Preminger (2014): Agreement and Its Failures

Preminger accounts for φ-agreement in the Kichean Agent-Focus construction (chapters 3 to 5 and 7), whose single agreement slot follows the hierarchy 1st/2nd person > 3rd plural > 3rd singular in subject and object alike (22), (23). Two feature-relativized probes derive the hierarchy, a person probe seeking [participant], merged first, whose goal is clitic-doubled, and a number probe seeking [plural], whose exponent surfaces only when no clitic fills the slot (65), (71), (74). Béjar and Rezac's Person Licensing Condition makes the person restriction, at most one 1st/2nd person core argument, the consequence of a single person probe (75), (76), and under the obligatory-operations model of chapter 5 a probe that finds no goal ends unvalued (112), (113).

Main results

• Preminger2014.afTarget_eq, Preminger2014.afTarget_eq_rank: the slot reflects the participant if there is one, otherwise the plural argument.
• Preminger2014.af_paradigm, Preminger2014.afMarker_comm: the probes deliver the hierarchy's marker, symmetrically in subject and object.
• Preminger2014.personRestriction_iff_plc: the person restriction is the Person Licensing Condition.
• Preminger2014.participant_marker: the clitic carries its goal's whole φ-set (68), (69).
• Preminger2014.afTarget_eq_none_iff, Preminger2014.failed_agree_tolerated: failed Agree converges with the null exponent.
• Preminger2014.plural_marker: an available plural goal must be agreed with (114).
• Preminger2014.relativization_contrast: relativization separates the pattern from the Person Case Constraint (§4.2).
• Preminger2014.hierarchy_silent_on_restriction: a hierarchy cannot state the person restriction (§7.1).

Implementation notes

The probes are the substrate's Probe.Target.participant and .plural, and their competition for the slot (71) is their Probe.cascade; the marker is the fragment's Set B exponent of the cascade's goal. The paradigm (22) enters as the hierarchy (23) read as rank. The morphophonology (§3.4), §4.5–§4.6, and the Zulu and Basque studies of chapter 6 are prose; the Zulu analysis is Studies/Halpert2012.lean.

References

• [Pre14]
• [BR03]
• [HR02]
• [Nev11]
• [Hal12]

The probes and the slot (§4.4)

def Preminger2014.piProbe : Minimalist.Probe Agreement.Bundle

π⁰, the person probe, relativized to [participant].

Equations

• Preminger2014.piProbe = Minimalist.Probe.Target.participant.toProbe

def Preminger2014.numProbe : Minimalist.Probe Agreement.Bundle

#⁰, the number probe, relativized to [plural].

Equations

• Preminger2014.numProbe = Minimalist.Probe.Target.plural.toProbe

def Preminger2014.afTarget (subj obj : Agreement.Bundle) : Option Agreement.Bundle

The Agent-Focus slot reflects the person probe's goal, else the number probe's, else none, the competition for the single slot (71) run as a cascade over the subject's and object's cells.

Equations

• Preminger2014.afTarget subj obj = Minimalist.Probe.cascade [Preminger2014.piProbe, Preminger2014.numProbe] [subj, obj]

def Preminger2014.Plc (subj obj : Agreement.Bundle) : Prop

The Person Licensing Condition holds of the clause's two core arguments when the person probe's search licenses each argument bearing [participant].

Equations

• Preminger2014.Plc subj obj = Preminger2014.piProbe.AllLicensed (fun (x : Agreement.Bundle) => x.visibleTo Minimalist.Probe.Target.participant) [subj, obj]

@[instance_reducible]

instance Preminger2014.instDecidablePlc (subj obj : Agreement.Bundle) : Decidable (Plc subj obj)

Equations

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

def Preminger2014.exponent (c : Agreement.Bundle) : List Morphology.Morph

The absolutive exponent of a cell, empty where the paradigm has none.

Equations

• Preminger2014.exponent c = (Agreement.Paradigm.realize Kaqchikel.setBExponent c).getD []

def Preminger2014.afMarker (subj obj : Agreement.Bundle) : Option (List Morphology.Morph)

The Agent-Focus marker is the exponent of the slot's goal, the empty exponent when both probes fail, and undefined when the Person Licensing Condition fails.

Equations

• Preminger2014.afMarker subj obj = if Preminger2014.Plc subj obj then some ((Option.map Preminger2014.exponent (Preminger2014.afTarget subj obj)).getD []) else none

def Preminger2014.PersonRestriction (subj obj : Agreement.Bundle) : Prop

The person restriction (25) allows at most one core argument to bear [participant].

Equations

• Preminger2014.PersonRestriction subj obj = ¬(subj.IsParticipant ∧ obj.IsParticipant)

@[instance_reducible]

instance Preminger2014.instDecidableRelBundlePersonRestriction : DecidableRel PersonRestriction

Equations

• Preminger2014.instDecidableRelBundlePersonRestriction s o = { decide := !decide (s.IsParticipant ∧ o.IsParticipant), reflects_decide := ⋯ }

Relativized probing (§4.2, §4.4)

theorem Preminger2014.afTarget_eq (s o : Agreement.Bundle) : afTarget s o = if s.IsParticipant then some s else if o.IsParticipant then some o else if s.IsPlural then some s else if o.IsPlural then some o else none

Under skipping the slot reflects a participant if either argument is one, the subject first, otherwise a plural argument, and otherwise nothing (66), (73).

def Preminger2014.rank (c : Agreement.Bundle) : ℕ

The rank of a cell on the hierarchy (23) puts [participant] above [plural] above the rest.

