Béjar & Rezac 2003 — Person Licensing and the Derivation of PCC Effects

[BR03]

[BR03]: the Person Case Constraint ([Bon91]: in combinations of a phonologically weak direct and indirect object, the direct object may not be 1st/2nd person) derives from two ingredients in a [Cho00] probe-goal system:

• Split probes (§3): [π] and [#] are separate probes on a single head F (v⁰ in double-object constructions, T⁰ in dative-nominative ones), probing in that order. The [π]-probe matches the closest goal — every NP bears a person value, the dative's included (their (8): dative π=3 matches) — but the dative is inactive (its Case already valued), so [π] is absorbed without Agree: it "never enters into an Agree relationship with the accusative; remaining unvalued, it gets a default value".
• The PLC (§3): "An interpretable 1st/2nd person feature must be licensed by entering into an Agree relation with a functional category." Datives, PP-embedded themes, and strong pronouns are licensed by their own φ-bearing F (§4: the applicative P, dative marker, or focus F — inherent Case reduces to structural Case from F); a weak 1st/2nd accusative has only the [π]-probe, which the dative absorbs — the PCC.

Through Probe/Basic.lean, the [π]-probe is the off-diagonal licensing shape: visibility is total (pi.vis = ⊤ — closest goal), neediness is bearing [participant] — the same shape as Mam's Voice_TR (visible, halting, non-valuing intervener; Studies/Scott2023.lean) and Zulu's L⁰ (Studies/Halpert2012.lean). [Pre14] Ch. 4's Kichean application moves this very system onto the diagonal by feature-relativizing the probes.

Repairs (§4–6): embed the theme under P (their (3)); or — the French/Spanish dative-nominative repair (their (16)–(17)) — raise the nominative over the dative, whereupon the projection of T introduces a fresh [π]-probe and a second Agree cycle finds the nominative first. Icelandic, where the dative itself satisfies the EPP and stays highest, keeps the PCC in dative-nominative constructions (their (12)). Modeled here as a list of probe cycles, each an ordered goal sequence. The second-cycle mechanism prefigures [BR09]'s cyclic Agree (see CyclicAgree.lean), but the two are formally distinct: 2003 varies the goal order under one probe; 2009 varies the relativization (per-segment) over one order.

structure BejarRezac2003.Argument : Type

A weak (X⁰) nominal in a single Case-licensing domain: its person value, and whether it sits under a φ-bearing functional category F (applicative P, dative marker, focus F). F assigns the nominal's Case — deactivating it for outside Agree — and licenses its [π] itself (§4).

• person : Person
• fLicensed : Bool

def BejarRezac2003.instDecidableEqArgument.decEq (x✝ x✝¹ : Argument) : Decidable (x✝ = x✝¹)

Equations

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

@[implicit_reducible]

instance BejarRezac2003.instDecidableEqArgument : DecidableEq Argument

Equations

• BejarRezac2003.instDecidableEqArgument = BejarRezac2003.instDecidableEqArgument.decEq

def BejarRezac2003.instReprArgument.repr : Argument → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance BejarRezac2003.instReprArgument : Repr Argument

Equations

• BejarRezac2003.instReprArgument = { reprPrec := BejarRezac2003.instReprArgument.repr }

def BejarRezac2003.Argument.IsParticipant (a : Argument) : Prop

Bears an interpretable 1st/2nd person feature (the PLC's domain), via [HR02] decomposition.

Equations

• a.IsParticipant = ((Minimalist.decomposePerson a.person).hasParticipant = true)

@[implicit_reducible]

instance BejarRezac2003.instDecidablePredArgumentIsParticipant : DecidablePred Argument.IsParticipant

Equations

• BejarRezac2003.instDecidablePredArgumentIsParticipant a = BejarRezac2003.instDecidablePredArgumentIsParticipant._aux_1 a

def BejarRezac2003.pi : Minimalist.Probe Argument

One cycle of [π]-Agree over an ordered goal sequence: the probe matches the closest goal (every NP bears [π], per their (8), so visibility is total) and Agrees with it only if it is active — not licensed by its own φ-bearing F. An inactive match absorbs the probe without valuing it (their (9)). (The paper glosses activity as Caselessness but leaves open why same-projection Case valuation does not deactivate the French nominative for the second cycle; ¬F gives the right extension.)

Equations

• BejarRezac2003.pi = { vis := fun (x : BejarRezac2003.Argument) => true, act := fun (a : BejarRezac2003.Argument) => !a.fLicensed }

def BejarRezac2003.piAgree (goals : List Argument) : Option Argument

One cycle of [π]-Agree: pi.agree over the ordered goals.

