Anaphoric and rhetorical WNFQs are distinguished in terms of their antecedent conditions. As noted in previous studies (e.g., Merchant 2006; Hofmann 2018; Stockwell to appear), anaphoric WNFQs morpho-syntactically require a negative antecedent. This condition holds even when the WNFQ construction occurs in an embedded clause:

In (8a), the antecedent clause with the sentential negator not licenses the anaphoric WNFQ.

Note that the negation in the antecedent clause need not be the sentential negative adverb not. As pointed out by Hofmann (2018) and Stockwell (to appear), other negative adverbs, a negative quantifier, or a negative determiner in the antecedent clause can license the anaphoric WNFQ construction:

These negative expressions make the antecedent clause negative, as evidenced by the neither-tag identified by Klima (1964) as a test for sentential negativity. Unlike these negative expressions, neither constituent negation nor lexical negation, as in (10) and (11), allow the anaphoric WNFQ construction. Hofmann (2018) and Stockwell (to appear) note this contrast by testing their sentential negativity with respect to neither-tag responses.

As seen in (9)–(11), the previous studies take anaphoric WNFQs to be only compatible with the context where the neither-tag is available. Therefore, the negative antecedent condition cannot be satisfied by constituent negation or lexical negation, which does not express sentential negation.

Note that the sentential negativity need not be introduced by an explicitly negative expression in the antecedent. It can also be provided implicitly or pragmatically (Horn 1978; Hofmann 2018; Stockwell to appear). Consider the following examples taken from Hofmann (2018: (16a) and (16c)).

The sentential negation is obtained from the context by means of the Neg-raising (12a) or the disjunction or (12b) (Hofmann 2018). Such data show us that licensing conditions of anaphoric WNFQs are not purely syntactic but also dependent upon contextual environments.

As Hofmann (2018: 8) notes, rhetorical WNFQs require an antecedent that has modal semantics encoding possibility or necessity:

In (13a), the imperative antecedent is interpreted as a suggestion opening up the possibility of playing the game or not. In (13b), the meaning of the modalized declarative antecedent involves the necessity of submitting the paper. In (13c), the polar interrogative antecedent is used as a request for coming in. The rhetorical WNFQ in each case is used to accept the suggestion/directive/request by the addressee.

Note that the modal antecedent condition for the rhetorical uses can be satisfied by the context. See the following contrast taken from Hofmann (2018: (18)):

In (14a), the positive declarative is an informative assertion that involves no modal semantics required. This is why additional context or discourse reason is required to make the declarative as an appropriate antecedent. In (14b), however, the non-modalized declarative can function as the fragment’s antecedent with no additional context since the negative attitude toward the situation of John’s going to the movies again is much more saliently presented. This also shows that licensing conditions of rhetorical WNFQs are quite context-dependent.

Before we move to the next licensing condition, it is worth to note that rhetorical WNFQs have two different usages. One is that they are used to accept the addressee’s directive/suggestion/offer, as in (13a) and (13b), or to accede to the addressee’s request, as in (13c). The other usage is that they function as canonical rhetorical questions to convey an assertion of the opposite polarity from their surface form, as in (14b) (Han 2002). As pointed out by a reviewer, rhetorical WNFQs conveying acceptance are differentiated from those conveying an assertion: unlike the latter, the former are restricted to dialogue, and the non-elliptical variants of the former, unlike those of the latter, cannot be used as responses like the following:

In what follows, we distinguish between the two usages of rhetorical WNFQs when necessary.

Hofmann (2018: 9–10) notes that anaphoric WNFQs can have a cataphoric (or backward anaphoric) antecedent, but rhetorical ones cannot. The following Hofmann’s examples illustrate this difference:

In (16b), the anaphoric WNFQ is licensed by the negative cataphoric antecedent John isn’t going to school today. As seen from (17b), this kind of cataphoric relationship is disallowed for the rhetorical WNFQ.

Both types of matrix WNFQs can be licensed not just by an overt linguistic antecedent, but also by a non-linguistic antecedent, as seen in the following (a)-examples (Hofmann 2018):

However, as indicated in the (b)-examples, when the WNFQ is embedded, the non-linguistic antecedent makes it sound slightly odd. The availability of non-linguistic antecedent shows that the semantic resolution of WNFQs is dependent upon contextual environments.

