Karttunen 1971: Implicative Verbs @cite{karttunen-1971} #
Implicative Verbs. Language 47(2): 340–358.
Core Contribution #
Complement-taking predicates that take infinitival complements divide into implicative and non-implicative classes based on complement entailment:
- Implicative (manage, remember, bother): "managed to VP" → VP; "didn't manage to VP" → ¬VP. Two-way entailment.
- Non-implicative (hope, want, intend): no complement entailment.
- Negative implicatives (fail, forget): entail ¬complement.
- Sufficient-only (force, cause): affirmative → complement, but negation ↛ ¬complement.
- Necessary-only (be able, possible): negation → ¬complement, but affirmative ↛ complement.
Historical Context #
Karttunen's 2×2 classification (necessary × sufficient) was the original
descriptive taxonomy. The modern consensus (@cite{nadathur-2023}) derives
the entailment patterns from causal structure rather than from
presuppositional schemas. The theory layer (Causation/Implicative.lean)
implements the modern causal analysis; this study file preserves
Karttunen's original classification and bridges it to the modern types.
Key differences from the modern analysis:
- Karttunen treats the entailment as arising from a presupposition that v(S) is a nec/suf condition for S. Nadathur derives it from causal sufficiency in a structural equation model.
- Karttunen's classification ignores aspect. Nadathur shows that be able is aspect-governed (perfective triggers entailment, imperfective doesn't).
- Karttunen groups force/cause/make together (ex. 56) as having the same entailment pattern (sufficient-only). Nadathur & Lauer show they have the same entailment pattern but different truth conditions: make/force assert causal sufficiency, while cause asserts causal necessity. This difference surfaces in overdetermination scenarios.
Karttunen's schemas: - (37) nec + suf: PRESUP v(S) is nec+suf for S. PROP v(S). - (41) nec + suf (neg): same but for ¬S. - (54) nec only: PRESUP v(S) is nec for S. PROP v(S). - (59) suf only: PRESUP v(S) is suf for S. PROP v(S). - neither: no complement entailment.
Karttunen's descriptive classification of complement-entailing predicates as a 2×2: necessary × sufficient × polarity.
This is the historical taxonomy from the 1971 paper. The modern
causal analysis uses ImplicativeClass (which adds aspectGoverned)
and CausativeBuilder (which distinguishes causal mechanisms).
- isSufficient : Bool
v(S) is sufficient for S: affirmative entails complement.
- isNecessary : Bool
v(S) is necessary for S: negation entails ¬complement.
- polarity : Nadathur2024.Implicative.ImplicativeBuilder
Positive (manage: entails S) vs negative (fail: entails ¬S).
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- Phenomena.Complementation.Studies.Karttunen1971.instBEqKarttunenClass.beq x✝¹ x✝ = false
Instances For
Equations
- Phenomena.Complementation.Studies.Karttunen1971.KarttunenClass.manage = { isSufficient := true, isNecessary := true, polarity := Nadathur2024.Implicative.ImplicativeBuilder.positive }
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- Phenomena.Complementation.Studies.Karttunen1971.KarttunenClass.fail = { isSufficient := true, isNecessary := true, polarity := Nadathur2024.Implicative.ImplicativeBuilder.negative }
Instances For
Sufficient only: "forced X to VP" → VP; "didn't force" ↛ ¬VP.
Equations
- Phenomena.Complementation.Studies.Karttunen1971.KarttunenClass.force = { isSufficient := true, isNecessary := false, polarity := Nadathur2024.Implicative.ImplicativeBuilder.positive }
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Sufficient only, negative: "prevented X from VP-ing" → ¬VP.
Equations
- Phenomena.Complementation.Studies.Karttunen1971.KarttunenClass.prevent = { isSufficient := true, isNecessary := false, polarity := Nadathur2024.Implicative.ImplicativeBuilder.negative }
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Necessary only: "wasn't able to VP" → ¬VP; "was able" ↛ VP.
Equations
- Phenomena.Complementation.Studies.Karttunen1971.KarttunenClass.beAble = { isSufficient := false, isNecessary := true, polarity := Nadathur2024.Implicative.ImplicativeBuilder.positive }
Instances For
Neither: hope, want, intend.
Equations
- Phenomena.Complementation.Studies.Karttunen1971.KarttunenClass.hope = { isSufficient := false, isNecessary := false, polarity := Nadathur2024.Implicative.ImplicativeBuilder.positive }
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- k.isTwoWay = (k.isNecessary && k.isSufficient)
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- k.hasEntailment = (k.isNecessary || k.isSufficient)
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manage and fail differ only in polarity.
force and prevent differ only in polarity.
