Lucy 1994: The role of semantic value in lexical comparison

[Luc94] argues that lexical classes must be identified morpho-distributionally, not denotationally: the notional class "motion verbs", assembled by English intuition, coincides with no morphologically defined Yucatec class. The diagnostic is which derivation a root requires to form a transitive stem:

Derivation	Predicate root class (p. 630)	Size (p. 629)
=t (affective)	agent salient	well over 100
=∅ (zero)	agent-patient salient	some 500
=s (causative)	patient salient	fewer than 75

Positional roots (over 100) fall outside this three-way cut: they take the positional derivation =lah (incompletive =tal) and are formally interstitial — čin 'bend' also zero-derives a transitive (ex. (6)). Notional motion roots land in the smallest predicate class, patient salient (ex. (4)); at best the five #-marked roots lacking the -Vl imperfective form "a formal class of 'motion verbs'" (p. 641), a distinction invisible to the entailment grid.

Main results

• predicted_matches_attested: applicability derived from (kind signature × valency) reproduces every derivation Lucy attests.
• transitiviser_adds_compl: each class's required transitiviser adds exactly the Boolean complement of its underived stem's valency — the three-way diagnostic is complementation in the valency lattice.
• motion_roots_not_separate_class: motion roots share their predicted class with plain state-change roots like kíim 'die'.
• positional_crosscuts_transitiviser_classes: the positional diagnostic overlaps =∅ (čin) and the diagnostic gap (kul) — Lucy's classes are not a partition.
• hash_not_signature_definable: the # motion subclass is not a function of the entailment grid.

Implementation notes

The reconstruction is two-dimensional — B&K-G kind signature × root valency ([BKG20]; [Coo19]; both postdate Lucy and serve as project-canonical substrate). Valency carries the agent-patient class: Lucy's =∅ roots "require two arguments" (p. 629) and are not signature-homogeneous (p'is 'measure' is manner-only, k'os 'cut' manner+result), so no feature configuration could carry the class. The signature separates the two intransitive classes, matching the Sapir 1917 Fillmore 1968 Perlmutter 1978 unaccusativity lineage Lucy cites (p. 630). "Salience" is Lucy's term for "a set of default semantic values in a root or stem that influence an overt case marking" (p. 628). Root name strings follow Lucy's orthography. The =t class is inflated by denominal and loanword verbalization (p. 629), so =t applicability is a weaker signal of manner entailments than =∅ or =s are of theirs.

The salience classes and the pair-level classifier (ArgumentStructure.SalienceClass.ofKinds) are substrate (Semantics/ArgumentStructure/SalienceClass.lean); this file supplies the Yucatec roots, diagnostic operators, and attested derivations.

Agent-salient roots (p. 629, ex. (1a))

def Lucy1994.siit : Verb.Root

síit' 'jump' (ex. (1a)).

Equations

• Lucy1994.siit = { name := "síit'", entailments := {Verb.LexEntailment.hasManner "jumping"} }

def Lucy1994.tziib : Verb.Root

¢'iib' 'write' (p. 629).

Equations

• Lucy1994.tziib = { name := "¢'iib'", entailments := {Verb.LexEntailment.hasManner "writing"} }

def Lucy1994.miis : Verb.Root

mìis 'sweep' (p. 629); denominal from 'broom'.

Equations

• Lucy1994.miis = { name := "mìis", entailments := {Verb.LexEntailment.hasManner "sweeping"} }

def Lucy1994.cheh : Verb.Root

čé'eh 'smile' (p. 629).

Equations

• Lucy1994.cheh = { name := "čé'eh", entailments := {Verb.LexEntailment.hasManner "smiling"} }

def Lucy1994.paak : Verb.Root

páak 'weed' (p. 629).

Equations

• Lucy1994.paak = { name := "páak", entailments := {Verb.LexEntailment.hasManner "weeding"} }

Agent-patient salient roots (p. 629, ex. (1b))

Root transitives. They carry no uniform signature: kuč, p'is, ha¢, loš are manner-only (surface contact without entailed result, B&K-G's hit type), while k'os 'cut' is manner+result (their cut type).

def Lucy1994.kuc : Verb.Root

kuč 'carry' (ex. (1b)).

Equations

• Lucy1994.kuc = { name := "kuč", entailments := {Verb.LexEntailment.hasManner "carrying"} }

def Lucy1994.kos : Verb.Root

k'os 'cut' (p. 629); manner+result.

