2009} formalize it as Cyclic Agree. @cite{preminger-2014} §4.4 applies the same B&R 2003 mechanism to Kichean Agent Focus — explicitly reframing earlier "omnivorous hierarchy" accounts in terms of two independently relativized probes π⁰ ([participant]) and #⁰ ([plural]). @cite{preminger-2014} Ch. 7 then argues against direct hierarchy/scale primitives like [+participant] > [+plural] > default, on four grounds: restrictedness of "salience" effects to AF, K'ichee' formal addressee la (a 2nd-person form patterning as 3rd-person under AF), the AF person restriction (1+2 blocked but 3pl+3pl licit), and the morphophonological 1st/2nd vs 3rd asymmetry (clitic doubling vs direct exponence, @cite{preminger-2014} §3.4 and §4.4). The relativized-probing mechanism derives the same surface patterns without committing to a salience scale.

Extended Geometry: [±proximate]

@cite{pancheva-zubizarreta-2018} extend the hierarchy with a [±proximate] feature for the Person Case Constraint:

[+author] ⊂ [+participant] ⊂ [+proximate]

1P and 2P are inherently [+proximate]. 3P arguments are [-proximate] by default but can be contextually marked [+proximate] (when co-occurring with another 3P). The [±proximate] distinction also captures the 3P proximate/obviative split in direct/inverse alignment systems (@cite{pancheva-zubizarreta-2018} §2.1 (11)).

Relationship to Core PersonFeatures

DecomposedPerson extends Features.Person.Features (the framework-neutral [±participant, ±author] decomposition) with the Minimalism-specific [±proximate] feature. The two-feature core is shared across all theoretical frameworks; [±proximate] is specific to @cite{pancheva-zubizarreta-2018}'s P-Constraint.

Person Type

decomposePerson takes Features.Prominence.PersonLevel (.first | .second |.third) — the canonical person type shared across the library — rather than a raw Nat. This eliminates meaningless person values and grounds the decomposition in the same type used by DifferentialIndexing, Prominence.PersonLevel.isSAP, etc.

Note on probeResolutionRank

The probeResolutionRank function below assigns rank 2 to [+participant] DPs, rank 1 to [+plural, −participant] DPs, and rank 0 elsewhere. This is a CONVENIENCE encoding of the surface effect of the two-probe (π⁰ ≫ #⁰) system on a single DP — useful for downstream computations that need a totally ordered target — but it should not be read as endorsing the salience-scale analysis @cite{preminger-2014} Ch. 7 argues against. The actual derivation goes via two independently relativized probes; the rank is a derived quantity, not a primitive.

structure Minimalist.DecomposedPersonextends Features.Person.Features : Type

Person features decomposed according to @cite{preminger-2014}'s geometry, extended with [±proximate] from @cite{pancheva-zubizarreta-2018}.

Extends Features.Person.Features (the framework-neutral [±participant, ±author] core) with the Minimalism-specific [±proximate] feature:

• [proximate] marks potential point-of-view centers. 1P/2P are inherently [+proximate]; 3P can be contextually [+proximate].
• [participant] distinguishes 1st/2nd from 3rd person.
• [author] distinguishes 1st from 2nd person.

The geometry imposes a containment hierarchy: [+author] → [+participant] → [+proximate]

Note: The paper treats these as privative features: 3rd person simply LACKS [participant], rather than bearing [−participant]. We encode this as Bool for computational convenience; the well-formedness constraint wellFormed ensures the privative entailments are maintained.

• hasParticipant : Bool
• hasAuthor : Bool
• hasProximate : Bool

  Bears [proximate]? SAPs inherently; 3P contextually.

def Minimalist.instDecidableEqDecomposedPerson.decEq (x✝ x✝¹ : DecomposedPerson) : Decidable (x✝ = x✝¹)

Equations

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

@[implicit_reducible]

instance Minimalist.instDecidableEqDecomposedPerson : DecidableEq DecomposedPerson

Equations

• Minimalist.instDecidableEqDecomposedPerson = Minimalist.instDecidableEqDecomposedPerson.decEq

def Minimalist.instReprDecomposedPerson.repr : DecomposedPerson → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Minimalist.instReprDecomposedPerson : Repr DecomposedPerson

Equations

• Minimalist.instReprDecomposedPerson = { reprPrec := Minimalist.instReprDecomposedPerson.repr }

def Minimalist.DecomposedPerson.wellFormed (dp : DecomposedPerson) : Bool

Geometry well-formedness: [author] → [participant] → [proximate]. Each feature entails the next in the containment hierarchy.

