Strong versus weak negative polarity and two types of exhaustification: the case of exceptive ʔilla in Levantine Arabic

1 Exceptive ʔILLA: a paradigm of negative polarity

As it is the case in the English exceptive construction utilizing markers such as ‘but’, ‘except’, and ‘except for’, exceptive ʔilla in Palestinian/Jordanian Arabic base their truth conditional meaning on the semantic inferences of subtraction and unique minimality (see von Fintel 1993, 1994).^[1] Consider the following example from exceptive ‘but’ in English and exceptive ʔilla in LA.^[2]

As shown in von Fintel (1993, 1994), exceptive sentences like (1) and (1′) have at the core of their truth conditional meaning the subtractive inference which holds that the set comprising the excepted individual { Khālid } is removed from the quantificational domain D of the universal quantifier.^[3] The exceptive sentences also carry with their subtractive meaning an additional semantic inference of what von Fintel (1993) called unique minimality. ^[4] This inference requires the excepted set { Khālid } to be uniquely minimal in such a way that it is subtracted from the quantificational domain of the exceptive and the quantificational claim remains true. For the excepted set, { Khālid }, to be uniquely minimal, it should be the case that the set in question be the only set with no proper subset as an excepted set. Accordingly, the exceptive sentences in (1.a) and (1′. a) are assigned true if and only if every student other than Khālid attended and it is not the case that every student attended. These semantic effects lead the interlocutors to infer that Khālid is the only student who did not come. Similarly, the exceptives in (1.b) and (1′. b) are assigned true if and only if it is not the case that some student other than Khālid attended and it is the case that some student attended. Again with these truth conditions, it can be inferred that Khālid is the only student who attended.^[5]

von Fintel (1993, 1994) showed that the two semantic inferences of subtraction and unique minimality accounts for the restricted distribution of exceptive sentences; i.e., the fact that the exceptive particle but/ʔilla tends to combine with universally quantified expressions and it may not combine with existentially quantified expressions as exemplified in (2) (Crnič 2018; von Fintel 1993).

von Fintel (1993,1994) argued that an exceptive sentence is only acceptable if its associate excepted set is uniquely minimal. For example, while the acceptable universally-interpreted exceptive sentences in (2.a, b) and (2′. a, b) involves a uniquely minimal excepted set (i.e., { Khālid }), the excepted set { Khālid } associated with the existentially interpreted unacceptable exceptive sentences in (2. c) and (2′.c) is far from minimal. To show this, let the empty set ∅ be a proper subset of the set { Khālid } (i.e., since the empty set ∅ is a proper subset of every set) and let the proposition ‘every/no student attended ’ involve excepting ∅, then by the downward monotonicity of the left argument of the universal quantifier, it follows that {x: x is a student} ∖ ∅ entails {x: x is a student} ∖ {{ Khālid }, meaning that the excepted set { Khālid } has no proper set ∅ such that if the universal claim is to hold true of the set { Khālid }, it is then the case that the universal claim holds true of its proper subset ∅. In this way, an excepted set modifying a universal quantifier is uniquely minimal and hence the exceptive phrase in this environment gives rise to consistent truth conditions based on subtraction and unique minimality.

By the same reasoning, the unacceptability of (2. c) and (2′.c) follows from the fact that the excepted set, {Khālid}, is not uniquely minimal. To show this, assume once again that the empty set ∅ is a proper subset of the set {Khālid} and that the proposition ‘some student attended’ involves excepting ∅. By the upward monotonicity of the left argument of the existential quantifier, it follows that {x: x is a student} ∖ { Khālid }entails {x: x is a student} ∖ ∅, meaning that the excepted set { Khālid }has a proper subset ∅ such that if the existential claim is to hold true of the set { Khālid }, it is then the case that the existential claim holds true of its proper subset ∅. In this way, an excepted set modifying an existential quantifier is not uniquely minimal and as a consequence the subtraction and unique minimality derived leads to contradictory truth conditions (von Fintel 1993, 1994).