Equations

• Lucy1994.kos = { name := "k'os", entailments := {Verb.LexEntailment.hasManner "cutting", Verb.LexEntailment.becomesState "cut"} }

def Lucy1994.pis : Verb.Root

p'is 'measure' (p. 629); no entailed change of state.

Equations

• Lucy1994.pis = { name := "p'is", entailments := {Verb.LexEntailment.hasManner "measuring"} }

def Lucy1994.hats : Verb.Root

ha¢ 'whip' (p. 629).

Equations

• Lucy1994.hats = { name := "ha¢", entailments := {Verb.LexEntailment.hasManner "whipping"} }

def Lucy1994.los : Verb.Root

loš 'punch' (p. 629); surface contact without entailed result.

Equations

• Lucy1994.los = { name := "loš", entailments := {Verb.LexEntailment.hasManner "striking"} }

Patient-salient roots (ex. (2), pp. 629–630)

Lucy's list (2) is arranged in antonym pairs "listed in vertical adjacency" (fn. 7): 'ah wen, siih kíim, tú'ub' k'a'ah, ču'un č'en, hó'op' ~ háaw. The order below is the list's.

def Lucy1994.ah : Verb.Root

'ah '(a)wake(n)' ('ah=s 'wake (someone)').

Equations

• Lucy1994.ah = { name := "'ah", entailments := {Verb.LexEntailment.becomesState "awake"} }

def Lucy1994.wen : Verb.Root

wen '(fall a)sleep' (ween=s 'put to sleep'); fn. 7 flags it as also denoting continuation in the state.

Equations

• Lucy1994.wen = { name := "wen", entailments := {Verb.LexEntailment.becomesState "asleep"} }

def Lucy1994.siih : Verb.Root

siih 'be born' (siih=s 'give birth, bear').

Equations

• Lucy1994.siih = { name := "siih", entailments := {Verb.LexEntailment.becomesState "born"} }

def Lucy1994.kiim : Verb.Root

kíim 'die' (ex. (1c); kíim=s 'kill').

Equations

• Lucy1994.kiim = { name := "kíim", entailments := {Verb.LexEntailment.becomesState "dead"} }

def Lucy1994.tuub : Verb.Root

tú'ub' 'forget' (tú'ub'=s 'distract, cause to forget').

Equations

• Lucy1994.tuub = { name := "tú'ub'", entailments := {Verb.LexEntailment.becomesState "forgotten"} }

def Lucy1994.kaah : Verb.Root

k'a'ah 'remember' (k'á'ah=s 'remind, mention, invoke').

Equations

• Lucy1994.kaah = { name := "k'a'ah", entailments := {Verb.LexEntailment.becomesState "remembered"} }

def Lucy1994.chuun : Verb.Root

ču'un 'begin activity' (ču'un=s 'cause to begin').

Equations

• Lucy1994.chuun = { name := "ču'un", entailments := {Verb.LexEntailment.becomesState "begun"} }

def Lucy1994.chen : Verb.Root

č'en 'stop, cease' (č'en=s 'cause to stop, suspend').

Equations

• Lucy1994.chen = { name := "č'en", entailments := {Verb.LexEntailment.becomesState "ceased"} }

def Lucy1994.hoop : Verb.Root

hó'op' 'begin, start' (hó'op'=s 'cause to begin').

Equations

• Lucy1994.hoop = { name := "hó'op'", entailments := {Verb.LexEntailment.becomesState "started"} }

def Lucy1994.haaw : Verb.Root

háaw 'stop, cease, heal' (háaw=s 'stop, revoke, medicate').

Equations

• Lucy1994.haaw = { name := "háaw", entailments := {Verb.LexEntailment.becomesState "stopped"} }

def Lucy1994.heel : Verb.Root

hé'el 'rest, stop at' (hé'e(l)=s 'rest').

Equations

• Lucy1994.heel = { name := "hé'el", entailments := {Verb.LexEntailment.becomesState "rested"} }

def Lucy1994.paat : Verb.Root

p'át 'remain' (p'át=s 'abandon').

Equations

• Lucy1994.paat = { name := "p'át", entailments := {Verb.LexEntailment.becomesState "remaining"} }

Motion roots (ex. (4), p. 640)

"Locational-spatial state-change predicates": notionally motion, formally plain members of the patient-salient class. The five #-marked roots "do not — and CANNOT — take the -Vl suffix in the imperfective"; fn. 17 adds that péek and 'ú'ul are also irregular in their agent-focused perfective forms, "where they pattern like agent-salient roots".

def Lucy1994.maan : Verb.Root

máan 'pass by' (#; máan=s 'pass, transfer, transport').

