[Mic04]: Type Shifting in Construction Grammar

Aspectual coercion without interpolated coercion operators: constructions denote semantic types, and the override principle — "if a lexical item is semantically incompatible with its morphosyntactic context, the meaning of the lexical item conforms to the meaning of the structure in which it is embedded" ((20)) — resolves mismatches in favor of the construction. Concord constructions denote the type they select ((27)); shift constructions denote a different one ((28)); both perform implicit type-shifting via the override, and only shift constructions shift explicitly (Table 3).

Main declarations

• Michaelis2004.inchoativeAddition, onsetSelection, conformToActivity: the reconciliation operators
• Michaelis2004.frameAdverbial (concord, Figure 5) and Michaelis2004.progressive (shift, Figure 6), meaning poles their composition rules
• Michaelis2004.frame_adverbial_activity_ambiguity: the two readings of ex. (41), derived from the two operators
• Michaelis2004.progressive_stativizes: progressive predications denote states whatever the complement's Aktionsart

Reconciliation operators

The override principle repairs a type mismatch by one of the paper's reconciliation operations on the input's aspectual representation.

def Michaelis2004.inchoativeAddition (p : Features.AspectualProfile) : Features.AspectualProfile

The addition operator under inchoative construal (§5.1.2): a change is added to the causal representation, so a state yields the achievement of its onset — "They were bored in a minute" denotes the onset of boredom — and an activity a bounded accomplishment. Other types are left as they are.

Equations

• Michaelis2004.inchoativeAddition p = if p.dynamicity = Features.Dynamicity.stative then Features.achievementProfile else if p = Features.activityProfile then Features.accomplishmentProfile else p

def Michaelis2004.onsetSelection (p : Features.AspectualProfile) : Features.AspectualProfile

The selection operator (§5.1.2): the onset phase of a durative situation is selected, an achievement — ex. (41)'s reading on which the frame measures the delay before the program began to air.

Equations

• Michaelis2004.onsetSelection p = if p.duration = Features.Duration.durative then Features.achievementProfile else p

def Michaelis2004.reconciliation : List (Features.AspectualProfile → Features.AspectualProfile)

The reconciliation operators available to the frame adverbial.

Equations

• Michaelis2004.reconciliation = [Michaelis2004.inchoativeAddition, Michaelis2004.onsetSelection]

def Michaelis2004.conformToActivity : Features.AspectualProfile → Features.AspectualProfile

The progressive's complement is inherently processual (§5.2.1): the override conforms any input to the activity type — states via the addition of hold and an effector to their causal representation, telic events via their processual construal.

Equations

• Michaelis2004.conformToActivity x✝ = Features.activityProfile

The frame adverbial construction (Figure 5, concord)

def Michaelis2004.frameAdverbialRule : ConstructionGrammar.CompositionRule Features.AspectualProfile

The frame adverbial's composition rule: the within frame demands a telic event and the construct denotes that same type.

Equations

• Michaelis2004.frameAdverbialRule [p] = if p.telicity = Features.Telicity.telic then some p else none
• Michaelis2004.frameAdverbialRule x✝ = none

def Michaelis2004.frameAdverbial : ConstructionGrammar.Construction (ConstructionGrammar.CompositionRule Features.AspectualProfile)

The frame adverbial construction (Figure 5): an in-headed adjunct added to the verbal valence.

Equations

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

The progressive construction (Figure 6, shift)

def Michaelis2004.progressiveRule : ConstructionGrammar.CompositionRule Features.AspectualProfile

The progressive's composition rule: an activity complement yields the state holding during the activity's interval, by selection of an intermediate rest in its temporal representation.

Equations

• Michaelis2004.progressiveRule [p] = if p = Features.activityProfile then some Features.stateProfile else none
• Michaelis2004.progressiveRule x✝ = none

def Michaelis2004.progressive : ConstructionGrammar.Construction (ConstructionGrammar.CompositionRule Features.AspectualProfile)

The progressive construction (Figure 6): auxiliary be with a participial complement whose subject unifies with the auxiliary's — an instance of [KF99]'s coinstantiation construction.

Equations

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

theorem Michaelis2004.progressive_coinstantiation : ConstructionGrammar.refGroupCount progressive.form = 1

Figure 6's raising property: the subject of be and the complement's subject form one coreference group, the coinstantiation pattern.

Concord vs. shift ((27), (28))

def Michaelis2004.PreservesType (r : ConstructionGrammar.CompositionRule Features.AspectualProfile) : Prop

A unary rule preserves type when its output type is its input's — (27)'s concord constructions; (28)'s shift constructions fail it.

Equations

• Michaelis2004.PreservesType r = ∀ (p q : Features.AspectualProfile), r [p] = some q → q = p

theorem Michaelis2004.frameAdverbial_concord : PreservesType frameAdverbialRule

The frame adverbial is a concord construction: it denotes the telic event type it selects.

theorem Michaelis2004.progressive_shift : ¬PreservesType progressiveRule

The progressive is a shift construction: it selects activities but denotes states.

Frame-adverbial predictions (§5.1.2)

theorem Michaelis2004.frame_adverbial_instantiation : frameAdverbialRule.override reconciliation [Features.accomplishmentProfile] = [Features.accomplishmentProfile]

"She solved the problem in ten minutes" (Figure 5's instantiation): a telic complement composes directly, with no coercion ambiguity.

theorem Michaelis2004.frame_adverbial_coerces_state : frameAdverbialRule.override reconciliation [Features.stateProfile] = [Features.achievementProfile]

Ex. (30), "They were bored in a minute": the stative input conforms by inchoative construal — the onset of boredom, an achievement.

theorem Michaelis2004.frame_adverbial_activity_ambiguity : frameAdverbialRule.override reconciliation [Features.activityProfile] = [Features.accomplishmentProfile, Features.achievementProfile]

Ex. (41), "My radio program ran in less than four minutes": an activity input is genuinely ambiguous — inchoative addition yields the accomplishment reading (the frame measures the running time), onset selection the achievement reading (the frame measures the delay before airing) — [dS98]'s observation, derived from the operator inventory.

Progressive predictions (§5.2.1)

theorem Michaelis2004.progressive_explicit : progressiveRule [Features.activityProfile] = some Features.stateProfile

"We were playing cards" (Figure 6's explicit shift): an activity complement yields a state directly.

theorem Michaelis2004.progressive_coerces_state : progressiveRule.override [conformToActivity] [Features.stateProfile] = [Features.stateProfile]

Exx. (31), (42)–(44), "We were living in Boulder": a stative complement conforms to the activity type and the predication is again a state — the "temporary state" reading.

theorem Michaelis2004.progressive_coerces_telic : progressiveRule.override [conformToActivity] [Features.accomplishmentProfile] = [Features.stateProfile]

"They were baking a cake": a telic complement is construed as its process, so the culmination is not entailed.

theorem Michaelis2004.progressive_stativizes (p : Features.AspectualProfile) : progressiveRule.override [conformToActivity] [p] = [Features.stateProfile]

Progressive predications denote states whatever the Aktionsart of the complement (§5.2.1): the apparent paradox of a stativizing construction accepting stative input dissolves under the override.