Recently, an approach to the semantics of exceptives has been developed which investigated the analogy between the distribution of exceptive phrases (e.g., but/ʔilla XP) and that of negative polarity items NPIs (see, in particular, Gajewski (2008, 2013) for English ‘but’ and Sauerland and Yatsushiro (2023) for exceptive sika in Japanese). Gajewski (2013), for example, argued that the exceptive phrase [ but/ʔilla XP] and weak NPIs are licensed under similar licensing conditions; the so-called antitone or downward monotonic environments, (e.g., the restrictor of universal quantifiers). Gajewski suggested, on the basis of the analogous distribution of the exceptive phrase and NPIs, that these two classes of expressions be given a unified semantic analysis: just as weak NPIs such as ‘any’ triggers alternatives which associate and are quantified over by an exhaustivity operator in grammar (Chierchia 2006; Kratzer and Shimoyama 2002; Krifka 1995), the exceptive ‘but XP’ can be analyzed as an alternatives-inducing expression that triggers grammatical exhaustification as well (i.e., For this kind of distributed analysis, see Crnič 2018; Gajewski 2008, 2013; Hirsch 2016; Spector 2014).

Clearly enough, exceptive ʔilla has a weak NPI-like distribution which is analogous to that of other weak NPIs and weak NPI-like expressions such as exceptive ‘but’ in English. In its weak NPI form, the ʔilla phrase (i.e., [ʔilla XP]) combines with universally quantified expressions under the requirement that the ʔilla phrase modify the left downward-entailing LDE quantifiers such as universals and it may not modify left upward-entailing LUE quantifiers such as existential quantifies as exemplified in (2′), repeated as (3). In this use, exceptive ʔilla, just as exceptive ‘but’ in English, patterns with other weak NPIs such as ‘any’ or ‘ever’ in being licensed in (Strawson) Downward Entailing environments such as the left argument of universal quantifiers.^[7] Such an environment does not license strong NPIs (e.g., in weeks) as shown in (3′) (Gajewski 2013; Sauerland and Yatsushiro 2023).^[8]

In its strong form, the ʔilla phrase (i.e., [ʔilla XP]) occurs in arbitrary pro-subject sentences. In this case, ʔilla associates with no overt NP as exemplified in (4), below.^[9]

Despite the fact that the exceptive phrase [ʔilla XP] is licensed in the immediate scope of sentential negation, which is of course a downward entailing (DE) environment, it may not be licensed by other Strawson downward entailing operators which typically license weak NPIs such as the left argument of universal quantifiers and free choice ʔii ‘any’ in (5), the complement of other presuppositional triggers such as the antecedent of conditional if in (6) and the negative factive predicates of ‘sorry’ ʔaasif and ‘surprised’ tafaadʒaʔ in (7).

In this way, [ʔilla XP] patterns with other strong NPIs such as expressions like ‘in week’, ‘until’, and ‘either’ in English which can never be licensed in the weak NPI licensing environments as in (8).^[10]

What is special about the strong use of ʔilla in (4) is that it induces a domain broadening effect. For this variant of strong ʔilla, let us use ʔilla _D+  to distinguish it from the default case of ʔilla that combines with universally quantified expressions. Intuitively, the two uses of ʔilla and ʔilla _D+  differ in the following way. While the exceptive operator ʔilla in (2′) subtracts its complement from the restrictor’s domain of the universal quantifier D which is a set of individuals salient in the context of use (say our high school students, Sorbonne’s doctoral students, etc.…), the exceptive operator ʔilla _D+ in (4) associates with a contextually-determined broader domain of discourse D+ (i.e., where D ⊂ D+) which includes more marginal specimens of the kind under consideration (e.g., student or non-student sets of individuals). In this way, the use of exceptive ʔilla _D+ in arbitrary pro-subject sentences is logically stronger than default ʔilla as used in universally quantified sentences. Following Chierchia (2006, 2013), we assume that a polarity item like the domain broadener ʔilla _D+ , which is inclined to go for a wider domains of discourse D+, is more emphatic than its non-polarity variant ʔilla, which involves a contextually fixed smaller domain of discourse D, (i.e., where D ⊂ D+).^[11]

Another fact that speaks of the analogy between the strong and weak NPIs, on one hand, and strong ʔilla _D+ and weak ʔilla, on the other hand concerns syntactic locality. As observed (see Zeijlstra 2022 and the references therein), weak and strong NPIs differ with respect to syntactic locality in such a way that unlike the weak NPIs in (9), strong NPIs like (10) may not be licensed in non-local environments such as embedded finite clause and adjunct islands.