Hofmann (2018) points out that the two types of WNFQs differ in their factive embeddings. For instance, consider the following examples taken from Hofmann (2018: 6):

As observed in (20a), anaphoric why not can be embedded under factive predicates like know, regardless of whether the verbs are negated or not. On the other hand, (20b) shows that rhetorical why not is disallowed to be embedded under non-negated factive verbs.2

The embedding behavior of anaphoric WNFQs is also restricted. Observe the following examples drawn from Hofmann (2018: 37):

The anaphoric WNFQ is not licensed in the embedded context of possibility or wonder where its complement proposition is not an assertion (or a presupposition) (Hofmann 2018).

According to Sadock (1974), Han (2002) and others, canonical rhetorical questions are taken as assertions in that they can occur with the introductory item after all and can be followed by a yet-clause:

In this connection, note that rhetorical WNFQs conveying an assertion can appear in the same embedded environments, as attested by the following corpus examples:

In (24a), the WNFQ occurs with after all, and in (24b), it is followed by the yet-clause. In these examples, the rhetorical WNFQs are not interpreted as conveying acceptance. The above data, therefore, show that such uses of rhetorical WNFQs can be viewed as assertions, just like canonical rhetorical wh-questions.

English employs so-called why-stripping, which consists of the interrogative word why and a non-wh remnant, as exemplified in (64) (see Merchant 2012; Ortega-Santos et al. 2014; Yoshida et al. 2015; Kim & Abeillé 2019; Kim 2024; among others).

Why-stripping has a propositional meaning. For instance, the occurrence in (64a) is interpreted as Why did John eat kimchi (and not another food)?

A remnant in why-stripping can be realized as various syntactic categories, as long as it gets a focal stress (Ginzburg & Sag 2000; Yoshida et al. 2015; Kim & Abeillé 2019):

We propose that WNFQs should be analyzed as a subtype of why-stripping where the negative adverb not serves as a focused remnant (cf. Stockwell to appear). This view can be supported by parallels between WNFQs and why-stripping in many grammatical respects. For one thing, both of the constructions do not allow other wh-words to take part in them. This is illustrated in (69) for why-stripping (Yoshida et al. 2015) and in (70) for WNFQs (Hofmann 2018; Stockwell to appear).

Another similarity between the two constructions is that the fragment XP following why receives focal stress (Quirk et al. 1985; Yoshida et al. 2015; Alves-Castro 2020):9

Next, the two constructions pattern alike in that the ellipsis operation is obligatory; that is, the rest of the clause except for the remnant should be elided (Yoshida et al. 2015; Hofmann 2018):

Further, note that like why-stripping, the two types of WNFQs can occur in embedded contexts, as discussed (Yoshida et al. 2015; Hofmann 2018; Stockwell to appear):

In addition, both why-stripping and WNFQs can be licensed by a non-linguistic antecedent, but not when they are embedded (Yoshida et al. 2015; Hofmann 2018):10

Why-stripping is known as being insensitive to strong islands like complex NP islands, as in (81) (Yoshida et al. 2015). Such island insensitivity is also observed in WNFQs, as attested by the corpus examples in (82) (cf. Stockwell to appear).11

In (81), the correlate in the antecedent clause that is linked to the remnant NP occurs inside the complex NP island. The same holds for the WNFQ in (82) where the remnant not is associated with its correlate buried inside the island.12

Last but not least, why-stripping, like WNFQs, can be interpreted either as an information-seeking question, as in (83a), or a rhetorical question with assertive force, as in (83b):

Based on these syntactic and semantic parallels we have observed so far, we suggest that WNFQs can be subsumed under why-stripping, while carrying their own constructional constraints. That is, the WNFQ serves as a subtype of the why-stripping construction.

As noted by Needham (2012) and Meijer (2022), English uses propositional anaphors that refer to a proposition introduced in the context. Consider the following:

Here the propositional anaphors refer to the contextually provided salient proposition ‘Kim is coming to the party’. But anaphoric not differs from the other two in that it negates the salient proposition, yielding the negative one.

Anaphoric so can occur with why, forming a why so fragment question, as illustrated by the following corpus examples:

Unlike WNFQs, this fragment question is used to inquire about an event expressed by a salient positive proposition.

