@cite{grimm-2011}: Semantics of Case — Lattice Predictions #
@cite{grimm-2011} @cite{aissen-2003} @cite{von-heusinger-2008}
Study file connecting @cite{grimm-2011}'s agentivity lattice
(Theories/Semantics/Events/AgentivityLattice.lean) to the differential
object marking profiles in Phenomena/Case/Studies/Aissen2003.lean.
Key results #
Russian DOM matches the lattice exactly: for canonical transitives (quPersBeginning),
DomPredictedByLatticeholds for exactly {animate, human} — the same cells Russian marks.Spanish DOM is a proper subset: the lattice predicts DOM for {animate, human}, but Spanish only marks {human}.
Two frameworks, same predictions: the lattice-derived DOM is always monotone in @cite{aissen-2003}'s sense, and the lattice's canonical transitive prediction exactly matches Aissen's OT Type 2.
Full case region table: every canonical verb is mapped through the lattice to a case region, connecting argument selection to morphological case.
Verb class effect: the lattice predicts that creation verb objects are entirely outside the transitivity region (DOM inapplicable), while contact and consumption verbs have objects in the canonical patient region. This connects to @cite{von-heusinger-2008}'s observation that DOM regularized earliest for agent-patient verbs.
@cite{grimm-2011} p.534: "it is a combination of verbal and nominal
properties which trigger DOM." This substrate maps nominal animacy to
a baseline agentive position on the lattice, combines it with verbal
persistence to predict a case region, and packages the residual
"object outside ACC/ABS" condition as DomPredictedByLattice.
Map nominal animacy to baseline agentive capacity on the lattice.
Only inherent referent properties are mapped — not event-specific ones like instigation or motion:
- Human: volition + sentience (capacity for intentional action)
- Animate: sentience (conscious but non-volitional)
- Inanimate: ⊥ (no inherent agentive capacity)
The exclusion of instigation and motion is principled: these are event properties (did the participant instigate THIS event? move during THIS event?), not referent properties. Volition and sentience are inherent capacities of the referent type.
Equations
- Grimm2011.animacyToAgentivity Features.Prominence.AnimacyLevel.human = { volition := true, sentience := true, instigation := false, motion := false }
- Grimm2011.animacyToAgentivity Features.Prominence.AnimacyLevel.animate = { volition := false, sentience := true, instigation := false, motion := false }
- Grimm2011.animacyToAgentivity Features.Prominence.AnimacyLevel.inanimate = ⊥
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All animacy-derived nodes satisfy volition → sentience.
The mapping is monotone: higher animacy → higher agentivity. This is a structural property of the feature-subset ordering, not a stipulation.
Combine a referent's nominal agentivity (from animacy) with the verb's persistence profile for the object.
Equations
- Grimm2011.objectNodeWithAnimacy animacy verbPersistence = { agentivity := Grimm2011.animacyToAgentivity animacy, persistence := verbPersistence }
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The key non-circular derivation. For canonical transitive objects (quPersBeginning = contact verbs like kick, hit, push):
- Inanimate:
⟨⊥, qPB⟩→toCaseRegion= accAbs (prototypical patient, no DOM needed) - Animate:
⟨{S}, qPB⟩→toCaseRegion= dative (sentience shifts it into the dative region, Fig. 7) - Human:
⟨{V,S}, qPB⟩→toCaseRegion= dative (volition + sentience, also in dative region)
toCaseRegion is defined in the substrate for general case theory,
not for DOM. That it automatically separates inanimate objects (accAbs)
from animate/human objects (dative) is the lattice's genuine prediction.
DOM is predicted when the object is in the transitivity region but its nominal agentivity pushes it outside the ACC/ABS case region. Both conditions use infrastructure defined for general case theory, not for DOM.
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Equations
- Grimm2011.instDecidableDomPredictedByLattice a p = id inferInstance
Inanimate objects of canonical transitives: in ACC/ABS, no DOM.
Animate objects of canonical transitives: outside ACC/ABS, DOM predicted. The lattice reason: sentience pushes the object into the dative region (Fig. 7).
Human objects: also outside ACC/ABS, DOM predicted.