Equations

• Preminger2014.rank c = if c.IsParticipant then 2 else if c.IsPlural then 1 else 0

theorem Preminger2014.afTarget_eq_rank (s o : Agreement.Bundle) : afTarget s o = if rank s = 0 ∧ rank o = 0 then none else if rank o ≤ rank s then some s else some o

The probes derive the hierarchy, since the slot reflects the higher-ranked argument, the subject at a tie, and nothing when both rank lowest.

def Preminger2014.hierarchyMarker (subj obj : Agreement.Bundle) : List Morphology.Morph

The hierarchy (23) as an account is the morphological competition of §3.3.2, in which the slot shows the higher-ranked argument's absolutive marker.

Equations

• Preminger2014.hierarchyMarker subj obj = Preminger2014.exponent (if Preminger2014.rank obj ≤ Preminger2014.rank subj then subj else obj)

theorem Preminger2014.af_paradigm (s : Agreement.Bundle) : s ∈ Agreement.Bundle.personNumberCells → ∀ o ∈ Agreement.Bundle.personNumberCells, PersonRestriction s o → afMarker s o = some (hierarchyMarker s o)

On every licit pair of person–number cells of the paradigm (22), (74), the probes deliver the hierarchy's marker.

theorem Preminger2014.afMarker_comm (s : Agreement.Bundle) : s ∈ Agreement.Bundle.personNumberCells → ∀ o ∈ Agreement.Bundle.personNumberCells, afMarker s o = afMarker o s

The marker is symmetric in subject and object (22, note a), (74), a consequence of skipping, since the probe finds its goal in either position.

Licensing (§4.4.2)

theorem Preminger2014.personRestriction_iff_plc (s o : Agreement.Bundle) : PersonRestriction s o ↔ Plc s o

The person restriction is the Person Licensing Condition on the clause's two core arguments (76), since a single person probe licenses at most one [participant] feature.

theorem Preminger2014.afMarker_eq_none_iff (s o : Agreement.Bundle) : afMarker s o = none ↔ ¬PersonRestriction s o

The marker is undefined exactly when the person restriction is violated; two plural arguments in particular are never excluded (77).

theorem Preminger2014.participant_marker (s o : Agreement.Bundle) (h : ¬(s.IsParticipant ∧ o.IsParticipant)) : (s.IsParticipant → afMarker s o = some (exponent s)) ∧ (o.IsParticipant → afMarker s o = some (exponent o))

The clitic is featurally coarse (68), (69). With one participant argument, the marker is that argument's whole exponent, its number included, whether it is the subject or the object and whatever the other argument's number.

Obligatory operations (chapter 5)

theorem Preminger2014.afTarget_eq_none_iff (s o : Agreement.Bundle) : afTarget s o = none ↔ piProbe.outcome [s, o] = Minimalist.Probe.Outcome.unvalued ∧ numProbe.outcome [s, o] = Minimalist.Probe.Outcome.unvalued

The slot is empty exactly when both probes end unvalued, so failed Agree at the level of outcomes and at the level of the slot are one fact.

theorem Preminger2014.failed_agree_tolerated (s o : Agreement.Bundle) (hs : ¬s.IsParticipant) (ho : ¬o.IsParticipant) (hsp : ¬s.IsPlural) (hop : ¬o.IsPlural) : afTarget s o = none ∧ afMarker s o = some []

Failed Agree is tolerated (112), (113). With no participant and no plural argument, both probes end unvalued, the derivation converges, and the slot carries the null exponent.

theorem Preminger2014.plural_marker (s o : Agreement.Bundle) (hs : ¬s.IsParticipant) (ho : ¬o.IsParticipant) : (s.IsPlural → afMarker s o = some (exponent s)) ∧ (¬s.IsPlural → o.IsPlural → afMarker s o = some (exponent o))

There is no gratuitous nonagreement (114). With no participant argument, a plural argument must be agreed with, and the slot carries its exponent, the subject's first.

Against the alternatives (§4.2, chapter 7)

theorem Preminger2014.relativization_contrast : ¬BejarRezac2003.PLC (BejarRezac2003.v.derive [BejarRezac2003.Nominal.dat (Agreement.Bundle.personNumber Person.third Number.singular), BejarRezac2003.Nominal.caseless (Agreement.Bundle.personNumber Person.first Number.singular)]) ∧ Plc (Agreement.Bundle.personNumber Person.third Number.singular) (Agreement.Bundle.personNumber Person.first Number.singular)

A relativized probe escapes the Person Case Constraint (§4.2). The unrelativized person probe of [BR03] is absorbed by a Case-licensed third-person dative above a participant, the PCC, whereas the Kichean probe, relativized to [participant], skips the third-person argument and licenses the participant below it.

theorem Preminger2014.hierarchy_silent_on_restriction : afMarker (Agreement.Bundle.personNumber Person.first Number.singular) (Agreement.Bundle.personNumber Person.second Number.singular) = none ∧ hierarchyMarker (Agreement.Bundle.personNumber Person.first Number.singular) (Agreement.Bundle.personNumber Person.second Number.singular) = exponent (Agreement.Bundle.personNumber Person.first Number.singular) ∧ afMarker (Agreement.Bundle.personNumber Person.third Number.plural) (Agreement.Bundle.personNumber Person.third Number.plural) = some (exponent (Agreement.Bundle.personNumber Person.third Number.plural))

There is an asymmetry a hierarchy cannot state (§7.1). It assigns a marker to two participant arguments, which the probes exclude, while two plural arguments are admitted by both.