Convert KarttunenClass to ImplicativeClass (Nadathur 2023).
Note: aspectGoverned is always false because Karttunen's 1971
analysis does not account for aspect — a limitation the modern
analysis corrects.
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- One or more equations did not get rendered due to their size.
Instances For
Derive KarttunenClass from an ImplicativeBuilder (two-way cell).
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Map modern CausativeBuilder to the Karttunen cell that matches the
builder's entailment pattern (Karttunen's original criterion).
All positive causative builders (make, force, enable, cause) share the same Karttunen cell: sufficient-only. This is because:
- Affirmative "V-ed X to VP" → VP (all require the effect occurred)
- Negation "didn't V X to VP" ↛ ¬VP (effect might occur from other causes)
The modern insight of @cite{nadathur-lauer-2020} is that these verbs
differ in causal MECHANISM (sufficiency vs necessity) despite sharing
the same ENTAILMENT PATTERN. See cause_make_same_cell_different_mechanism.
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- One or more equations did not get rendered due to their size.
Instances For
cause and make have the same Karttunen entailment cell
(sufficient-only) despite having different causal mechanisms.
This is the central insight of @cite{nadathur-lauer-2020}: same
entailment pattern ≠ same truth conditions. The difference emerges
in overdetermination scenarios where makeSem is true but causeSem
is false (see builders_truth_conditionally_distinct in Builder.lean).
All positive causative builders map to KarttunenClass.force
(Karttunen's sufficient-only cell).
Verify that Fragment verb entries carry the correct annotations, matching Karttunen's inventory (ex. 2, p.341).
happen is a raising verb, not subject-control. "It happened to rain" is grammatical — the matrix subject receives no theta role from happen. Karttunen (§9) describes happen's presupposition as chance-dependence, but does not discuss its syntactic control type.
dare and bother have both presupposition (occasion verbs) AND implicative entailment: "John dared to speak" presupposes risk AND entails "John spoke." These are compatible per Karttunen §9.
The key diagnostic: factives preserve complement presupposition under negation; implicatives reverse the complement entailment.
"John didn't realize he had no money" — still presupposes "he had no money."
"John didn't manage to solve it" — entails "he didn't solve it."
The grounding chain: KarttunenClass → ImplicativeBuilder → causal semantics → complement entailment.
For sufficient-positive classes, the chain is:
`KarttunenClass.manage.polarity` = `.positive`
→ `ImplicativeBuilder.positive.toSemantics` = `manageSem`
→ `manage_entails_complement`: manageSem sc = true → complement true
These theorems derive the entailment from the classification,
not just re-export the theory-layer theorem.
A sufficient-positive KarttunenClass predicts complement truth via the polarity field's grounded semantics.
A sufficient-negative KarttunenClass predicts complement falsity.
Instantiation: KarttunenClass.manage entails complement truth.
Instantiation: KarttunenClass.fail entails complement falsity.
Double negation cancellation is a signature property of implicative verbs. Karttunen's examples:
- (13) "John didn't remember not to lock his door" → "John locked his door."
- (40a) "John didn't forget to lock his door" → (40d) "John locked his door."
The current causal semantics models the *positive* direction
(manageSem → complement true) and the *negative* direction
(failSem → complement false) separately. Full double negation
— where matrix negation and complement negation interact to yield
a positive entailment — would require compositional negation over
the causal model, which is not yet formalized.
What we CAN verify: the two directions (positive entailment, negative
entailment) are separately grounded, and two-way KarttunenClasses
predict both directions.
Two-way classes predict entailment in BOTH directions: the positive polarity grounds the affirmative direction, the negative polarity grounds the negation direction.
All four cells of the 2×2 are populated by Fragment entries.
be able is NOT a lexical implicative — it has no implicativeBuilder.
The actuality entailment is aspect-governed (@cite{nadathur-2023}):
perfective "was able to VP" → VP; imperfective "was able to VP" ↛ VP.
Karttunen (§11) notes these verbs are ambiguous between implicative
and non-implicative readings.
be able takes infinitival complement with subject control. "He was able to leave" — the subject has the ability (theta role).
Tension with Noonan's Reality Status #
@cite{noonan-2007} classifies achievement CTPs (*manage*, *fail*) as
IRREALIS because they take infinitival complements. But Karttunen shows
these verbs ENTAIL complement truth — semantically realis. Complement
*form* (irrealis) and complement *entailment* (realis) diverge for
implicative verbs.