Firstly, let us establish how the structure of sentences with negative concord would look on a nonnegative approach to the meaning of neg-words, assuming their licensing is syntactic and reduces to an application of Agree (Chomsky 2001). If the internal argument carries an unvalued polarity feature, [Σ:_] (Laka 1990), and the negation marker a valued one, [Σ:¬], then the fragment answer in (2) would have the simplified structure in (11). To be explicit, I assume, with Merchant (2004); Watanabe (2004); Weir (2020), the movement approach to fragment answers, noting in passing that the issue is not settled (see Griffiths et al. 2023 for a recent discussion). Following the valuation of the polarity feature, the NCI is fronted to a left-peripheral position, and the material to its right is elided.6

Regardless of how one analyses feature valuation (i.e. as copying, feature sharing, feature union etc.), the ellipsis remnant in (11), by virtue of morphologically reflecting an Agree dependency with a goal internal to the ellipsis site, unambiguously identifies the presence of that goal, allowing ellipsis to be recovered even in the presence of a polarity mismatch. It is this featural dependency between the remnant and negation that sets the negative fragment answer apart from the nonnegative ones, as I discuss in §4.2 below.

To lend credence to the idea that agreement, broadly construed, is significant for the recoverability of elided material, it would now be instructive to abstract away from negative concord and NCI licensing and view the structure in (11) in a generalised form. This is shown in (12) without reference to any particular linguistic phenomenon.

If [F:α] in (12) is a semantically contentful feature, then its appearance on a goal properly included in the ellipsis site amounts to a semantic mismatch between the antecedent proposition and the elided proposition. As I show directly below, this configuration characterises such routinely available varieties of ellipsis as VP-ellipsis, NP-ellipsis and sprouting.

Example (13) below, adapted from Merchant (2013a: 539, ex. 4a), involves a number mismatch in the antecedent and ellipsis site.

The singular-plural mismatch between the antecedent and the ellipsis site in (13) is a genuine semantic mismatch from the point of view of e-givenness, since the two propositions (or, rather, their F-closures, see Merchant 2001) are not in a mutual-entailment relation. Whilst the existence of several minibars entails the existence of one, the opposite is not true. Other mechanisms of ensuring semantic identity in the face of an apparent φ-feature mismatch, such as Referential Parallelism (Fox 2000), also fail, since the mismatching singular and plural NPs do not have the same referent.

The Russian example (14) illustrates the same mismatch but one that involves an agreeing lexical verb rather than an auxiliary. Again, as above, the two propositions are not in a mutual entailment relation: the reception of one invitation does not entail the reception of multiple invitations.

The relevant configuration is the desired one irrespective of the particular analysis of (14) in terms of argument ellipsis, represented in (15), or verb-stranding VP-ellipsis, represented in (16).7

In (15) representing the argument-ellipsis analysis, the singular neuter morphology on the finite verb prishlo ‘came’ in the remnant allows for the identification of the singular neuter NP priglashenie ‘invitation’ in the ellipsis site, making it recoverable. The same applies to the analysis in (16), with the main difference being the size of the elided constituent.

We have seen that the presence of overt φ-features on a valued clausal probe in the ellipsis remnant aids in recovering its valuer in the ellipsis site even in the face of a semantic mismatch in number. A minimally different case involves the interaction of agreement on prenominal modifiers and nominal ellipsis, illustrated in (17) below.

An agreeing possessive pronoun, moë ‘my.n’, in the ellipsis remnant overtly realises the singular neuter agreement features of the head noun priglashenie ‘invitation’ inside the elided NP ‘invitation to the ceremony’, notated by the Δ. As above, semantic identity is violated because of a lack of mutual entailment between the antecedent and the ellipsis site.

A final example of successful ellipsis resolution in the presence of a syntactic and semantic mismatch is presented by sprouting/sluicing, on the C′-deletion approach to clausal ellipsis (Heck & Müller 2007; Thoms 2010; Messick & Thoms 2016). Sluicing is the kind of ellipsis which involves a wh-expression in the ellipsis remnant — whose in (18) and (19) — while the rest of the clause is elided; in regular sluicing, the surviving wh-expression normally has an overt indefinite correlate in the antecedent. In sprouting, the antecedent contains no correlate. Example (18) below illustrates matrix sprouting, whereas example (19) illustrates embedded sprouting.

If finite declarative clauses are CPs, then the antecedent in (19) and (20) is a declarative clause headed by a non-interrogative complementiser, C_[decl] in (20), which is a simplified structural representation of (18). The sprout, on the other hand, is a question, either a matrix or an embedded one, headed by an interrogative complementiser, C_[iQ], whose specifier is targeted by wh-movement. We thus witness a clause-type mismatch on the semantic side, yet ellipsis is licensed without any difficulty. The same applies to the embedded sprouting structure in (21) modulo T-to-C movement.