As noted by Huddleston & Pullum (2002: 849) and earlier in the paper, anaphoric not is typically used as a pro-form for a negative clausal complement:

In (86B), the negation refers back anaphorically to the positive proposition evoked in the previous discourse and negates it, expressing that they are not honest.

It is also possible for anaphoric not to occur with a PP adjunct (Huddleston & Pullum 2002: 849):

The COCA corpus also yields examples where anaphoric not is used with a coordinating conjunction like or or and:

As also noted, similar to WNFQs, the anaphoric negator can follow an adverbial expression, with which it functions as a fragment (Kim 2025), as illustrated by the following attested examples:

Hofmann (2018) would analyze the not in such cases as occurring in the Σ head with no semantic meaning. This negative concord approach would work with a negative antecedent. However, as pointed out earlier, such fragments do not always require a negative antecedent, as shown in the attested examples below:

The antecedent clause includes no negative expression, but the fragment denotes a negative proposition (e.g., Absolutely you should not go back to work for (90b)). For this semantic resolution, as noted, Hofmann (2018) posits two versions of not: uninterpretable negation for the negative neutralization, and interpretable one for cases where the antecedent is positive. This approach makes sense based on Zeijlstra’s (2004) analysis of negative concord dependencies that Hofmann (2018) adopts. In this study, however, we attempt to present a unified treatment of remnant not in such cases as a propositional anaphor that picks up a positive proposition from discourse.

In addition, as noted earlier, anaphoric not serves as remnant in many other environments including the following:

It seems difficult to insist that the first remnant not, referring to the positive proposition in these examples, is interpretable while the second one, present in the WNFQs, is uninterpretable.

The same question arises with rhetorical uses of WNFQs. See the following corpus examples:

Here the WNFQ would mean a modal proposition in the form of ‘Why shouldn’t …?’ (e.g., Why shouldn’t I love this? for (92a) and Why shouldn’t you offer me coffee? for (92b)). That is, such rhetorical WNFQs involve a negative meaning. We could not ignore the negative reading of the remnant in these rhetorical uses. In what follows, we suggest an alternative view in which the remnant not in anaphoric and rhetorical WNFQs functions as a propositional anaphor referring to the salient proposition evoked in the given context, rather than being recovered by resorting to syntactic identity between the antecedent clause and the unpronounced material.

As we have seen earlier, our corpus data question the ellipsis-based sentential analyses where WNFQs involve a negative sentential source and are derived via a deletion operation under semantic identity to their antecedent clause. Departing from such ellipsis-based approaches, we propose an alternative direct interpretation (DI) approach in which the remnant in why-stripping as well as in WNFQs projects into an NSU (non-sentential utterance) via the head-fragment construction stated in (93) (Ginzburg & Sag 2000; Kim & Abeillé 2019; Kim 2021; 2024):

This construction rule allows any constituent (XP) to function as an NSU as long as it represents a focus representing salient information. For instance, the why-stripping in (94) would have the simple syntax given in (95):

The focus establishing constituent Arizona serves as the sole daughter of an S-node with no reference to ellipsis.13 The wh-expression why, bearing the positive question feature ([que+]), combines with the fragment and generates a well-formed information-seeking wh-question. This simple syntax is then linked to the process of semantic resolution which involves two key tasks: identifying the source parallel to the sentential meaning of the remnant and resolving the sentential content by referring back to the proposition evoked in the previous discourse (Fernández et al. 2007).

In the DI framework the present analysis adopts, structured discourse and context play a key role in the semantic resolution of elided material. Following Ginzburg & Sag (2000), and others, we take the dialogue context (ctxt) to include at least information about question-under-discussion (qud) and focus establishing constituent (fec), as represented in the feature-structure format:

The max-qud identifies the maximal qud among a number of questions evoked in a given context. The fec represents a salient or focal constituent of the utterance and serves as a potential parallel element. This attribute can also include not only semantic but also syntactic information such as case and categorial information (Ginzburg & Sag 2000).

To illustrate how this system works, consider the following:

The declarative antecedent clause makes an assertion that Mimi didn’t pass the exam (¬[pass(m,e)]), as represented in the following simple feature structure:

As shown in (98), the declarative antecedent is communicatively complete and its semantic content represents a proposition as a subtype of message (Ginzburg & Sag 2000).14

The why FQ as well as the why not FQ in (97) ask for a reason for the event described by the negative proposition of the antecedent. This information is triggered by the qud referring to the context involving the previous negative assertion. We could represent this as in the following feature structure:15

This information-seeking FQ asks for a reason for Mimi’s not passing the exam.

