@cite{boneh-doron-2013} — Hab and Gen in the Expression of Habituality

In Genericity (Mari, Beyssade, Del Prete eds.), OUP, Oxford Studies in Theoretical Linguistics 43.

Core Claim

HAB and GEN are distinct covert operators, not a single operator with different parameters. They share the same quantificational skeleton (covertQ in CovertQuantifier.lean) but differ in:

1. Quantificational force: HAB is a modalized existential quantifier over sums of events; GEN is a modalized universal quantifier.
2. Restrictor requirement: GEN requires an explicit restrictor (e.g., "after dinner" in ex. (4a)); HAB does not — it uses INIT to anchor to an initiating event.
3. Structural position: HAB sits low as a VP adverb selected by AspP; GEN sits high in MoodP (parallel to would).

The chapter provides English evidence from three habitual verb forms: the simple past tense form, the periphrastic used to, and would.

English Habitual Forms (Table (41))

Form	Viewpoint aspect	Perspective
simple form	imperfective/perfective	internal/retrospective
used to	imperfective	retrospective
would	imperfective	internal

Connection to Existing Infrastructure

• CovertQuantifier.lean: shared skeleton covertQ; gen_is_covertQ and hab_is_covertQ show both operators instantiate it.
• Aspect/Core.lean: ViewpointAspectB — the aspectCompatibility bridge connects B&D's Table (41) to the aspectual infrastructure.
• DelPrete2013.lean: Del Prete's Same-Object Effect (SOE) is the Italian analogue of the same-object readings in B&D's exx. (4b), (6b), (7b). The sameObjectParallel theorem makes this connection explicit.

inductive Phenomena.Generics.Studies.BonehDoron2013.QForce : Type

Quantificational force of a covert operator.

@cite{boneh-doron-2013} §6.2.1: HAB is a "modalized existential quantifier over sums of events"; GEN is a "modalized universal quantifier" (Krifka et al. 1995).

• existential : QForce

  Existential: HAB ∃-quantifies over event sums via ITER.

• universal : QForce

  Universal: GEN ∀-quantifies over individuals/events meeting the restrictor.

instance Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqQForce : DecidableEq QForce

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqQForce x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Generics.Studies.BonehDoron2013.instReprQForce : Repr QForce

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instReprQForce = { reprPrec := Phenomena.Generics.Studies.BonehDoron2013.instReprQForce.repr }

def Phenomena.Generics.Studies.BonehDoron2013.instReprQForce.repr : QForce → ℕ → Std.Format

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def Phenomena.Generics.Studies.BonehDoron2013.instBEqQForce.beq : QForce → QForce → Bool

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instBEqQForce.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Generics.Studies.BonehDoron2013.instBEqQForce : BEq QForce

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instBEqQForce = { beq := Phenomena.Generics.Studies.BonehDoron2013.instBEqQForce.beq }

structure Phenomena.Generics.Studies.BonehDoron2013.CovertQConfig : Type

Configuration for a covert quantifier, recording the structural differences between GEN and HAB beyond the shared covertQ skeleton.

• force : QForce

  Quantificational force (existential vs universal)

• requiresExplicitRestrictor : Bool

  Whether the operator requires an explicit restrictor in the clause. GEN requires one (e.g., "after dinner"); HAB uses INIT instead.

• isModal : Bool

  Whether the operator is modalized (references a modal base MB). Both GEN and HAB reference MB in their denotations (eqs. (13), (21)).

instance Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqCovertQConfig : DecidableEq CovertQConfig

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqCovertQConfig = Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqCovertQConfig.decEq

def Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqCovertQConfig.decEq (x✝ x✝¹ : CovertQConfig) : Decidable (x✝ = x✝¹)

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def Phenomena.Generics.Studies.BonehDoron2013.instReprCovertQConfig.repr : CovertQConfig → ℕ → Std.Format

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instance Phenomena.Generics.Studies.BonehDoron2013.instReprCovertQConfig : Repr CovertQConfig

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instReprCovertQConfig = { reprPrec := Phenomena.Generics.Studies.BonehDoron2013.instReprCovertQConfig.repr }

def Phenomena.Generics.Studies.BonehDoron2013.instBEqCovertQConfig.beq : CovertQConfig → CovertQConfig → Bool

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• Phenomena.Generics.Studies.BonehDoron2013.instBEqCovertQConfig.beq x✝¹ x✝ = false

instance Phenomena.Generics.Studies.BonehDoron2013.instBEqCovertQConfig : BEq CovertQConfig

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instBEqCovertQConfig = { beq := Phenomena.Generics.Studies.BonehDoron2013.instBEqCovertQConfig.beq }

def Phenomena.Generics.Studies.BonehDoron2013.genConfig : CovertQConfig

GEN configuration: universal, requires explicit restrictor, modal.