The clause type mismatch in the sprouting examples is exactly parallel to the polarity mismatch in the negative concord example above and to the number mismatches in VP- and NP-ellipsis.8 Here too, the ellipsis site contains a head that was absent from the antecedent: the interrogative C_[iQ] in sprouting mismatches the declarative C_[decl] in the antecedent just as the negative [Σ: ¬] in the fragment answer mismatches the affirmative polarity in the antecedent and the plural φ-features on the agreement-controlling NP in the antecedent mismatch the singular φ-features on the elided agreement-controlling NP in the ellipsis site. Crucially, however, the presence of the elided heads or features is signalled, in overt morphology, by the elements that have entered into an Agree relationship with them. The wh-item whose is in a featural relationship with C_[iQ] in (21) just as the neg-word/NCI nikogo ‘nobody’ is in a featural relationship with [Σ: ¬] in (11) or the agreeing finite verb is in a featural relationship with the elided clausal subject in (13), (15) and (16). This appears to be sufficient for successfully, and unambiguously, recovering the elided material in the absence of a full formal semantic or syntactic identity with the antecedent.

Unlike the NCI-fragment answer, in which an ellipsis remnant is featurally linked to a negative element inside the ellipsis site, morphologically spelling out the features of the elided Neg head, non-NCI fragment answers and responses involve no such featural dependency. In particular, the referential remnant, Masha, in (3), carries no unvalued features that could be valued by the Neg head’s [Σ: ¬] feature and receive morphological realisation, signalling the presence of Neg in the ellipsis site. Even if the elided part of the sentence contained negation, it would not be recoverable for the addressee, which is why there would be no reason for the speaker to recourse to an elliptical response in these circumstances.

Contemporary literature on the identity and recoverability of ellipsis has identified several contexts in which elided negation is recoverable, on the basis of a nonnegative antecedent, even in the absence of a featural relationship between negation and the remnant (Kroll & Rudin 2017; Rudin 2019; Kroll 2020; Ranero 2021). As mentioned in the previous section in the context of fragment responses, this polarity mismatch also requires there to be an inference for ellipsis to be felicitous. An example is given in (22) involving a nonnegative antecedent proposition, Iraq will comply with the mandate, embedded under a lexical negation verb doubt. The bracketed antecedent clause does not contain an overt negation, yet sluicing can be recovered as containing such a negation.

Given the presence of negation in the ellipsis site and the nonnegative character of the bracketed antecedent, the inference required to make ellipsis recoverable could amount to establishing a loose equivalence relation between doubt that p and believe that ¬p.9

Something similar could be argued to obtain in (23), which involves a tense mismatch (future in the antecedent as opposed to the past in the ellipsis site) in addition to the polarity mismatch.

The inference making the elided negation recoverable could amount to postulating an additional unpronounced conditional, as schematised in (23) above, which does contain negation and could be viewed as the actual antecedent for the elided negative proposition (see Stockwell 2022 for such an approach to licit voice mismatches under sluicing made recoverable by double ellipsis).10

As a final example of a polarity mismatch in the absence of an Agree dependency let us consider the cooccurrence restrictions imposed on the Korean adverbial acik ‘still/yet’. As shown in (24), acik ‘still/yet’ is compatible with what can pretheoretically be described as ‘continuous’ predicates, such as iss- ‘stay’, but incompatible with ‘noncontinuous’ predicates such as tochakha ‘arrive’.

Negating a ‘noncontinuous’ predicate such as tochakha ‘arrive’ from above yields a ‘continuous’ predicate, with which acik ‘still/yet’ is also compatible, as shown in (25).

Now, acik ‘still/yet’ can be used as a fragment answer to a nonnegative yes/no-question involving both a ‘continuous’ and a ‘noncontinuous’ predicate. Again, I illustrate this in (26) using the same verbs, tochakha ‘arrive’ and iss- ‘stay’, as before. As shown in (26B) and (26B′), the fragment can only be interpreted as a negative answer if the elided verb is tochakha ‘arrive’ and as an affirmative answer if the elided verb is iss- ‘stay’.

We can make sense of the contrast in (26B) and (26B′) by appealing to what we have already established for the other fragments above. The adverbial remnant acik ‘stll/yet’ is similar to the non-NCI fragment Masha in (3) and the wh-remnant in the sluicing examples (22) and (23) in not being featurally connected to a negation inside the ellipsis site. The ‘continuous’ predicate iss- ‘stay’ works precisely like the Masha examples (4) and (5): acik ‘stll/yet’ being compatible with both the affirmative and negative instances of this predicate and there being no negation present in either the antecedent or the ellipsis remnant, just as in (5B), the inference necessary for the recovery of potentially elided negation is simply not triggered. The hearer has no evidence on which to base a departure from the null hypothesis of full identity between the antecedent and the ellipsis site. Consequently, the only available interpretation is that of an affirmative fragment answer. Because the affirmative-answer interpretation would result in an incompatibility of acik ‘still/yet’ and the ‘noncontinuous’ predicate tochakha ‘arrive’, on the other hand, it is discarded, and the only remaining interpretation is that of a negative answer.