As noted by Bromberger (1992: 160–161), unlike other wh-words, why functions as a focus assigner. Compare the following:

The possible answers here tell us the key difference between why and other wh-questions. Unlike when, the interpretation of why differs depending on where focus is placed in its prejacent. That is, when itself carries a focus value, while why assigns a focus to the phonologically prominent expression. This difference predicts that the remnant not cannot occur with other wh-phrases as an FQ, as in (102), since these cannot assign a focus value to the negator:

As noted earlier, the negator not (inducing a neg-relation) serves as a propositional anaphor selecting a contextually salient proposition (℘) as its semantic argument. This lexical information could be represented by the following:

Taken together, the proposed DI approach would then allow the following structure for the FQ Why not? in (97):

The focused fragment not as a propositional anaphor can project into an NSU via the head-fragment construction. For its semantic resolution, it takes as its argument the salient proposition (pass(m,e)) contextually provided from the antecedent clause, yielding the negative propositional meaning (¬[pass(m,e)]). The expression why then asks for a reason for Mimi’s not passing the exam. In the present system, anaphoric not selecting a salient proposition as its semantic argument (¬(℘)) captures the sentential negativity of WNFQs.

The present approach thus relies on discourse structure for the resolution of the anaphoric not. Hofmann (2022; 2023) also suggests an anaphoric analysis, but under a syntactic identity condition. Consider the following structure that Hofmann (2023: (49)) postulates:

Hofmann suggests that the anaphoric not here refers to a proposition in the scope of the negation and undergoes clausal ellipsis under the syntactic isomorphism condition in (106):

The elided vP of the WNFQ in (105) satisfies this condition. Such an ellipsis approach, however, would be challenged by attested examples like the following, which we repeat from Section 3:

As tested by neither-tags, the negator not in the antecedent clause here is constituent negation. Hofmann’s movement-and-delete approach would take the elided parts of the WNFQs in (107) to be syntactically isomorphic to their antecedents, as given in (108):

The possible issue here is that these putative sources yield different interpretations from what the WNFQs in (107) really mean. The ellipsis analysis would then require not to interpret one of the negators.16

The present DI approach, taking the structured discourse and context to play a pivotal role in the semantic resolution of WNFQs, could avoid such an issue. Consider again the following examples involving constituent and lexical negation:

In the present system, the remnant not need not refer to a syntactic or semantic representation of the antecedent. As shown here, within the present analysis, the interpretation of the anaphoric remnant not depends on the salient discourse information in the given context. Given that declaratives evoke a QUD construed as a polar question that asks whether p is true or not (Ginzburg et al. 2000), the propositional anaphor not in (109) would refer to a positive proposition in the scope of the negation, which is provided by the QUDs in question:

The QUD evoked by the antecedent in (109a) includes a subquestion of whether Mimi is going or not, and the remnant not refers to this for its semantic resolution while the QUD in (109b) asks whether the computer is able to comply or not. As such, the meaning of the fragment is resolved with no recourse to syntactic structures.17

It is generally assumed that the truth of the propositional content of information-seeking why-questions is presupposed (Bromberger 1992; Fitzpatrick 2005). Observe (111).

The infelicity of the response here is because its content contradicts the presupposed proposition that Kim left. Adopting Hofmann’s (2022; 2023) insights, we assume that this factivity property of why is inherited by anaphoric WNFQs, alongside a construction-specific contextual constraint, as stated in (112).

This contextual constraint on the anaphoric WNFQ construction could account for the negative antecedent condition imposed on it:

The factivity presupposition of the negative prejacent (¬℘) of why requires that its antecedent clause assert a negative proposition (Hofmann 2018; 2022). However, in (113), the factivity condition is not met because of the conflict between the negative prejacent (i.e., Mimi didn’t pass the exam) and the positive antecedent asserting that Mimi passed the exam.