Similarly and as expected, strong [ʔilla _D+  NP ] may not be licensed by the negative licensor outside its local domain as shown in (11); externally to the embedded finite clause and an adjunct island. This indicates that [ʔilla _D+  NP], just as other strong NPIs, is sensitive to locality condition (Zeijlstra 2022).

From the data discussed, we capture the following descriptive generalization: while exceptive ʔilla modifying quantifiers has a weak-NPI distribution, the same exceptive particle ʔilla _D+  occurring in an arbitrary pro-subject predicate forms a strong NPI. It is useful to summarize these descriptive facts formally as follows.

The facts just described leave us with the following theoretical puzzle: it is clear that exceptive ʔilla may exhibit both a weak and strong NPI distribution. As a weak NPI- like expression, exceptive ʔilla combines with universally quantified expressions which patterns with other weak NPIs and weak exceptive particles in other languages such ‘but’ or ‘except’ in English. This is the default case which induces no domain broadening in the syntax. As a strong NPI-like expression, ʔilla _D+  occurring in arbitrary pro-subject sentences induces a domain broadening effect and in this case it patterns with other strong NPIs such as ‘in week’ and ‘either’ and other strong NPI-like exceptives in other languages such as Japanese sika (Sauerland and Yatsushiro 2023).

The question then arises: for exceptive ʔilla, what accounts for its ambiguous behavior between a weak and another strong NPI-like distribution? This question may be addressed using one of two strategies. The first strategy is to assume that exceptive ʔilla is lexically ambiguous in such a way that we have two variants of particle ʔilla with different lexical entries that distinctly predict ʔilla’s weak and strong NPI uses. This strategy is easy to apply but it is far from correct. A strategy based on lexical ambiguity is not only uninteresting but implausible. Having two semantically and phonetically identical variants of exceptive ʔilla for its weak and strong NPI use is problematic in two ways: either it makes exceptive ʔilla an idiosyncratic construction that departs from the general unified semantic theory of exceptives or it overgenerates unattested uses for other intra-linguistic and cross-linguistic cases of an exceptive (i.e., we know, for example, exceptive ‘but’ in English and exceptive sika in Japanese have each a strictly weak and strictly strong NPI distribution, respectively). Therefore, we exclude this option.

The other strategy is a uniform analysis which maintains a unified semantics for exceptive ʔilla and it derives the variable distributional strength of ʔilla through an additional grammatical machinery that distinguish between the strong and weak uses of ʔilla based on factors such as association of focus associated with domain widening. This paper will adopt this strategy in solving the distributional puzzle of exceptive ʔilla. In the remaining part of this paper, we first review the (multidimensional) exhaustification approaches used to derive strong and weak NPI-like expressions in explaining the cross-linguistic difference between the English-like exceptive ‘but’ and exceptive sika in Japanese in terms of distributional strength. Section three extends the multidimensional exhaustification mechanism to the case of ʔilla; an analysis which is shown to be explanatory enough to account for ʔilla’s weak and strong NPI sensitivity. The last section concludes the paper.

2 An exhaustification-based analysis for exceptives

To capture the analogy between the distribution of exceptive ‘but’ and that of weak NPIs, Gajewski (2008, 2013) reconsidered the integrated semantics of exceptive ‘but’, which lexicalizes the two semantic inferences of subtraction and unique minimality in the lexical entry of exceptive ‘but’ (i.e., as originated in von Fintel 1993, 1994).^[12] Gajewski proposed a distributed semantics for ‘but’ in which only subtraction follows from the lexical semantics of ‘but’ and unique minimality is enforced by an application of grammatical exhaustification. On the exhaustification analysis (Crnič 2018; Gajewski 2008, 2013), only subtraction follows from the lexical semantics of ‘but’ and unique minimality^[13] is enforced by an application of grammatical exhaustification.^[14] In a nutshell, Gajewski took the subtraction inference to follow from the lexical semantics of the exceptive operator ‘but’ defined as in (12).