The same pattern holds for resultative verbs (break, destroy): inanimate objects stay in ACC/ABS, animate/human objects do not.
Creation verb objects (build, invent — exPersEnd) are outside the transitivity region at ALL animacy levels. The object does not exist at event start, so it cannot "intrude" on the agent's role. DOM is inapplicable, not merely unnecessary.
Whether the subject maps to the NOM/ERG case region. When true, the verbal semantics alone provides maximal contrast between subject (NOM/ERG) and object (ACC/ABS or below), and DOM can regularize — it is redundant for disambiguation.
@cite{von-heusinger-2008}: matar 'kill' (Class 1, subject → NOM/ERG) regularized DOM centuries before ver 'see' (Class 2, subject → oblique).
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Equations
- Grimm2011.instDecidableSubjectInAgentRegion p = id inferInstance
Kick subject → NOM/ERG: maximal verbal contrast. Corresponds to matar 'kill' — DOM regularized early.
See subject → NOT NOM/ERG: insufficient verbal contrast. Corresponds to ver 'see' — DOM remained variable.
Build subject → NOM/ERG: high verbal contrast, but moot because the object is outside the transitivity region (§0.5).
The lattice reproduces @cite{aissen-2003}'s monotonicity prediction: if DOM is predicted for a lower animacy level, it is also predicted for all higher levels. Universally quantified over persistence.
This is NOT stipulated — it follows from:
animacyToAgentivityis monotone (higher animacy → more features)toCaseRegionmaps ⊥ agentivity to accAbs, non-⊥ to dative/oblique- Once agentivity is non-⊥, adding features keeps it non-⊥
For totalPersistence objects (perception verbs: see, hear, know),
toCaseRegion maps ⟨⊥, totalPersistence⟩ to oblique, not accAbs,
because totalPersistence is not in {exPersBeginning, quPersBeginning}.
This means DomPredictedByLattice returns true for ALL animacy levels,
including inanimate — overpredicting DOM for perception verb objects.
This reflects a genuine theoretical point: Grimm's system treats
perception verb objects as non-prototypical patients (they are not
affected or changed). But it means `DomPredictedByLattice` is most
informative for verbs in the transitivity region's core: contact
(quPersBeginning) and resultative effective (exPersBeginning) verbs.
The lattice predicts DOM when an object is in the transitivity region but its nominal agentivity pushes it outside ACC/ABS. For canonical transitives (quPersBeginning), this predicts DOM for {animate, human} but not {inanimate}. We check each attested animacy-based DOM language against this prediction.
Russian DOM marks exactly the animacy levels where the lattice predicts DOM for canonical transitives. The lattice and Russian agree on every cell of the animacy scale.
Russian: animate + human marked, inanimate unmarked. Lattice: animate + human shift to dative region (outside ACC/ABS), inanimate stays in ACC/ABS. Exact match.
Spanish DOM is a proper subset of the lattice's prediction. Both agree on inanimate (no DOM) and human (DOM), but diverge on animate: the lattice predicts DOM (sentience alone shifts to dative), but Spanish does not mark animate objects.
Hindi DOM is consistent with the lattice on the animacy dimension: inanimate objects are never marked regardless of definiteness, and both animate and human are marked at some definiteness level. The lattice correctly predicts the animacy boundary even though it has no definiteness dimension.
Every animacy-based DOM language in the sample marks only animacy levels where the lattice predicts DOM. The lattice's prediction is a superset of every attested animacy-based pattern.
@cite{aissen-2003} derives DOM monotonicity from OT constraint
interaction (harmonic alignment of iconicity and economy constraints).
@cite{grimm-2011} derives it from lattice geometry (animacy maps
monotonically to agentivity, and toCaseRegion preserves the boundary).
Two independent frameworks, same prediction.
A DOM profile derived from the lattice's predictions at a fixed
persistence level. Since DomPredictedByLattice is monotone in
animacy (§21.7 of AgentivityLattice.lean), this profile is
automatically an upper set on the animacy scale.
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Every lattice-derived DOM profile is monotone in @cite{aissen-2003}'s sense (upper set in the bidimensional grid). Universally quantified over all 5 persistence levels.