Equations

• Lucy1994.maan = { name := "máan", entailments := {Verb.LexEntailment.becomesState "past"} }

def Lucy1994.peek : Verb.Root

péek 'move, vibrate' (#; pek=s 'cause to move, vibrate').

Equations

• Lucy1994.peek = { name := "péek", entailments := {Verb.LexEntailment.becomesState "in-motion"} }

def Lucy1994.bin : Verb.Root

b'in 'go' (#; bi(n)=s 'take').

Equations

• Lucy1994.bin = { name := "b'in", entailments := {Verb.LexEntailment.becomesState "gone"} }

def Lucy1994.taal : Verb.Root

tàal 'come (here)' (#; tàa(l)=s 'bring').

Equations

• Lucy1994.taal = { name := "tàal", entailments := {Verb.LexEntailment.becomesState "come"} }

def Lucy1994.uul : Verb.Root

'ú'ul 'arrive (here)' (#; 'ú'uh=s 'bring it to here').

Equations

• Lucy1994.uul = { name := "'ú'ul", entailments := {Verb.LexEntailment.becomesState "arrived"} }

def Lucy1994.ok : Verb.Root

'ok 'enter, intrude' ('òok=s 'move it in(to)').

Equations

• Lucy1994.ok = { name := "'ok", entailments := {Verb.LexEntailment.becomesState "inside"} }

def Lucy1994.luub : Verb.Root

lúub' 'fall' (lúub'=s 'fell').

Equations

• Lucy1994.luub = { name := "lúub'", entailments := {Verb.LexEntailment.becomesState "fallen"} }

def Lucy1994.liik : Verb.Root

líik' '(a)rise, ascend' (lii(k)'=s 'raise, lift, put away').

Equations

• Lucy1994.liik = { name := "líik'", entailments := {Verb.LexEntailment.becomesState "risen"} }

def Lucy1994.naak : Verb.Root

ná'ak '(a)rise, ascend' (ná'ak=s 'raise'); distinct from náak 'arrive, reach, hit', not sampled here.

Equations

• Lucy1994.naak = { name := "ná'ak", entailments := {Verb.LexEntailment.becomesState "ascended"} }

Positional roots (ex. (7), p. 643)

def Lucy1994.cin : Verb.Root

čin 'bow, bend down, bend over' (ex. (5)–(7)); zero-derives a transitive, ex. (6) 'I bent it'.

Equations

• Lucy1994.cin = { name := "čin", entailments := {Verb.LexEntailment.hasState "bent"} }

def Lucy1994.kul : Verb.Root

kul 'sit' (p. 645, fn. 24: relational 'x is-seated [on y]').

Equations

• Lucy1994.kul = { name := "kul", entailments := {Verb.LexEntailment.hasState "seated"} }

Valency and class lists

def Lucy1994.rootTransitives : List Verb.Root

Roots attested forming a transitive stem by zero derivation: the sampled =∅ predicate roots (p. 629) plus the positional čin (ex. (6)).

Equations

• Lucy1994.rootTransitives = [Lucy1994.kuc, Lucy1994.kos, Lucy1994.pis, Lucy1994.hats, Lucy1994.los, Lucy1994.cin]

def Lucy1994.valency (r : Verb.Root) : ArgumentStructure.Valency

Root valency for the sample ([Coo19]'s √TV as {.internal}): zero-derivers introduce their internal argument; every other sampled root introduces none. Sample-local — the assignment defaults to ∅ off the sample.

Equations

• Lucy1994.valency r = if r ∈ Lucy1994.rootTransitives then {ArgumentStructure.ArgPosition.internal} else ∅

def Lucy1994.agentSalientRoots : List Verb.Root

The sampled agent-salient roots.

Equations

• Lucy1994.agentSalientRoots = [Lucy1994.siit, Lucy1994.tziib, Lucy1994.miis, Lucy1994.cheh, Lucy1994.paak]

def Lucy1994.agentPatientSalientRoots : List Verb.Root

The sampled agent-patient salient (=∅ predicate) roots.

Equations

• Lucy1994.agentPatientSalientRoots = [Lucy1994.kuc, Lucy1994.kos, Lucy1994.pis, Lucy1994.hats, Lucy1994.los]

def Lucy1994.patientSalientRoots : List Verb.Root

The sampled patient-salient roots of list (2), in Lucy's order.

Equations

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

def Lucy1994.motionRoots : List Verb.Root

The sampled motion roots of ex. (4).