Unique minimality arises from an application of exhaustification which associates and quantifies over the structured set of alternatives ALT to the exceptive phrase.^[15] Simply put, an exhaustivity operator EXH is defined as a two-place function which takes proposition p(w) and the set of alternative propositions to p(w), ALT(p(w)), as its arguments and it asserts p(w) and excludes all relevant non-weaker propositions in ALT(p(w)) which represent the alternative denotations to p(w) with the complement of the exceptive phrase being replaced with the denotations of the complement’s subsets as defined in (13).^[16]

Let us show how exhaustifying the basic subtractive meaning of exceptives (e.g., 2. a,b; 2′. a,b) well predicts their restricted distribution. As shown in (14) and (14′), exhaustifying the basic subtractive meaning of the exceptive associating with the universal quantifier gives rise to the consistent and correct truth conditions which is based on subtraction and minimality: while subtraction is encoded in the semantics of the exceptive operator, minimality is derived by an application of exhaustification which excludes all of the non-weaker propositions involving the subsets of the complement of but including the empty set ∅, of course.^[18]

As predicted, when the associate quantifier in an exceptive is an existential, exhaustification fails to eliminate the alternative propositions involving subsets of the complement of but since they are not (innocently) excludable (i.e., the alternatives involving the subsets of the complement of ‘but’, namely subsets denotations of { Khālid }, are weaker than the basic meaning of the exceptive with the complement { Khālid }).

Gajewski (2013) suggested that the vacuous application of exhaustification in (15) violates an economy condition on the use of the exceptive phrase EP which necessitates the elimination of all the relevant alternatives triggered by the exceptive phrase [but XP]. As argued in Gajewski (2013), the failure of the exhaustivity operator to exclude all the subsets of the exception set means that the exceptive set in question is no longer a uniquely minimal one, which suffices to rule out the occurrence of exceptive ‘but’ modifying left upward monotonic quantifier such as the existential quantifier in (15). It is clear that the exhaustification analysis just previewed correctly predicts the distributional facts of the NPI-like of the exceptive using the same compositional mechanism of grammatical exhaustification which has been used to predict the distribution of weak NPI themselves (see Chierchia 2006; Chierchia 2013; Crnič 2018; Kratzer and Shimoyama 2002 and the related work cited there).^[19]

Cross-linguistically, there exist other cases of exceptives with even stronger NPI distribution. A representative case is exceptive sika in Japanese. Sauerland and Yatsushiro (2023) discussed two interesting facts about exceptive sika in this language. First, sika may not combine with quantificational phrases: it occurs with or without an associate NP. Second, exceptive sika is only licensed in the local scope of negation (i.e., nai ‘neg’) and it is never licensed by other weak NPI licensors. The following data exemplify these facts.

Based on these facts, Sauerland and Yatsushiro (2023) concluded that exceptive sika forms a strong NPI. On this conception, a cross-linguistic parametric variation is identified in the domain of exceptives with respect to their strength of distribution: while the English-like exceptive ‘but’ behaves like a weak NPI, the Japanese-like sike forms a strong NPI. Inspired by the multidimensional exhaustification approach that derives the strong and weak NPIs in English (Chierchia 2013; Gajewski 2011), Sauerland and Yatsushiro (2023) proposed that the two types of exceptives involve different applications of exhaustification in grammar: while the weak ‘but’ only operates on the truth conditional dimension of meaning (i.e., by only exhaustifying the assertive component of the proposition in which exceptive ‘but’ occurs), the strong sika operates on the non-truth conditional dimension of meaning (i.e., by exhaustifying the presupposition-enriched proposition in which exceptive sika occurs). To illustrate the point, let us look at (17.a) in which exceptive sika is unacceptable in the restrictor of the universal quantifier. Assume with Sauerland and Yatsushiro (2023) that the trivalent proposition of (17.a) is given in the form of the fraction notation a/p (i.e., in the style of Harbour (2014)) with the numerator a denotes assertion and the denominator p denotes presupposition.^[20] Assume further that the sika operator has an inherent existential force. Now, the exceptive sentence in (17.a) has the following presupposition-enriched proposition in which the universal quantifier triggers an existential presupposition.

For exhaustifying the presupposition-enriched proposition in (19), the two notions of strong excludability and exhaustification in terms of Chierchia (2013) are given as in (20) and (21). For Sauerland and Yatsushiro (2023), the relevant alternatives are structured under focus semantics in the standard terms of Rooth (1985).

