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Semantics of Case

Grimm, S. (2011). Morphology, 21, 515–544

Grimm recasts Dowty's proto-role entailments as four privative agentivity properties and four persistence properties, whose product orders participant types by semantic prominence, and treats a case as a connected region of that lattice. This file supplies the paper's placements on the lattice of Semantics/ArgumentStructure/ and reads its predictions off the interval characterizations of the case regions.

Implementation notes

The paper's remarks on differential object marking, deferred to Grimm (2005), and on the size of the nominative or ergative region in a given language are not formalized. Definiteness is the paper's three-step hierarchy (14), the referring feature being the one that entails existence. The entailments of a node, which subject selection counts, are its agentivity and persistence features (entailmentCount). The subject of kiss dominates its object at any common persistence level, since kissing changes neither (kiss_subject_dominates).

Errata

Subject selection picks "the argument which has the greater number of entailments, or equivalently, the dominant or higher position in the lattice structure" (p. 527). The two are not equivalent: dominance implies the greater count (entailmentCount_strictMono), but two nodes of the lattice with different counts may be incomparable (exists_entailmentCount_lt_incomparable), so the count selects where dominance does not.

References

Grimm 2011, Semantics of Case
Dowty 1991, Thematic Proto-Roles and Argument Selection formalized
Tsunoda 1985, Remarks on transitivity
Grimm 2005, The Lattice of Case and Agentivity
Fillmore 1968, The Case for Case

The canonical verb chain, section 2.2

Each verb adds one property to the last: a chain from the bottom to the top of the agentivity lattice, the paper's illustration that height is degree of agentivity.

theorem canonical_verb_chain L68–73

sitAgentivity ⊂ knowAgentivity ∧ knowAgentivity ⊂ discoverAgentivity ∧ discoverAgentivity ⊂ lookAtAgentivity ∧ lookAtAgentivity ⊂ assassinateAgentivity

Built from , , , ,

L75–78

L80–81

Dowty's Proto-Patient entailments and persistence, section 2.1

Grimm relates two of Dowty's Proto-Patient entailments to persistence (EntailmentProfile.Admits): a change of state excludes qualitative persistence at the end, and dependent existence, which conflates creation and destruction, excludes existential persistence at both ends. Dowty counts coming into existence as a change of state (his (30a)) and attributes all of (28) to the object of build, so read literally the correspondences exclude the creation level, existential persistence (end), at which Grimm places the objects of verbs of creation.

The object of build, with Dowty's entailments, admits only total non-persistence and existential persistence (beginning), not the creation level Grimm assigns it.

theorem build_object_admits_iff L92–97

(l : ArgumentStructure.PersistenceLevel) :

(Dowty1991.entailed Dowty1991.Examples.buildObject).Admits l ↔ l = ArgumentStructure.PersistenceLevel.totalNonPersistence ∨ l = ArgumentStructure.PersistenceLevel.exPersBeginning

Argument ranges and subject selection, section 2.3

The argument whose node dominates the other's is selected as subject. The agent of kill need only instigate, so natural forces such as electricity and eventive nominals such as the explosion are acceptable subjects, and so is every node above them: agents are upward closed. The patient of hit canonically changes qualitatively, but the object of the conative hit at is unaffected and an object may happen to be destroyed, while an entity that does not exist when the event begins cannot be hit: patients are closed downward to the existence of the entity.

Everything above the minimal instigator is in the nominative or ergative region: the range of the subject of kill, from the interval characterization of that region.

theorem kill_subject_range L108–112

{n : ArgumentStructure.ParticipantType} (h : ArgumentStructure.minimalInstigator ≤ n) :

n.toCaseRegion = ArgumentStructure.CaseRegion.nomErg

L114–116

The persistence levels an entity that exists when the event begins can have are the up-set of existential persistence (beginning): the range of the patient of hit and, in section 3, the persistence axis of the transitivity region.

theorem transitive_region_eq_Ici L118–123

(n : ArgumentStructure.ParticipantType) :

n.InTransitiveRegion ↔ ArgumentStructure.PersistenceLevel.exPersBeginning ≤ n.2

The pseudo-cleft (5) presupposes that its object exists when the event begins: a destroyed object meets the presupposition, What John did to the table was ruin it, and a created one does not, *What John did to the table was build it.

theorem pseudoCleft_presupposition L125–133

{T : Type u_1} {Q : Type u_2} [LinearOrder T] [DecidableEq Q] {life run : NonemptyInterval T} {q : T → Q} :

(ArgumentStructure.PersistenceLevel.ofLifespan life run q = ArgumentStructure.PersistenceLevel.exPersBeginning → run.toProd.1 ∈ life) ∧ (ArgumentStructure.PersistenceLevel.ofLifespan life run q = ArgumentStructure.PersistenceLevel.exPersEnd → run.toProd.1 ∉ life)

The transitivity region and the effectiveness hierarchy, section 3

Tsunoda 1985's hierarchy, the paper's (8): resultative effective action verbs (break) above contact verbs (shoot) above pursuit verbs (search). The agent of the first two classes entails instigation and motion; the agent of pursuit adds sentience (Fig. 5).

L170–172

Along the hierarchy the patient moves away from the maximal patient: the patient of break is the maximal patient, that of shoot lies above it inside the transitivity region, and that of search outside it, while the agents stay in the nominative or ergative region.

theorem transitivity_hierarchy L174–184

Built from

L186–190

Core case marking systems, section 4

The maximal agent and patient map to the two core cases of either alignment (Fig. 6).

theorem pole_alignment L194–200

ArgumentStructure.maximalAgent.toCaseRegion.toAccusativeCase = Case.nom ∧ ArgumentStructure.maximalPatient.toCaseRegion.toAccusativeCase = Case.acc ∧ ArgumentStructure.maximalAgent.toCaseRegion.toErgativeCase = Case.erg ∧ ArgumentStructure.maximalPatient.toCaseRegion.toErgativeCase = Case.abs

Extensions of the dative, section 5.1

The recipient of geben (9) is consciously involved as a possessor and qualitatively changed in its possessions; the dative experiencer of the Urdu ghussa aana 'get angry' (10) is sentient and undergoes a psychological change; the second argument of danken and gratulieren undergoes caused possession in the cognitive realm and that of dienen and helfen a change through the benefit conferred. All three require sentience at qualitative persistence (beginning), the substrate's sentientNonInstigator.

L211–212

The recipient's node lies in the dative region (Fig. 7).

theorem recipient_dative L214–215

recipient.toCaseRegion = ArgumentStructure.CaseRegion.dative

Built from

The genitive/accusative alternation in Russian, section 5.2

Ivan ždët tramvaj (accusative) 'Ivan is waiting for the/a certain tram' against Ivan ždët tramvaja (genitive) 'Ivan is waiting for a tram', (12). The governed genitive marks the entity whose existence is not entailed, the bottom node of the lattice; the accusative region contains the node of existential persistence (beginning). An opacity-creating verb entails nothing for its object, so the noun phrase decides: a referring one exists when the event begins.

The object is in the accusative region iff the noun phrase refers, and otherwise at the bottom node of the governed genitive (12).

theorem genitive_accusative_alternation L243–248

(d : Definiteness) :

((opacityObject d).toCaseRegion = ArgumentStructure.CaseRegion.accAbs ↔ d.Referring) ∧ (opacityObject d = ⊥ ↔ ¬d.Referring)

Built from , ,

L250–252