Equations

• BejarRezac2003.piAgree goals = BejarRezac2003.pi.agree goals

def BejarRezac2003.PLCOk (cycles : List (List Argument)) (args : List Argument) : Prop

The PLC over a derivation's [π]-Agree cycles: every interpretable 1st/2nd person feature enters an Agree relation with a functional category — its own F, or some cycle's [π]-probe. Intended invariant (not enforced): each cycle is a reordering of args (the French repair re-probes the same two arguments in reversed order). Differs from the substrate Minimalist.PLC — Preminger's single-cycle, search-only, probe-relativized rendering — by the paper's F-licensing disjunct and the multiplicity of cycles; the single-cycle case collapses onto the substrate shape (plcOk_singleCycle_iff_allLicensed).

Equations

• BejarRezac2003.PLCOk cycles args = ∀ a ∈ args, a.IsParticipant → a.fLicensed = true ∨ ∃ goals ∈ cycles, BejarRezac2003.piAgree goals = some a

@[implicit_reducible]

instance BejarRezac2003.instDecidablePLCOk (cycles : List (List Argument)) (args : List Argument) : Decidable (PLCOk cycles args)

Equations

• BejarRezac2003.instDecidablePLCOk cycles args = BejarRezac2003.instDecidablePLCOk._aux_1 cycles args

The strong PCC, derived

theorem BejarRezac2003.piAgree_absorbed (dat acc : Argument) (hd : dat.fLicensed = true) : piAgree [dat, acc] = none

A dative absorbs the [π]-probe without valuing it: the closest goal matches but is inactive, so the cycle Agrees with nothing — "remaining unvalued, it gets a default value". The default is not a crash (a Probe.outcome of unvalued, tolerated per [Pre14] Ch. 5); ungrammaticality comes only from the PLC.

theorem BejarRezac2003.plcOk_singleCycle_iff_allLicensed (goals : List Argument) : PLCOk [goals] goals ↔ Minimalist.Probe.indiscriminate.AllLicensed (fun (a : Argument) => decide a.IsParticipant && !a.fLicensed) goals

Single-cycle collapse onto the substrate's (needs, vis) licensing shape: one [π]-cycle over the base order satisfies the PLC iff AllLicensed holds with neediness "participant and not F-licensed" and total visibility. The recoding is lossy by design: it folds the F-licensing route into ¬needy, whereas the paper counts F-licensing as itself an Agree relation; and the multi-cycle repairs ((16)–(17)) escape this signature entirely.

theorem BejarRezac2003.strong_pcc (dat acc : Argument) (hd : dat.fLicensed = true) (ha : acc.fLicensed = false) : PLCOk [[dat, acc]] [dat, acc] ↔ ¬acc.IsParticipant

The PCC (their (1)/(7), generalized): in a double-object configuration — dative over accusative, one [π]-Agree cycle on v⁰ — the PLC holds iff the accusative is 3rd person. Left-to-right is Bonet's strong PCC; right-to-left says 3rd-person accusatives and F-licensed datives of any person are unconstrained.

theorem BejarRezac2003.french_cluster : PLCOk [[{ person := Person.third, fLicensed := true }, { person := Person.third, fLicensed := false }]] [{ person := Person.third, fLicensed := true }, { person := Person.third, fLicensed := false }] ∧ ¬PLCOk [[{ person := Person.third, fLicensed := true }, { person := Person.second, fLicensed := false }]] [{ person := Person.third, fLicensed := true }, { person := Person.second, fLicensed := false }]

The French clitic cluster (their (1)): le lui licit, *te lui a PCC violation.

Repairs

theorem BejarRezac2003.pp_repair : PLCOk [[{ person := Person.second, fLicensed := false }, { person := Person.third, fLicensed := true }]] [{ person := Person.second, fLicensed := false }, { person := Person.third, fLicensed := true }]

Repair by P-embedding (their (3), je te ai présenté à lui): in the prepositional construction the theme is the highest goal and the dative sits in a low PP — the [π]-probe finds the active theme and Agrees, and the PP-internal goal is licensed by P itself.

theorem BejarRezac2003.dnc_split : ¬PLCOk [[{ person := Person.third, fLicensed := true }, { person := Person.second, fLicensed := false }]] [{ person := Person.third, fLicensed := true }, { person := Person.second, fLicensed := false }] ∧ PLCOk [[{ person := Person.third, fLicensed := true }, { person := Person.first, fLicensed := false }], [{ person := Person.first, fLicensed := false }, { person := Person.third, fLicensed := true }]] [{ person := Person.third, fLicensed := true }, { person := Person.first, fLicensed := false }]

The dative-nominative split (their (12) vs. (13)/(16)–(17)): Icelandic datives satisfy the EPP and stay highest, so the [π]-cycle is absorbed and a 1st/2nd nominative violates the PLC (þið, their (12)). (Modeled as a single cycle; per their (25c) Icelandic also projects a second one, but the dative still intervenes — extensionally the same.) In French the nominative raises over the dative and T's projection opens a second [π]-cycle over the reversed order, which finds the now-highest active nominative — PCC obviated (their (13)).