Equations

• Lucy1994.motionRoots = [Lucy1994.maan, Lucy1994.peek, Lucy1994.bin, Lucy1994.taal, Lucy1994.uul, Lucy1994.ok, Lucy1994.luub, Lucy1994.liik, Lucy1994.naak]

def Lucy1994.hashMarked : List Verb.Root

The #-marked subset of ex. (4): the roots lacking the -Vl imperfective — for Lucy, the only candidate "formal class of 'motion verbs'" (p. 641).

Equations

• Lucy1994.hashMarked = [Lucy1994.maan, Lucy1994.peek, Lucy1994.bin, Lucy1994.taal, Lucy1994.uul]

def Lucy1994.positionalRoots : List Verb.Root

The sampled positional roots.

Equations

• Lucy1994.positionalRoots = [Lucy1994.cin, Lucy1994.kul]

def Lucy1994.sampledRoots : List Verb.Root

Every sampled root.

Equations

• Lucy1994.sampledRoots = Lucy1994.agentSalientRoots ++ Lucy1994.agentPatientSalientRoots ++ Lucy1994.patientSalientRoots ++ Lucy1994.motionRoots ++ Lucy1994.positionalRoots

Diagnostic operators

structure Lucy1994.DiagOp : Type

A diagnostic derivational operator: exponent plus structural applicability condition, with bundled decidability so profiles compute (the inventory holds heterogeneous conditions, so a per-operator instance cannot serve). Selection machinery comes from the Morphology.Exponence.Rule instance.

• exponent : String

  The suffix, in Lucy's orthography.

• adds : ArgumentStructure.Valency

  The core-argument positions the derivation adds (transitiviser_adds_compl).

• Applies : Verb.Root → Prop

  The structural condition on the root.

• decApplies : DecidablePred self.Applies

  Bundled decidability of the condition.

@[instance_reducible]

instance Lucy1994.instRuleDiagOpRootString : Morphology.Exponence.Rule DiagOp Verb.Root String

Equations

• Lucy1994.instRuleDiagOpRootString = { exponent := Lucy1994.DiagOp.exponent, Applies := Lucy1994.DiagOp.Applies }

@[instance_reducible]

instance Lucy1994.instDecidableRelDiagOpRootAppliesString : DecidableRel Morphology.Exponence.Applies

Equations

• Lucy1994.instDecidableRelDiagOpRootAppliesString op r = op.decApplies r

@[simp]

theorem Lucy1994.applies_iff (op : DiagOp) (r : Verb.Root) : Morphology.Exponence.Applies op r ↔ op.Applies r

def Lucy1994.affectiveT : DiagOp

Affective =t: transitivises an agent-salient root by adding a patient argument.

Equations

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

def Lucy1994.zeroDeriv : DiagOp

Zero derivation =∅: the root alone supports a transitive stem.

Equations

• Lucy1994.zeroDeriv = { exponent := "=∅", adds := ∅, Applies := fun (r : Verb.Root) => ArgumentStructure.ArgPosition.internal ∈ Lucy1994.valency r, decApplies := inferInstance }

def Lucy1994.causativeS : DiagOp

Causative =s: transitivises a patient-salient root by adding an agent argument.

Equations

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

def Lucy1994.positionalLah : DiagOp

Positional derivation, realized =lah ~ =tal by status (the =tal incompletive is the anomalous member, apparently compounding with tàal 'come').

Equations

• Lucy1994.positionalLah = { exponent := "=lah", adds := ∅, Applies := fun (r : Verb.Root) => ArgumentStructure.IsPositional r.kinds, decApplies := inferInstance }

def Lucy1994.inventory : List DiagOp

The diagnostic inventory, in the order of Lucy's presentation: the three transitivisers of ex. (1), then the positional.

Equations

• Lucy1994.inventory = [Lucy1994.affectiveT, Lucy1994.zeroDeriv, Lucy1994.causativeS, Lucy1994.positionalLah]

def Lucy1994.predictedExponents (r : Verb.Root) : List String

The exponents of the inventory's applicable operators at r, in inventory order — the root's predicted derivational behaviour.

Equations

• Lucy1994.predictedExponents r = List.map Lucy1994.DiagOp.exponent (Morphology.Exponence.applicable Lucy1994.inventory r)

Predicted vs attested derivations

def Lucy1994.attestations : List (Verb.Root × List String)

The derivations Lucy attests per sampled root: =t for the p. 629 activity roots, =∅ for the root transitives, =s for lists (2) and (4), =lah for positionals — with čin attested for both =∅ (ex. (6)) and =lah (ex. (5)).