Equations

• Phenomena.Generics.Studies.BonehDoron2013.genConfig = { force := Phenomena.Generics.Studies.BonehDoron2013.QForce.universal, requiresExplicitRestrictor := true, isModal := true }

def Phenomena.Generics.Studies.BonehDoron2013.habConfig : CovertQConfig

HAB configuration: existential, no explicit restrictor needed, modal.

Equations

• Phenomena.Generics.Studies.BonehDoron2013.habConfig = { force := Phenomena.Generics.Studies.BonehDoron2013.QForce.existential, requiresExplicitRestrictor := false, isModal := true }

theorem Phenomena.Generics.Studies.BonehDoron2013.gen_hab_distinct : genConfig ≠ habConfig

GEN and HAB have distinct configurations despite sharing covertQ.

theorem Phenomena.Generics.Studies.BonehDoron2013.gen_hab_modal_agreement : genConfig.isModal = habConfig.isModal

GEN and HAB agree on modality (both are modalized) but differ on quantificational force and restrictor requirement.

theorem Phenomena.Generics.Studies.BonehDoron2013.gen_hab_differ_on_force_and_restrictor : genConfig.force ≠ habConfig.force ∧ genConfig.requiresExplicitRestrictor ≠ habConfig.requiresExplicitRestrictor

inductive Phenomena.Generics.Studies.BonehDoron2013.HabitualForm : Type

The three English verb forms that express habituality.

@cite{boneh-doron-2013} §6.1, ex. (1): "In the good old days, people dressed/used to dress/would dress elegantly to go to the opera."

• simpleForm : HabitualForm

  Simple past tense form: "people dressed elegantly."

• usedTo : HabitualForm

  Periphrastic used to: "people used to dress elegantly."

• would : HabitualForm

  Periphrastic would: "people would dress elegantly."

instance Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqHabitualForm : DecidableEq HabitualForm

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instDecidableEqHabitualForm x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Generics.Studies.BonehDoron2013.instReprHabitualForm : Repr HabitualForm

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instReprHabitualForm = { reprPrec := Phenomena.Generics.Studies.BonehDoron2013.instReprHabitualForm.repr }

def Phenomena.Generics.Studies.BonehDoron2013.instReprHabitualForm.repr : HabitualForm → ℕ → Std.Format

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instance Phenomena.Generics.Studies.BonehDoron2013.instBEqHabitualForm : BEq HabitualForm

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• Phenomena.Generics.Studies.BonehDoron2013.instBEqHabitualForm = { beq := Phenomena.Generics.Studies.BonehDoron2013.instBEqHabitualForm.beq }

def Phenomena.Generics.Studies.BonehDoron2013.instBEqHabitualForm.beq : HabitualForm → HabitualForm → Bool

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• Phenomena.Generics.Studies.BonehDoron2013.instBEqHabitualForm.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.Generics.Studies.BonehDoron2013.admitsPerfective : HabitualForm → Bool

Whether a habitual form admits perfective aspect.

@cite{boneh-doron-2013} Table (41): only the simple form admits perfective; the periphrastic forms are imperfective only.

Equations

• Phenomena.Generics.Studies.BonehDoron2013.admitsPerfective Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.simpleForm = true
• Phenomena.Generics.Studies.BonehDoron2013.admitsPerfective Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.usedTo = false
• Phenomena.Generics.Studies.BonehDoron2013.admitsPerfective Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.would = false

def Phenomena.Generics.Studies.BonehDoron2013.hasRetrospective : HabitualForm → Bool

Whether a habitual form has a retrospective perspective.

@cite{boneh-doron-2013} Table (41): the simple form can be either, used to is retrospective, would is internal (not retrospective).

Equations

• Phenomena.Generics.Studies.BonehDoron2013.hasRetrospective Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.simpleForm = true
• Phenomena.Generics.Studies.BonehDoron2013.hasRetrospective Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.usedTo = true
• Phenomena.Generics.Studies.BonehDoron2013.hasRetrospective Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.would = false

def Phenomena.Generics.Studies.BonehDoron2013.requiresActualization : HabitualForm → Bool

Whether a habitual form requires actualization (habit must be instantiated by actual episodes in the world).