It is clear that the instance of strong exhaustification in (21) results into inconsistent truth conditions: negating the alternative propositions p’ to the basic meaning of the presupposition p in (21.ii) leads to contradiction. The proposition ¬ [ some_x {D_e∖{k} ∩ Player(x) ≠ ∅] ⇔ every_x {D_e∖ { k } → ¬ Player(x) ≠ ∅ is inconsistent with the basic meaning of the presupposition [ some_x {D_e∖{susi} ∩ Player(x) ≠ ∅] where {susi}⊆ { k } holds under focus semantics. In this way, a contradiction generating exhaustivity operator that applies at the presuppositional dimension of meaning rules out instances like (18) in which sika exceptive is embedded within presupposition triggers, hence predicting its strong NPI behavior.

3 A unified analysis: the puzzle of ʔilla’s NPI distribution addressed

3.3 Strong use of ʔilla_D+

Let us now turn to the more interesting case of ʔilla _D+  associating with an arbitrary pro subject as exemplified in (31), repeated from (4).

(31)

a.

* pro	ħadˤar	ʔilla	xa:lid
3.SG.M	attended	except	Khālid
‘Someone attended except Khālid.’

b.

ma	pro	ħadˤar	ʔilla	xa:lid
Neg	3.SG.M	attended	except	Khālid
‘No one attended except Khālid.’

In section (1), we saw evidence that ʔilla _D+  forms a strong NPI. It never occurs in an unembedded positive sentence. It may not occur in environments which license weak NPI such as the Strawson-DE environment of presuppositional triggers (e.g., the left argument of universal quantifiers). Exceptive ʔilla _D+  however is only licensed in the local scope of negation. In this way, strong ʔilla _D+  has a narrower NPI distribution than the default weak ʔilla has; just as other strong NPIs such as ‘in weak’ and ‘until’ which have a narrower NPI distribution that that of weak NPIs such as ‘any’ or ‘ever’. To address this puzzle, we have two ways to proceed: either we deal with the weak and strong uses of exceptive ʔilla (namely, weak ʔilla and strong ʔilla _D+ ) as two distinct semantic expressions with each having a distinct semantic analysis that captures its NPI strength? or we give exceptive ʔilla a unified semantic analysis of the two uses of ʔilla and we derive the variation in NPI strength between the two uses in terms of other grammatical factors? The first option is not only uninteresting but a wrong one: it is just an ad hoc analysis that may not be extended with a general theory of exceptives. It also ignores a crucial aspect of difference between strong ʔilla _D+ and weak ʔilla in terms of domain broadening: while strong ʔilla _D+  induces a domain broadening effect, weak ʔilla does not.

We will go for the second option based on a uniform analysis. Our strategy is simple. We will assume that exceptive ʔilla has a unified semantics: ʔilla introduces the plain subtractive meaning, [D (P ∖ X) (Q)] which triggers the set of pragmatically-open alternatives ALT_σ (p) representing the alternative denotations to D (P ∖ X) (Q) with the complement of the exceptive phrase XP [ʔilla XP] being replaced with the denotations of the XP’s subsets (following Gajewski 2013). The ALT_σ (D (P ∖ X) (Q)) induced triggers pragmatic exhaustification with EXH associating and quantifying over relevant scalar alternatives in ALT_σ (D (P ∖ X) (Q)). Pragmatic exhaustification in this case is confined to operating on the set of scalar alternatives ALT_σ (p). Since weak ʔilla induces no domain broadening effect, no subdomain alternatives ALT_D (p) are involved via a focus-marked quantificational domain variable of discourse D+ in the syntax. This is the default case that captures the truth conditional meaning of weak ʔilla and other exceptives such as ‘but’ in English under the exhaustification-based approach to exceptives (Gajewski 2008, 2013; Crnič 2018; Hirsch 2016; Spector 2014). If as argued by Zeijlstra (2022) that pragmatic exhaustification derives weak NPIs, an analysis based on weak exhaustification for weak ʔilla makes a correct prediction: pragmatic exhaustification operates in weak ʔilla which both captures the truth conditional and distributional facts of ʔilla and by virtue of being a pragmatic operation that is indifferent to syntactic locality, it allows EXH to operate non-locally from the highest CP level of the structure into an environment delineated by the quantificational restrictor domains of universal quantifiers.

