Karttunen (1971) #

Karttunen identifies the implicative verbs, manage, remember, bother, dare, happen and the others listed in (2), whose assertion commits the speaker to the complement and whose negation commits the speaker to its negation. He analyzes such a sentence as a presupposition–proposition pair: the proposition v(S) is what is asserted, negated or questioned, and the presupposition says what condition v(S) is for the complement. Schema (37) makes v(S) necessary and sufficient for S (manage), (41) necessary and sufficient for ¬S (fail, forget), (54) necessary only (be able, be possible), and (59) sufficient only (the positive verbs of (56), cause, make, have and force); the non-implicatives hope, want and try carry no such presupposition.

Each schema fixes an implication signature: (37) is +/−, (41) −/+, (54) ◦/− and (59) +/◦, and the negative verbs of (56), prevent and dissuade, are −/◦. The analysis is Implicative.sentence under the material interpretation of the conditions (Implicative.Interpretation.material), which gives the paper's entailment facts: double negation cancels as in (13) (manage_neg_neg_imp), and the one-way schemas and the non-implicatives leave the other direction open (force_neg_not_entails, beAble_not_entails, nonImplicative_not_entails). The English fragment's entries for the verbs of (2), (38), (44) and (56) carry the signatures of their schemas (implicative_eq) and so are presupposition triggers (isTrigger_of_mem_english), while its entries for the non-implicatives of (2) carry ◦/◦ (implicative_eq_bot).

Implementation notes #

Karttunen states (59) for the positive verbs of (56) only. The negative ones are read with the matching presupposition, v(S) sufficient for ¬S.

References #

[Kar71a]

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theorem Karttunen1971a.manage_neg_neg_imp {W : Type u_1} {v S : W → Prop} {w : W} (hs : (-Implicative.sentence (Implicative.Interpretation.material W) { positive := ↑Polarity.positive, negative := ↑Polarity.negative } v fun (w : W) => ¬S w) w = 1) :

S w

Double negation cancels, so that John didn't remember not to lock his door commits the speaker to John locked his door (13).

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theorem Karttunen1971a.force_neg_not_entails :

∃ (v : Unit → Prop) (S : Unit → Prop), (-Implicative.sentence (Implicative.Interpretation.material Unit) { positive := ↑Polarity.positive, negative := ⊥ } v S) () = 1 ∧ S ()

(58) John didn't force Mary to stay home leaves open whether she stayed.

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theorem Karttunen1971a.beAble_not_entails :

∃ (v : Unit → Prop) (S : Unit → Prop), Implicative.sentence (Implicative.Interpretation.material Unit) { positive := ⊥, negative := ↑Polarity.negative } v S () = 1 ∧ ¬S ()

(55) John was able to come leaves open whether he came.

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theorem Karttunen1971a.nonImplicative_not_entails :

(∃ (v : Unit → Prop) (S : Unit → Prop), Implicative.sentence (Implicative.Interpretation.material Unit) ⊥ v S () = 1 ∧ ¬S ()) ∧ ∃ (v : Unit → Prop) (S : Unit → Prop), (-Implicative.sentence (Implicative.Interpretation.material Unit) ⊥ v S) () = 1 ∧ S ()

A non-implicative, whose signature ◦/◦ gives it no presupposition, commits the speaker to nothing about its complement in either polarity (5).

The English lexicon #

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def Karttunen1971a.english :

List (Verb × NaturalLogic.ImplicationSignature)

The English fragment's entries for the implicatives of (2), with the signature of schema (37), for the negative implicatives of (38), with that of (41), for be able of (44), with that of (54), and for the verbs of (56), with that of (59) or its negative counterpart, as far as the fragment covers the lists. Its get is the causative sense, its avoid takes a noun phrase, and it has no dissuade.

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