Equations

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

theorem Lucy1994.predicted_matches_attested (p : Verb.Root × List String) : p ∈ attestations → predictedExponents p.1 = p.2

The derivations predicted from (signature × valency) reproduce every derivation Lucy attests. Unlike the classifier theorems below, this check is against a column transcribed from the paper, independent of the encoding.

The derived classification

def Lucy1994.predictedClass (r : Verb.Root) : Option ArgumentStructure.SalienceClass

A root's predicted salience class.

Equations

• Lucy1994.predictedClass r = ArgumentStructure.SalienceClass.ofKinds r.kinds (Lucy1994.valency r)

def Lucy1994.exponentOf : ArgumentStructure.SalienceClass → String

The transitiviser each salience class requires.

Equations

• Lucy1994.exponentOf ArgumentStructure.SalienceClass.agent = "=t"
• Lucy1994.exponentOf ArgumentStructure.SalienceClass.agentPatient = "=∅"
• Lucy1994.exponentOf ArgumentStructure.SalienceClass.patient = "=s"

theorem Lucy1994.predictedExponents_eq (r : Verb.Root) : predictedExponents r = List.map exponentOf (predictedClass r).toList ++ if ArgumentStructure.IsPositional r.kinds then ["=lah"] else []

Predicted derivational behaviour decomposes as the class's transitiviser followed by the positional derivation when the signature licenses it — the applicability profile is the classification, plus the cross-cutting positional diagnostic.

theorem Lucy1994.agentSalient_class (r : Verb.Root) : r ∈ agentSalientRoots → predictedClass r = some ArgumentStructure.SalienceClass.agent

theorem Lucy1994.agentPatientSalient_class (r : Verb.Root) : r ∈ agentPatientSalientRoots → predictedClass r = some ArgumentStructure.SalienceClass.agentPatient

theorem Lucy1994.patientSalient_class (r : Verb.Root) : r ∈ patientSalientRoots → predictedClass r = some ArgumentStructure.SalienceClass.patient

theorem Lucy1994.rootTransitives_not_signature_uniform : ∃ r ∈ agentPatientSalientRoots, ∃ r' ∈ agentPatientSalientRoots, r.kinds ≠ r'.kinds

The =∅ class is not signature-homogeneous (p'is manner-only vs k'os manner+result) — root transitivity is carried by valency, not by any feature configuration.

The "motion verbs" non-class

theorem Lucy1994.motion_roots_not_separate_class (r : Verb.Root) : r ∈ motionRoots → predictedClass r = predictedClass kiim

Lucy's central typological point: notional motion roots do not form their own salience class — each is classified exactly as the plain state-change root kíim 'die'.

theorem Lucy1994.hash_not_signature_definable : ∃ r ∈ hashMarked, ∃ r' ∈ motionRoots, r' ∉ hashMarked ∧ r.kinds = r'.kinds ∧ valency r = valency r'

The # subclass — Lucy's only candidate formal motion class — is not a function of the entailment grid: péek (#) and lúub' (plain) agree in signature and valency. The class is carried by an idiosyncratic morphological gap, not by lexical semantics.

theorem Lucy1994.transitiviser_adds_compl : affectiveT.adds = ArgumentStructure.SalienceClass.agent.stemValencyᶜ ∧ zeroDeriv.adds = ArgumentStructure.SalienceClass.agentPatient.stemValencyᶜ ∧ causativeS.adds = ArgumentStructure.SalienceClass.patient.stemValencyᶜ

The transitiviser system is complementation in the valency lattice: each class's required derivation adds exactly the Boolean complement of its underived stem's valency — =t supplies the patient the unergative agent stem lacks, =s the agent the unaccusative patient stem lacks, =∅ nothing, the root-transitive stem being already complete.

Positional interstitiality

theorem Lucy1994.positional_crosscuts_transitiviser_classes : ArgumentStructure.IsPositional cin.kinds ∧ predictedClass cin = some ArgumentStructure.SalienceClass.agentPatient ∧ ArgumentStructure.IsPositional kul.kinds ∧ predictedClass kul = none

The positional diagnostic cross-cuts the transitiviser cut: čin is positional yet zero-derives a transitive (agent-patient salient), while kul is positional and outside the cut altogether. Lucy's classes are diagnostics, not a partition.

Closure robustness

theorem Lucy1994.predictedClass_closure_invariant (r : Verb.Root) (h : ¬r.HasCause) : ArgumentStructure.SalienceClass.ofKinds r.closedKinds (valency r) = predictedClass r

For cause-free roots — every root in this sample — collocational closure does not change the predicted class.