Similarly, strong ʔilla _D+  has the same semantics: a plain subtractive meaning D (P ∖ X) (Q) that undergoes exhaustification over the set of scalar alternatives ALT_σ (D (P ∖ X) (Q)) which ʔilla triggers in grammar. In addition, because strong ʔilla _D+  induces a domain broadening effect, it triggers an extra set of subdomain alternatives ALT_D (p) in which a Focus-marked quantificational domain D+ of discourse triggers subdomain alternatives (i.e., where D ⊂ D+). Domain broadening is syntactically translated into an Agree relation between D+ and the exhaustivity operator EXH+ in question. Strong ʔilla _D+ , therefore, triggers a set of alternatives comprising both scalar and subdomain alternatives ALT_D+σ (D (P ∖ X) (Q)) for the plain subtractive meaning (D (P ∖ X) (Q)) as defined in (32).

(32)

ALTD+σ (p) (D (P ∖ X) (Q)) =: ALTσ (p) ∪ ALTD (p) =:

{D (P ∖ X) (Q), D (P ∖ X′) (Q) ∣ {X′} ⊆ {X}} ∪ {D+ (P ∖ X) (Q), D′ (P ∖ X) (Q) ∣ D′ ⊆ D+}

Let us see how the paradigm of the strong ʔilla _D+ is derived under the unified sematic analysis based on exhaustification. Given the Focus-marked domain variable D+, we suggest that the exhaustivity operator EXH+ takes the role of the Focus-sensitive operator which associates and quantifies over both the scalar and subdomain alternatives ALT_D+σ (p) in the syntax. This is an instance of syntactic exhaustification that is Focus-related. As assumed, syntactic exhaustification operates locally at the enriched truth conditions of the plain subtractive meaning. Let us see how we can derive the paradigm of the strong ʔilla _D+ in (31).

Following Shlonsky (1988), we assume that the arbitrary pro subject introduces an existential force of quantification.^[23] This assumption is directly supported by the fact that the arbitrary pro subject in (31) shows the characterizing properties of existential arbitrary pro subjects as noted in Cinque (1988) and Spyropoulos (2002): first, the arbitrary pro-subject is compatible with a single individual meeting the description. Second, the arbitrary pro-subject is only compatible with a specific time reference. Third, the arbitrary pro-subject can only be an external argument. Given these arguments, we follow Shlonsky (1988) in assuming an existentially quantified analysis for the sentence in (1).^[24]

The semantic and distributional facts of the strong ʔilla _D+  sentences in (31) are correctly derived within the common exhaustification approach with EXH+ associating and quantifying over the scalar and subdomain alternatives ALT_D+σ (p) for the plain subtractive meaning (D (P ∖ X) (Q)). For the ungrammatical use of ʔilla _D+ in (31), syntactic exhaustification only excludes domain alternatives which are the only non-weaker member of the set ALT_D+σ (p). As a result, contradictory truth conditions arise.

(33)

a.

Plain subtractive meaning of (31. a)

⟦*31. a⟧ =: D+ ∖{ Khālid } ∩ Attended ≠ ∅ in w

b.

Syntactically exhaustified truth conditions

i.

ALTσ (p(w)) =: {D+ ∖ { Khālid } ∩ Attended ≠ ∅ in w;

D+ ∖ ∅ ∩ Attended ≠ ∅ in w}

ii.

ALTD (p(w)) =: {D+ ∖ { Khālid } ∩ Attended} ≠ ∅ in w;

D ∖ { Khālid } ∩ Attended ≠ ∅ in w ∣ D ⊂ D+}}

iii.

ALTD+σ (p) =: ALTD (p(w)) ∪ ALTσ (p(w)) =:

{D+ ∖ { Khālid } ∩ Atended ≠ ∅ in w; D+ ∖ ∅ ∩ Attended ≠ ∅ in w;

D ∖ { Khālid } ∩ Attended ≠ ∅ in w}

c.

EXH+ (ALT σ+D (⟦31. a⟧)) (⟦31. a⟧) is true if and only if

[ D+ ∖{ Khālid } ∩ Attended ≠ ∅ in w ] is true and ¬ [D ∖ { Khālid } ∩ Attended ≠ ∅ in w ]

(i.e., Contradictory truth conditions: it may not hold that some individual in D+ except Khalid came in w and it is false that some individual in D, where D is any proper subset of D, attended).

