Coon & Keine 2021 — Feature Gluttony [CK21] #

[CK21] (LI 52(4)): hierarchy effects — PCC, dative-nominative restrictions, copula effects — do not come from failed Agree or failed nominal licensing, but from feature gluttony: a single probe entering more than one Agree dependency. Agree (their (14)) is segment-based ([BR09]'s articulated probes): each segment [uF] independently agrees with the closest accessible DP bearing [F], copying that DP's whole geometry (coarse copying; not Multiple Agree — each segment agrees with at most one DP, their fn. 10). Probing is obligatory but failure-tolerant ([Pre14]).

Gluttony — distinct segments agreeing with distinct DPs (their (15)–(16)) — arises only in inverse configurations: when the lower DP bears probe-relevant segments the higher DP lacks (gluttonous_only_inverse). It is not itself fatal; for clitic-doubling probes, their (30) (every segment-agreed DP must cliticize onto the host) is jointly unsatisfiable under gluttony (cliticizing one-at-a-time violates (30) mid-derivation; cliticizing simultaneously violates binary Merge) — that argument is carried in prose; pccViolation states its upshot, gluttony itself.

PCC typology from probe articulation (their (39)) #

Weak (weakProbe, Catalan (22)–(32)): *3>[PART].
Ultrastrong (ultrastrongProbe): additionally *2>1.
Me-First (meFirstProbe, missing intermediate segment — their fn. 22 flags this as non-innocuous): the probe derives *{2,3}>1; their table 1 describes Me-First as *1/2/3>1 — the 1>1 cell is where description and mechanism part ways (cf. their fn. 22's alternative treatment of Me-First as clitic ordering).
Strong (Basque (35)–(38)): weak probe + K-opaque datives (datives expose only [PERS], their §3.4.1) — or the branching probe of their fn. 22 (i) with φ-transparent datives.

Universal predictions (§3.4.2): no probe bans [PART]>3 or 3>3 (direct_never_banned — the geometry makes such gluttony impossible); for [uPERS]-rooted probes a [PART]>[PART] ban entails a 3>[PART] ban (ban_part_part_implies_ban_three_part, bundled as Probe.Articulated.ban_part_part); a single-segment probe never gluttons (not_gluttonous_single_segment, their fn. 21). The articulation laws themselves — downward closure along the geometry, the (40) probe-specification hierarchy — live in the Probe articulation section below (IsArticulated, Probe.Articulated, Probe.Stage); meFirstProbe_not_articulated is their fn. 22 made formal.

Rival accounts (their §2, comparisons drawn by the paper) #

Against PLC/licensing accounts ([BR03]): hierarchy effects track the probe, not licensing needs — in probeless environments (their (10), Basque nonfinite clauses) PCC vanishes; a PLC with no probe to satisfy it predicts the opposite (probeless_divergence_from_plc; B&R's own F-licensing route is the escape their §4 provides, so the disagreement is over where the explanatory work happens).
Against [PZ18]'s P-Constraint (criticized in their §2 as stipulating the licensing parameter): the gluttony tables match PConstraint.IsLicit exactly for the weak and strong grammars, and diverge on one cell each for ultrastrong (2>2) and me-first (1>1) — *_matches_pConstraint / *_diverges_from_pConstraint.

Segments are CyclicAgree.Segment — the same inventory, since both formalizations descend from [BR09]. ckSpec follows their (11), where SPKR and ADDR are sister leaves in one geometry (2nd person always bears ADDR); it differs from CyclicAgree.personSpec .standard only there (ckSpec_filter_eq_personSpec), and is grounded in decomposePerson (ckSpec_grounded).

Gluttony and agreement (§4) #

For agreement (vs. clitics) the crash is at PF: each acquired value demands a Vocabulary item; only one can be inserted; syncretic demands rescue gluttony. icelandic_dat_nom derives the DAT-NOM person restriction (their (75)) with the (84) syncretism fix and the fully-syncretic singular; german_copula derives the assumed-identity restriction (their (51)) with the past-tense war fix (their fn. 32). not_gluttonous_singleton is their (86): many probes on one DP is never gluttony.

Number, reverse PCC, repairs (§3.4.3–§3.5, (40)–(42)) #

The segment-generic core (GluttonousOn) instantiates at the number geometry (their (12)): no_number_case_constraint derives the missing "Number Case Constraint" — π's clitic doubling starves #'s search space in ditransitives — against German copula number gluttony (*SG>PL), where nothing doubles. reverse_pcc_diagnoses_strong is their fn. 26: Slovenian's order-flipping Strong PCC is derivable by the branching probe but not by K-opacity. repairs_shield_goals covers the §3.5 repairs: PP/FP encapsulation, y-cliticization, and Basque absolutive displacement all shrink the probe's search space below two.

Probe articulation (relocated from Minimalist/Phi/Articulation.lean) #

The φ-feature geometry ([HR02]; [CK21]'s (11)) is a partial order on CyclicAgree.Segment: [π] is bottom and [speaker]/[addressee] are the maximal leaves, with s ≤ t read as "bearing t entails bearing s". Two laws of probe systems then become order theory:

Articulation ([BR09]; [CK21] (13)): a probe's segments are downward-closed along the geometry — IsArticulated, equivalent to mathlib's IsLowerSet (isArticulated_iff_isLowerSet). Goal specifications are also lower sets (personSpec_isArticulated): that is the geometric containment (author ⊂ participant ⊂ π) as order theory. [CK21]'s fn. 22 flags probes with missing intermediate segments (their Me-First probe) as non-innocuous — here, they are exactly the non-lower-set probes. Probe.Articulated bundles the laws.
The probe-specification hierarchy ([CK21] (40)): [uφ] → [uπ] → [uπ ▷ u#] → [uπ ▷ u# ▷ uΓ]. Probe.Stage carries the hierarchy as a type: a number probe without a person probe is unrepresentable, which is how the account derives the missing "Number Case Constraint" (see no_number_case_constraint below).

Main declarations:

Segment.below, the PartialOrder Segment instance — the geometry.
IsArticulated — downward-closure of a segment list; decidable.
Probe.Articulated — segments + rootedness in [π] + closure.
Probe.Stage — the (40) hierarchy, with number_requires_person / gender_requires_number as theorems.

Coon & Keine 2021 — Feature Gluttony [CK21] #

PCC typology from probe articulation (their (39)) #

Rival accounts (their §2, comparisons drawn by the paper) #

Gluttony and agreement (§4) #

Number, reverse PCC, repairs (§3.4.3–§3.5, (40)–(42)) #

Probe articulation (relocated from Minimalist/Phi/Articulation.lean) #

The segment order #

Articulation as downward closure #

The probe-specification hierarchy ([CK21] (40)) #

before Γ) is carried by the stage itself. #

Feature geometry and goals (their (11), §3.4.1) #

Probes and segment-based Agree (their (13), (14), (39)) #

Gluttony is limited to inverse configurations #

The PCC tables, derived (their §3.3–3.4) #

Universal predictions (their §3.4.2) #

Rival accounts (their §2) #

Gluttony and agreement: values, Vocabulary, syncretism (§4) #

Icelandic dative-nominative constructions (§4.2) #

German copula constructions (§4.1) #

The number probe and the missing "Number Case Constraint" #

Reverse PCC (§3.4.4) #

PCC repairs (§3.5) #