Equations

• dp.wellFormed = ((!dp.hasAuthor || dp.hasParticipant) && (!dp.hasParticipant || dp.hasProximate))

def Minimalist.decomposePerson : Features.Prominence.PersonLevel → DecomposedPerson

Decompose a person value into sub-features.

• 1st person: [+proximate, +participant, +author]
• 2nd person: [+proximate, +participant, −author]
• 3rd person: [−proximate, −participant, −author]

3rd person is [-proximate] by default; contextual [+proximate] marking is handled by the P-Constraint evaluation.

Equations

• Minimalist.decomposePerson Features.Prominence.PersonLevel.first = { hasParticipant := true, hasAuthor := true, hasProximate := true }
• Minimalist.decomposePerson Features.Prominence.PersonLevel.second = { hasParticipant := true, hasAuthor := false, hasProximate := true }
• Minimalist.decomposePerson Features.Prominence.PersonLevel.third = { hasParticipant := false, hasAuthor := false, hasProximate := false }

inductive Minimalist.ProbeTarget : Type

What a phi-probe seeks.

In the AF construction, two probes operate:

• π⁰ seeks [participant]: targets 1st/2nd person DPs
• #⁰ seeks [plural]: targets plural DPs

π⁰ structurally outranks #⁰ (person probing > number probing).

• participant : ProbeTarget

  π⁰: person probe, seeks [participant].

• plural : ProbeTarget

  #⁰: number probe, seeks [plural].

@[implicit_reducible]

instance Minimalist.instDecidableEqProbeTarget : DecidableEq ProbeTarget

Equations

• Minimalist.instDecidableEqProbeTarget x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Minimalist.instReprProbeTarget : Repr ProbeTarget

Equations

• Minimalist.instReprProbeTarget = { reprPrec := Minimalist.instReprProbeTarget.repr }

def Minimalist.instReprProbeTarget.repr : ProbeTarget → ℕ → Std.Format

Equations

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

def Minimalist.probeVisible (target : ProbeTarget) (person : Features.Prominence.PersonLevel) (isPlural : Bool) : Bool

Is a DP visible to this probe? Relativized probing: probes skip DPs that lack the feature they seek.

A DP with person value person and number isPlural is visible to the probe iff it bears the probe's target feature.

Equations

• Minimalist.probeVisible Minimalist.ProbeTarget.participant person isPlural = (Minimalist.decomposePerson person).hasParticipant
• Minimalist.probeVisible Minimalist.ProbeTarget.plural person isPlural = isPlural

def Minimalist.probeResolutionRank (person : Features.Prominence.PersonLevel) (isPlural : Bool) : ℕ

Probe resolution rank for a DP under the two-probe (π⁰ ≫ #⁰) system.

A surface-effect summary of which probe targets a given DP:

• Rank 2: visible to π⁰ ([+participant])
• Rank 1: visible to #⁰ but not π⁰ ([+plural, −participant])
• Rank 0: invisible to both probes (3SG default)

Derived from the probing mechanism (@cite{bejar-rezac-2003}), not stipulated as a salience scale: π⁰ takes priority over #⁰ by virtue of being structurally higher and earlier in the derivation, and each probe targets any DP bearing the sought feature. The rank captures the combined effect on a single DP. See module docstring for why this is a convenience encoding, not an endorsement of the salience-scale analyses @cite{preminger-2014} Ch. 7 argues against.

Equations

• Minimalist.probeResolutionRank person isPlural = if (Minimalist.decomposePerson person).hasParticipant = true then 2 else if isPlural = true then 1 else 0

theorem Minimalist.all_decompositions_wellFormed (p : Features.Prominence.PersonLevel) : (decomposePerson p).wellFormed = true

All person values yield well-formed decompositions.

theorem Minimalist.decomposePerson_toFeatures_eq (p : Features.Prominence.PersonLevel) : (decomposePerson p).toFeatures = p.toFeatures

decomposePerson is consistent with the framework-neutral PersonLevel.toFeatures: the [±participant, ±author] core of the Minimalist decomposition agrees with Core Person.Features.

theorem Minimalist.rank_hierarchy : probeResolutionRank Features.Prominence.PersonLevel.first false > probeResolutionRank Features.Prominence.PersonLevel.third true ∧ probeResolutionRank Features.Prominence.PersonLevel.third true > probeResolutionRank Features.Prominence.PersonLevel.third false

Rank is monotone in the probe hierarchy: any DP visible to π⁰ (rank 2) outranks any DP visible only to #⁰ (rank 1), which outranks any DP invisible to both (rank 0).