This connects the lattice's geometric structure to OT's constraint-based monotonicity prediction. The proof goes through because:
animacyToAgentivityis monotone (higher animacy → more features)toCaseRegionmaps ⊥ agentivity to accAbs, non-⊥ elsewhere- Once non-⊥, the object stays non-⊥ at higher animacy levels
The lattice's canonical transitive prediction matches @cite{aissen-2003}'s OT Type 2 (Hu + An, not In). Two independent theories converge on the Russian pattern.
Every canonical verb with an EntailmentProfile is mapped through
the lattice to a case region. This connects @cite{dowty-1991}'s
entailment profiles to @cite{grimm-2011}'s case theory:
| Verb | Subject region | Object region |
|------|---------------|--------------|
| kick | nomErg | accAbs |
| build | nomErg | oblique (creation) |
| eat | nomErg | accAbs |
| see | oblique | — |
| buy/sell | nomErg | — |
| run | oblique | — |
| arrive | oblique | — |
| die | — | accAbs (unacc. subj) |
The table shows that only verbs whose subjects have instigation
land in the NOM/ERG region. Perception and motion verbs without
instigation fall outside — the lattice predicts they are NOT
prototypical transitive subjects.
Objects land in ACC/ABS only when they have ⊥ agentivity and
exist-at-beginning persistence. Creation verbs (exPersEnd) map
to oblique because the object does not exist at the event's start.
kick: prototypical transitive. Subject → NOM/ERG, object → ACC/ABS.
build: creation verb. Subject → NOM/ERG (has instigation), but object → oblique (exPersEnd: object created, not an existing patient). The lattice correctly identifies creation verb objects as non-prototypical patients.
eat: consumption verb. Subject → NOM/ERG, object → ACC/ABS. The consumed object has exPersBeginning (exists before, ceases to exist after) — in the same region as destroyed objects.
run: unergative. Has volition + sentience + motion but NOT instigation → outside NOM/ERG. The lattice predicts the subject is not a prototypical agent — consistent with it being unergative in split-S systems.
see: experiencer verb. Subject has sentience but not instigation → outside NOM/ERG. Consistent with many languages giving experiencer subjects dative or oblique case (e.g., German mir gefällt, Icelandic mér líkar).
buy/sell: both subjects → NOM/ERG (both have instigation via causation). The lattice predicts both are prototypical agents — consistent with @cite{dowty-1991}'s prediction that buy/sell allow alternation.
@cite{grimm-2011}'s Tsunoda hierarchy distinguishes verbs by the persistence of their object. This connects @cite{dowty-1991}'s P-Patient entailments to @cite{grimm-2011}'s persistence levels:
| Verb | P-Patient features | Persistence | Tsunoda class |
|------|-------------------|-------------|--------------|
| kick | CoS+CA+St | quPersBeginning | contact (II) |
| eat | CoS+IT+CA | exPersBeginning | result. eff. (I) |
| build | CoS+IT+CA+DE | exPersEnd | creation (outside) |
| die | CoS+CA+DE | exPersBeginning | result. eff. (I) |
kick object → quPersBeginning: affected but persists (contact).
eat object → exPersBeginning: consumed (ceases to exist via SINC).
build object → exPersEnd: created (comes into existence).
die subject → exPersBeginning: ceases to exist (as patient).
kick and eat objects are in the transitivity region; build is not. This is the lattice's version of Tsunoda's observation that contact and resultative verbs form the core of transitivity.
@cite{von-heusinger-2008} observes that DOM regularized diachronically in Spanish at different rates depending on verb class:
- *matar* 'kill' (Class 1, agent-patient): DOM regularized first
- *ver* 'see' (Class 2, experiencer-theme): DOM regularized later
- *poner* 'put' (Class 3, agent-theme-location): DOM intermediate
The lattice connects this to subject case regions: when the subject
maps to NOM/ERG, there is maximal semantic contrast between subject
(prototypical agent) and object (prototypical patient). This contrast
makes DOM redundant for role identification — so it can regularize.
When the subject is NOT in NOM/ERG, there is less contrast and DOM
remains variable.