@cite{boneh-doron-2013} §6.3.2, ex. (42): used to requires actualization; the simple form and would do not.

Equations

• Phenomena.Generics.Studies.BonehDoron2013.requiresActualization Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.simpleForm = false
• Phenomena.Generics.Studies.BonehDoron2013.requiresActualization Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.usedTo = true
• Phenomena.Generics.Studies.BonehDoron2013.requiresActualization Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.would = false

def Phenomena.Generics.Studies.BonehDoron2013.aspectCompatibility : HabitualForm → Semantics.Tense.Aspect.Core.ViewpointAspectB → Bool

Which viewpoint aspects each habitual form is compatible with, connecting B&D's Table (41) to ViewpointAspectB in Aspect/Core.lean.

The simple form admits both imperfective and perfective; the periphrastic forms are imperfective only.

Equations

• Phenomena.Generics.Studies.BonehDoron2013.aspectCompatibility Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.simpleForm x✝ = true
• Phenomena.Generics.Studies.BonehDoron2013.aspectCompatibility Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.usedTo Semantics.Tense.Aspect.Core.ViewpointAspectB.imperfective = true
• Phenomena.Generics.Studies.BonehDoron2013.aspectCompatibility Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.usedTo Semantics.Tense.Aspect.Core.ViewpointAspectB.perfective = false
• Phenomena.Generics.Studies.BonehDoron2013.aspectCompatibility Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.would Semantics.Tense.Aspect.Core.ViewpointAspectB.imperfective = true
• Phenomena.Generics.Studies.BonehDoron2013.aspectCompatibility Phenomena.Generics.Studies.BonehDoron2013.HabitualForm.would Semantics.Tense.Aspect.Core.ViewpointAspectB.perfective = false

theorem Phenomena.Generics.Studies.BonehDoron2013.periphrastic_reject_perfective : aspectCompatibility HabitualForm.usedTo Semantics.Tense.Aspect.Core.ViewpointAspectB.perfective = false ∧ aspectCompatibility HabitualForm.would Semantics.Tense.Aspect.Core.ViewpointAspectB.perfective = false

Periphrastic forms reject perfective aspect.

theorem Phenomena.Generics.Studies.BonehDoron2013.simple_both_aspects : aspectCompatibility HabitualForm.simpleForm Semantics.Tense.Aspect.Core.ViewpointAspectB.imperfective = true ∧ aspectCompatibility HabitualForm.simpleForm Semantics.Tense.Aspect.Core.ViewpointAspectB.perfective = true

The simple form accepts both viewpoint aspects.

structure Phenomena.Generics.Studies.BonehDoron2013.EnglishDatum : Type

An English habituality datum.

• sentence : String
• form : HabitualForm
• felicitous : Bool
• operator : String

  Which operator the chapter's analysis assigns to this reading. Under B&D's proposal, the simple form typically involves Hab, would involves Gen, and used to involves Hab + aspectual marking.

• exNumber : String

instance Phenomena.Generics.Studies.BonehDoron2013.instReprEnglishDatum : Repr EnglishDatum

Equations

• Phenomena.Generics.Studies.BonehDoron2013.instReprEnglishDatum = { reprPrec := Phenomena.Generics.Studies.BonehDoron2013.instReprEnglishDatum.repr }

def Phenomena.Generics.Studies.BonehDoron2013.instReprEnglishDatum.repr : EnglishDatum → ℕ → Std.Format

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def Phenomena.Generics.Studies.BonehDoron2013.maryCigaretteAfterDinner : EnglishDatum

Ex. (4a): "Mary smokes a cigarette after dinner" — GEN with explicit restrictor "after dinner". Felicitous because the restrictor supplies Gen's required restriction over events.

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def Phenomena.Generics.Studies.BonehDoron2013.maryCigarette : EnglishDatum

Ex. (4b): "#Mary smokes a cigarette" — No explicit restrictor, so Gen cannot apply. Hab applies but the singular indefinite "a cigarette" scopes over events, forcing a same-object reading (smoke the same cigarette repeatedly), which is infelicitous.

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def Phenomena.Generics.Studies.BonehDoron2013.flowerGrows : EnglishDatum

Ex. (6b): "A flower grows out behind the old shed" — singular indefinite under Hab forces a same-object reading: the same flower grows out repeatedly. This is the same-object phenomenon that @cite{del-prete-2013} calls the Same-Object Effect (SOE).