Now, if elided negation can be recovered on the basis of an inference, the question arises why such an inference is unavailable when it comes to NPI fragments. This is the point made by Weir (2020) in the context of negation accommodation: why is elided negation not accommodated in ‘the presence of (something which is unambiguously) a negative polarity item’ (Weir 2020: §25.2), as shown in (27) for English and (28) for Russian?

While a unified principled explanation for the unacceptability of all NPIs as fragment answers would be preferable to each separate language being considered on a case-by-case basis, it should suffice to say for my present purposes that additional considerations contribute to making NPIs in English and Russian poor fragment answers. For the purposes of the present paper, I hypothesise that an important additional consideration is the overall makeup of the polarity system in individual languages. The negative answer to a wh-question can receive multiple surface realisations, and it is often the case that several quantificational expressions overlap in their distribution. In English, I did not see anyone is generally truth-conditionally equivalent to I saw no one but one of them will consistently win over the other in particular circumstances. The negative quantifier no one (as well as never, nowhere etc.) being restricted to exactly one environment and more informative than the NPI anyone (and ever, anywhere etc., respectively) ensures that the negative quantifier will always win over the NPI in exactly those cases where that stronger, more specific, component is necessary. Negative fragment answers to nonnegative questions are one such environment. Besides, some NPIs serving a double duty as Free Choice Items creates additional ambiguities in elliptical contexts, thus obfuscating the necessary inference that could otherwise lead to the recovery of the elided negation.

Likewise, in Russian, libo-NPIs such as kogo-libo ‘anyone’ in (28) are subject to competition with NCIs, a state of affairs known as the ‘bagel problem’ (Pereltsvaig 2006), since ‘the distribution [of libo-NPIs] is that of negative polarity items, but with the central core missing. The apparent source of the bagel problem is the existence, in Slavic, of negative concord, which takes precedence over alternative types of exponence involving indefinite polarity items under the scope of negation’ (Hoeksema 2010: 838).

This competition-based view makes two predictions. The first prediction concerns languages whose polarity systems have no negative quantifiers of the English type and also no NCIs of the Russian (and perhaps also Romance) type, such as Irish. In the absence of a stronger expression, either a negative quantifier or an NCI, regular NPIs in such a polarity system are predicted to be acceptable as fragment answers. This is a correct prediction. Example (29) illustrates the occurrence of an NPI, duine ar bith ‘anyone’, in a nonnegative interrogative environment (see Acquaviva 1996 and Irslinger 2013 for a detailed discussion of the inexistence of negative indefinites/quantifiers and NCIs in Irish and Bernini & Ramat 1996; Willis 2013 and especially McCloskey 2023 for evidence of the ar bith indefinites being NPIs, such as their incompatibility with almost-modification).11

Example (30) shows that the same type of NPI can appear as a fragment answer in the absence of negation in the antecedent.

The second prediction of the competition-based view outlined above is that, even in languages like English and Russian, where NPIs consistently lose to stronger competitors, it should be possible to override this constraint in precisely those circumstances where using the stronger competitor would no longer be advantageous. Again, this seems like a correct prediction. As observed by den Dikken et al. (2000); Weir (2020) and as brought to my attention by an anonymous reviewer, NPIs may instantiate felicitous fragment answers to negative questions for some speakers. I provide two illustrations in (31) and (32) below.

The negation in the English question (31A) and the Russian question (32A) deprives the negative-quantifier answer in English (no wine) and the NCI answer in Russian (nichego interesnogo ‘nothing of interest’) of any advantage over the NPI answer. The situation is somewhat similar to the Irish cases above but it obtains locally within an environment rather than globally within a language. That said, the fact that some speakers still dislike NPIs as fragment answers to such negative questions suggests that more factors are at play here than the recoverability of negation. It appears, then, that the inability of English and Russian NPIs to surface as fragment answers ought to be explained by the overall makeup of the polarity systems and the constraints characterising these particular items in these particular languages, rather than purely by what is inside the ellipsis site.

By way of summary, we have considered two premises that must hold for Watanabe’s (2004) argument against the ∀¬-theories to be valid. We have seen that the unavailability of the negative fragment answer interpretation in the absence of an NCI in the remnant follows independently from the semantics of questions and answers. We have also seen that NCI fragments, and not non-NCI fragments, make an additional contribution to the recoverability of an elided head by morphosyntactically signalling an Agree dependency with that head.