The lattice predicts three verb categories for DOM behavior:
- Agent-patient verbs (kick): subject → NOM/ERG, object → ACC/ABS. Maximal contrast → DOM can regularize.
- Experiencer verbs (see): subject → oblique, outside NOM/ERG. Less contrast → DOM remains sensitive to object animacy.
- Creation verbs (build): object outside transitivity entirely. DOM is structurally inapplicable, not merely unnecessary.
Creation verb objects are outside the transitivity region at ALL animacy levels. DOM is structurally inapplicable — the lattice predicts no language should have DOM for creation verb objects.
This is a stronger prediction than "no DOM": even animate/human creation objects (build a team, invent a character) should not trigger DOM, because the object does not exist at event start.
The lattice-to-case-region mapping predicts morphological case in both accusative and ergative systems. For prototypical transitives (kick, eat), both alignments produce the expected case assignments.
kick in an accusative system: subject → NOM, object → ACC.
kick in an ergative system: subject → ERG, object → ABS.
eat in an accusative system: subject → NOM, object → ACC. Consumption verbs pattern with canonical transitives for case.
build in an accusative system: subject → NOM, but object → INST (oblique). The lattice predicts creation verb objects are NOT canonical accusatives — consistent with Finnish partitive for incomplete creation and Russian genitive of negation being more readily available with creation verbs.
The lattice's toCaseRegion requires instigation for NOM/ERG.
This captures a cross-linguistic generalization: canonical
transitive subjects are instigators. Verbs whose subjects lack
instigation (see, run, arrive) have "oblique" semantics even
when they surface with NOM in accusative languages.
Summary: which verbs have subjects in NOM/ERG and which do not. The dividing line is instigation (Dowty's causation).
The dividing feature is exactly instigation. All NOM/ERG subjects have instigation; all non-NOM/ERG subjects lack it. Instigation = Dowty's causation mapped to Grimm's system.
The Russian genitive/accusative alternation arises when the object of an intensional verb (want, seek, await) falls in a region covered by two cases. The accusative covers existential persistence (beginning); the genitive covers total non-persistence (Fig. 8).
- Accusative (specific reading): the object is referential → exists → existential persistence (beginning) → ACC region.
- Genitive (non-specific reading): the object need not exist → total non-persistence → GEN region.
The alternation is limited to verbs whose objects have no persistence entailments — only intensional verbs like want, seek, await license the genitive (p.541).
- specificReading : Semantics.ArgumentStructure.AgentivityLattice.GrimmNode
The object node under the specific/referential reading.
- nonSpecificReading : Semantics.ArgumentStructure.AgentivityLattice.GrimmNode
The object node under the non-specific reading.
The specific reading has more persistence features.
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The canonical Russian gen/acc alternation for intensional verbs: ACC (specific) ↔ GEN (non-specific).
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The specific reading maps to the ACC/ABS region.
Semantic opposition between two GrimmNodes. Transitivity increases with the distance between agent and patient on the lattice. We measure this as the difference in total feature counts — higher opposition means more prototypically transitive.
Equations
- Grimm2011.semanticOpposition agent patient = ↑agent.featureCount - ↑patient.featureCount
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Maximal agent vs maximal patient has the highest opposition (8 - 2 = 6).
Class I (break) has more opposition than Class II (shoot): the patient is more affected (fewer persistence features).
Illustrates the agentivity lattice with a chain of canonical verbs, each adding one feature. Demonstrates that the lattice directly formalises "degree of agentivity" — higher on the lattice means more agentive.
sit/stand subject: ⊥ (no agentivity). p.523.
Equations
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know/see subject: sentience only. p.524.
Equations
- Grimm2011.knowAgentivity = { volition := false, sentience := true, instigation := false, motion := false }
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discover subject: sentience + instigation. p.524.
Equations
- Grimm2011.discoverAgentivity = { volition := false, sentience := true, instigation := true, motion := false }
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look at subject: sentience + instigation + motion. p.524.
Equations
- Grimm2011.lookAtAgentivity = { volition := false, sentience := true, instigation := true, motion := true }
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assassinate subject: all four features. p.524.