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def Phenomena.Generics.Studies.BonehDoron2013.maxKilledRabbit : EnglishDatum

Ex. (7b): "#Max killed a rabbit repeatedly" — singular indefinite under adverbial repeatedly forces same-object (same rabbit killed over and over), which is pragmatically absurd.

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def Phenomena.Generics.Studies.BonehDoron2013.wouldDressNoContext : EnglishDatum

Ex. (2c): "#In the good old days, people would dress elegantly" — would (Gen) is infelicitous even with a discourse context ("At the opera"). Gen requires an explicit in-sentence restrictor (e.g., a purpose clause "to go to the opera"), not just a contextual presupposition.

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def Phenomena.Generics.Studies.BonehDoron2013.wouldDressWithContext : EnglishDatum

Ex. (2d): "In the good old days, people would dress elegantly to go to the opera" — felicitous because "to go to the opera" provides the restrictor for Gen.

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def Phenomena.Generics.Studies.BonehDoron2013.sheWentByBus : EnglishDatum

Ex. (42a): "She went to work by bus" — simple form, TRUE even with a single episode. Can be read episodically or as a one-episode habit.

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def Phenomena.Generics.Studies.BonehDoron2013.sheWouldGoByBus : EnglishDatum

Ex. (42b): "She would go to work by bus" — would (GEN), TRUE even with a single episode. Gen is about what happens in normal worlds, not about actual iteration.

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def Phenomena.Generics.Studies.BonehDoron2013.sheUsedToGoByBus : EnglishDatum

Ex. (42c): "She used to go to work by bus" — used to, FALSE in single-episode context. Used to requires actualization: the habit must be instantiated by multiple actual episodes.

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def Phenomena.Generics.Studies.BonehDoron2013.usedToStand : EnglishDatum

Ex. (48a): "The London Bridge used to stand on the Thames" — used to (Hab) is compatible with individual-level predicates because Hab is an aspectual operator that selects for states.

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def Phenomena.Generics.Studies.BonehDoron2013.wouldStand : EnglishDatum

Ex. (48b): "*The London Bridge would stand on the Thames" — would (Gen) is incompatible with individual-level predicates when the subject is definite. Gen requires a restrictor, but a definite subject cannot serve as one, and "stand on the Thames" (individual-level) is incompatible with an episodic restrictor. Contrast with (47a), where the indefinite singular "a French teacher" provides Gen's restrictor.

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def Phenomena.Generics.Studies.BonehDoron2013.wouldKnowLatin : EnglishDatum

Ex. (3a)/(47a): "a French teacher would know Latin" — would (GEN) accepts an indefinite singular subject because Gen takes a nominal restrictor (the indefinite provides it). First introduced as (3a), discussed fully in §6.4 as (47a).

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def Phenomena.Generics.Studies.BonehDoron2013.usedToKnowLatin : EnglishDatum

Ex. (3b)/(47b): "*a French teacher used to know Latin" — used to rejects an indefinite singular subject. Used to involves Hab, which quantifies over events (not individuals). The indefinite singular "a French teacher" cannot serve as a restrictor for Hab's event quantification, unlike Gen which quantifies over individuals and can bind the indefinite as a nominal restrictor.

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def Phenomena.Generics.Studies.BonehDoron2013.englishData : List EnglishDatum

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theorem Phenomena.Generics.Studies.BonehDoron2013.restrictor_contrast : maryCigaretteAfterDinner.felicitous = true ∧ maryCigarette.felicitous = false

The restrictor contrast (4): "Mary smokes a cigarette after dinner" (✓) vs "#Mary smokes a cigarette" (✗). Gen requires an explicit restrictor; without one, Hab applies but the singular indefinite forces same-object.

theorem Phenomena.Generics.Studies.BonehDoron2013.would_restrictor_contrast : wouldDressNoContext.felicitous = false ∧ wouldDressWithContext.felicitous = true

The would restrictor contrast (2c-d): would (Gen) is infelicitous without an explicit in-sentence restrictor (2c), but felicitous with a purpose clause (2d). Same underlying mechanism as the (4a-b) contrast.

theorem Phenomena.Generics.Studies.BonehDoron2013.gen_restrictor_across_forms : maryCigaretteAfterDinner.felicitous = true ∧ maryCigarette.felicitous = false ∧ wouldDressWithContext.felicitous = true ∧ wouldDressNoContext.felicitous = false

The restrictor requirement is consistent across forms: both the simple form (4a-b) and would (2c-d) show Gen needs an explicit restrictor.

theorem Phenomena.Generics.Studies.BonehDoron2013.sameObjectParallel : flowerGrows.felicitous = true ∧ maxKilledRabbit.felicitous = false

The same-object effect (6b, 7b): singular indefinites under Hab force a same-object reading. When pragmatically implausible (7b), the sentence is infelicitous.