This contextual constraint can also account for why the antecedent of anaphoric WNFQs is disallowed in the complement clause whose propositional content is not asserted (Hofmann 2018; 2022). Consider the following (Hofmann 2018: (75)):

In (114a), the antecedent clause embedded under the question verb is not assertive, hence it leads to the unacceptability of the WNFQ. In (114b), the antecedent also occurs in the nonassertive context where it is embedded under the nonassertive predicate be a possibility/possible in the sense of Hooper (2012). On the other hand, in (114c), the strong assertive predicate be sure in Hooper’s view commits the speaker to the truth of the proposition expressed by the embedded antecedent, thus the assertion condition is satisfied.

In addition, the present analysis correctly predicts that anaphoric negation can serve as the antecedent for anaphoric WNFQs. Consider the following attested example:

In the above dialogue exchange, the first remnant negator in B’s response refers to the positive proposition (℘), yielding the negative meaning, i.e., You can’t help me out with a down payment (¬[℘]). The remnant not in the WNFQ is not different: the positive proposition (℘) serves as its argument, resulting in the same negative proposition (¬[℘]).

As for anaphoric WNFQs, Stockwell (to appear: 9–10) notes that both the reason and negative meanings introduced by why and not, respectively, must come from the same clause:

In (116), both of the why and why not FQs are interpreted as inquiring about a reason for John’s not telling. In (117), however, unlike the why-question, the WNFQ can only be associated with the negative embedded clause, but not the positive matrix clause, questioning a reason for John’s not going to the party. This clause-mate condition can be captured by the present analysis. Under the negative antecedent condition, the embedded clause serves as the antecedent. The propositional anaphor not in the WNFQ refers to the salient proposition evoked from the antecedent, yielding the negative proposition (¬[go(j, to.the.party)]). The wh-word why then directly takes this negative proposition as its semantic argument:

As noted before, anaphoric WNFQs are insensitive to complex NP islands, as in (119), repeated from (44).

Since the present analysis directly projects the negative fragment into a non-sentential utterance, it is expected that WNFQs involve no island-sensitive operations (cf. Stockwell to appear). The DI approach has no expectation that properties of unbounded dependencies are also projected in WNFQs.

In accounting for the rhetorical reading of WNFQs, we follow Han (2002) in assuming that the wh-phrase in rhetorical questions is mapped onto a negative quantifier (e.g., what as nothing, who as nobody); in other words, as sketched in (120) and (121), the value of a rhetorical wh-phrase denotes an empty set.

The semantic negation contributed by the rhetorical wh-phrase is responsible for the polarity reversal effect in the interpretation of rhetorical questions (see Han 2002 for detailed discussions on rhetorical questions).

Accepting Han’s approach, we assume that rhetorical why-questions like (122) express an assertion in which the value of the rhetorical why is the empty set and not some other set:

The rhetorical meanings of (122) would be derived as follows:

We assume that the why in rhetorical WNFQs like (124) also functions as the rhetorical why mapped onto a negative quantifier.

In deriving both of the rhetorical readings, the fragment not as a propositional anaphor evokes a negative proposition, as it does in anaphoric WNFQs. The rhetorical why takes this proposition as its semantic argument and is mapped onto a negative quantifier, as sketched in (125).

The classical rhetorical WNFQ in (124a) is interpreted as an assertion that there is no reason not to dance, which is paraphrasable roughly as We should dance. On the other hand, the one in (124b) is interpreted at a pragmatic level as an acceptance of the suggestion in the sense that the assertion implies a positive reception and a willingness to participate in the dancing suggested by the speaker A in the appropriate context.

The present analysis assumes that both anaphoric and rhetorical WNFQs basically involve a negative propositional meaning introduced by the fragment not. But they crucially differ in that in the former case, why inquires about a reason for the proposition, while in the latter case, it functions as a negative quantifier whose value is the empty set for the proposition. This analysis can be extended to account for the rhetorical meaning of why-stripping (see Zaitsu 2020 for discussion on rhetorical uses of Why-VP). Consider (126).

The NSU projected from the fragment dance denotes a positive proposition, and the rhetorical why takes this salient proposition and yields the rhetorical meaning like the following:

In sum, the remnant not in both types of WNFQs functions as a propositional anaphor that picks up a contextually salient proposition in the given context. The two different readings of WNFQs are captured by positing two different functions of why: information-seeking why for anaphoric uses and rhetorical why for rhetorical uses. This direction offers a uniform analysis for anaphoric as well as rhetorical uses of WNFQs.