Equations
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The canonical verb chain is totally ordered and forms a maximal chain from ⊥ to ⊤ in the agentivity lattice.
All canonical verb positions satisfy volition → sentience.
AgentivityNode kernel: two profiles map to the same agentivity node iff they agree on {V, S, C, M}. The 5th P-Agent feature (IE) and all 5 P-Patient features are irrelevant — they are dropped by the projection.
This formally characterizes the information loss: fromEntailmentProfile
is a surjection whose fibers are the equivalence classes of profiles
agreeing on {V, S, C, M}.
Independent existence is lost by the agentivity projection. Two profiles differing only in IE map to the same node. Concrete witness: full agent (IE=true) and agent-without-IE.
All P-Patient features are lost by the agentivity projection. A profile with 5 P-Patient features maps to the same node as one with 0.
wellFormedPair is not preserved by the Grimm projection.
@cite{dowty-1991}'s wellFormedPair constrains inter-argument entailment
pairings: causation→CoS, movement→stationary, IE→DE. These are
relational constraints between two profiles.
Grimm's system replaces them with a single persistence dimension on the patient side. The IE feature is dropped entirely from the agentivity projection, so the IE→DE constraint becomes invisible.
Witness: s₁ = {C} and s₂ = {C, IE} map to the same AgentivityNode (both have instigation only). With o = {CoS}, wellFormedPair holds for s₁ (IE=false, so IE→DE vacuously satisfied) but fails for s₂ (IE=true but DE=false). The Grimm system cannot detect this.
Class I patients (break) are in the transitivity region.
Class II patients (shoot) are in the transitivity region.
Class III patients (search) are OUTSIDE the transitivity region. This captures Tsunoda's observation that pursuit verbs deviate most strongly from the prototypical transitive paradigm.
Class I patient (break: exPersBeginning) has lower persistence than Class II patient (shoot: quPersBeginning). The Class I object is more affected — it ceases to exist.
Class I patient ≤ Class II patient on the lattice (exPersBeginning ≤ quPersBeginning).
Class III patient ≤ Class I patient (totalNonPersistence ≤ exPersBeginning).
Maximal agent maps to NOM/ERG region.
Maximal patient maps to ACC/ABS region.
The effector agent (instigation + motion, total persistence) maps to NOM/ERG. This is the agent of break/kill (Fig. 5, Ia).
Class I patient (break object: destroyed) maps to ACC/ABS.
Class II patient (shoot object: affected but persists) maps to ACC/ABS.
Accusative alignment: maximal agent → NOM, maximal patient → ACC.
Ergative alignment: maximal agent → ERG, maximal patient → ABS.
kick subject → agentivity {V,S,I,M} (full agent).
run subject → agentivity {V,S,M} (no instigation).
arrive subject → agentivity {M} (motion only).
see subject → agentivity {S} (sentience only).
sweep basic subject → agentivity {M} (motion only, variable agentivity).
sweep broom subject → agentivity {V,S,I,M} (instrument lexicalization adds full agentivity, @cite{rappaport-hovav-levin-2024}).
Instrument lexicalization strictly increases agentivity on the lattice: sweep basic {M} < sweep broom {V,S,I,M}.
Full pipeline: kick subject → GrimmNode → NOM/ERG → NOM (accusative).
Full pipeline: kick object → GrimmNode → ACC/ABS → ACC (accusative).
Build subject → NOM (full agent, total persistence).
Build object → OBLIQUE (not ACC). The object of build maps to exPersEnd (entity comes into existence), which falls OUTSIDE the transitivity region (p.529–530). Creation verbs are non-prototypically transitive — the object does not exist at the beginning of the event to "undergo its effects." This is a correct prediction: creation verb objects cross-linguistically show atypical case marking (e.g., pseudo-cleft asymmetry).
Full pipeline: see subject → OBLIQUE (not NOM/ERG). The see-subject has sentience but no instigation, so it falls outside the NOM/ERG region. Grimm's system predicts non-canonical case for perception verb subjects cross-linguistically.
Full pipeline: die subject (unaccusative) → ACC/ABS. The sole argument of die maps to the patient region (no agentivity, exPersBeginning). In an ergative system this → ABS (= intransitive subject).