This is the English counterpart of @cite{del-prete-2013}'s SOE in Italian. Del Prete's "Gianni leggeva un libro di filosofia" (HAB blocked, SOE implausible) parallels B&D's "#Max killed a rabbit repeatedly."

theorem Phenomena.Generics.Studies.BonehDoron2013.actualization_contrast : sheWentByBus.felicitous = true ∧ sheWouldGoByBus.felicitous = true ∧ sheUsedToGoByBus.felicitous = false

The actualization contrast (42): simple form and would are true even with a single episode; used to requires actualized iteration.

theorem Phenomena.Generics.Studies.BonehDoron2013.actualization_matches_form : requiresActualization HabitualForm.usedTo = true ∧ requiresActualization HabitualForm.simpleForm = false ∧ requiresActualization HabitualForm.would = false

Actualization requirement matches function: used to requires actualization; simple form and would do not.

theorem Phenomena.Generics.Studies.BonehDoron2013.individual_level_contrast : usedToStand.felicitous = true ∧ wouldStand.felicitous = false

Individual-level predicate contrast (48): used to accepts individual- level predicates (it selects states); would rejects them when the subject is definite (Gen needs a restrictor the definite can't provide).

theorem Phenomena.Generics.Studies.BonehDoron2013.would_vs_usedTo_puzzle : wouldKnowLatin.felicitous = true ∧ usedToKnowLatin.felicitous = false

The would vs used to puzzle (3)/(47): would accepts an indefinite singular subject; used to does not. This follows from would involving Gen (which can bind the indefinite as a nominal restrictor) while used to involves Hab (which quantifies over events, not individuals).

theorem Phenomena.Generics.Studies.BonehDoron2013.would_usedTo_complementarity : wouldKnowLatin.felicitous = true ∧ wouldStand.felicitous = false ∧ usedToKnowLatin.felicitous = false ∧ usedToStand.felicitous = true

(47) and (48) together show that would's acceptability depends on whether Gen's restrictor can be filled: indefinite singular fills it (47a ✓), definite subject with individual-level predicate does not (48b ✗). Meanwhile used to is the mirror: rejects indefinite singular (47b ✗) but accepts individual-level predicates freely (48a ✓).

theorem Phenomena.Generics.Studies.BonehDoron2013.perfective_only_simple : admitsPerfective HabitualForm.simpleForm = true ∧ admitsPerfective HabitualForm.usedTo = false ∧ admitsPerfective HabitualForm.would = false

Only the simple form admits perfective aspect; periphrastic forms are imperfective only (Table (41)).

theorem Phenomena.Generics.Studies.BonehDoron2013.would_no_retrospective : hasRetrospective HabitualForm.would = false ∧ hasRetrospective HabitualForm.simpleForm = true ∧ hasRetrospective HabitualForm.usedTo = true

Would lacks retrospective perspective; the other forms have it (Table (41)).

theorem Phenomena.Generics.Studies.BonehDoron2013.shared_skeleton : (∀ (sits : List Semantics.Lexical.Noun.Kind.Generics.Situation) (normal : Semantics.Lexical.Noun.Kind.Generics.NormalcyPredicate) (restrictor : Semantics.Lexical.Noun.Kind.Generics.Restrictor) (scope : Semantics.Lexical.Noun.Kind.Generics.Scope), Semantics.Lexical.Noun.Kind.Generics.traditionalGEN sits normal restrictor scope = Semantics.Lexical.CovertQuantifier.covertQ sits (fun (s : Semantics.Lexical.Noun.Kind.Generics.Situation) => normal s && restrictor s) scope) ∧ ∀ (occs : List Semantics.Lexical.Verb.Habituals.Occasion) (characteristic : Semantics.Lexical.Verb.Habituals.Characteristic) (activity : Semantics.Lexical.Verb.Habituals.Activity), Semantics.Lexical.Verb.Habituals.traditionalHAB occs characteristic activity = Semantics.Lexical.CovertQuantifier.covertQ occs characteristic activity

Despite the structural differences, both operators instantiate covertQ. This is not in tension with distinctness — covertQ is the skeleton, and the two operators differ in what fills its parameters.

GEN: covertQ individuals (normal ∧ kind) property HAB: covertQ occasions characteristic activity

The skeleton is shared; the interpretation is different.