As for (31.b), since negation reverses monotonicity, syntactic exhaustification, this time, is no longer contradictory or vacuous. It eliminates the non-weaker alternatives to the basic subtractive meaning of (33.i) leading to a strengthened meaning which induces a semantic effect on the overall meaning as shown in (34). In this case, syntactic exhaustification only excludes scalar alternatives which are the only non-weaker member of the set ALT_D+σ (p(w)). As a result, the correct truth conditions arise which hold that no person in a broad domain of context D+ except Khālid attended.

(34)

a.

Plain subtractive meaning of (31. b)

⟦31. a⟧ =: ¬ [D+ ∖{ Khālid } ∩ Attended ≠ ∅ in w ]

b.

Syntactically exhaustified truth conditions

i.

ALTσ (p(w)) =: { ¬ [D+ ∖ { Khālid } ∩ Attended ≠ ∅ in w ];

¬ [ D+ ∖ ∅ ∩ Attended ≠ ∅ in w ]}

ii.

ALTD (p(w)) =: { ¬ [ D+ ∖ { Khālid } ∩ Attended} ≠ ∅ in w];

¬ [ D ∖ { Khālid } ∩ Attended ≠ ∅ in w ] ∣ D ⊂ D+}}

iii.

ALTD+σ (p(w)) =: ALTD (p(w)) ∪ ALTσ (p(w)) =:

{ ¬ [D+ ∖ { Khālid } ∩ Attended ≠ ∅ in w ]; ¬ [ D+ ∖ ∅ ∩ Attended ≠ ∅ in w ];

¬ [D ∖ { Khālid } ∩ Attended ≠ ∅ in w]}

c.

EXH+ (ALT σ+D (⟦31. a⟧)) (⟦31. a⟧) is true if and only if

¬ [ D+ ∖{ Khālid } ∩ Attended ≠ ∅ in w] is true and [D+ ∖ ∅ ∩ Attended ≠ ∅ in w ] is true

⇔ D+ ∩ Attended = { Khālid } in w

The exhaustification analysis in (33) and (34) correctly predicts the paradigm of strong NPI of ʔilla _D+ in (31). For ʔilla _D+ , syntactic Agreement resulted from the domain broadening effect triggers the application of syntactic exhaustification which is a local operation based on features-based agreement that draws on features valuation in the syntax. Syntactically, a Focus-marked domain variable D+ (i.e., where D ⊂ D+) enters the syntactic derivation with the unvalued feature [uD] which triggers the presence of an Agreeing focus-sensitive operator in the syntax with an interpretable feature [iD]. An Agree relation is established in which the operator probes into local syntactic to value/check off the unvalued [uD] of the domain variable D+. Semantically, the associate focus-sensitive operator is realized as the exhaustivity operator EXH+ which associates and quantifies over the scalar and domain alternatives set ALT_D+σ (p(w)) to the plain enriched subtractive meaning p(w) which comprises its truth conditional (i.e., assertive) and non-truth conditional (e.g., presuppositional) dimensions of meaning.

As predicted, the use of [ʔilla _D+  XP] in the left argument of the universal quantifier in (35), repeated from (5.b) is unacceptable.

(35)

* kull	waraqa	min-illi	[ pro	naʃar-ha	ʔilla	xa:lid ]
Every	paper	Rel i	[ 3.SG.M	published-her i	except	Khālid]
ʔxðat	daʕim
received	fund
‘Every/no/any paper whichi [someone except Khālid published t i] received fund.’

Assume with Zeijlstra (2022) who built into Chierchia (2013) and Gajewski (2011) that A strong NPI-like expression like the exceptive phrase [ ʔilla _D+  XP], which introduces both scalar and domain alternatives, associates and is quantified over EXH+ through an instance of syntactic exhaustification. Under our analysis, EXH+ operates locally as looking into both the truth conditional and non-truth conditional components of meaning. To formalize this idea, let us take p_{⟨prs, asr⟩} to be the total meaning of proposition p which consists of the presuppositional component p_prs and the assertive component where ⟦ p_{⟨prs, asr⟩} ⟧=: ⟨⟦ p_prs ⟧, ⟦ p_asr ⟧ ⟩. Let us also take the item ! to be an operator that splits the total meaning of p_{⟨prs, asr⟩} into the conjunction of its presuppositional and assertive meanings p_prs and p_asr as in (36).

(36)

!( p) =: [ pprs & pasr ]

On the assumption that the universally quantified expression in (35) triggers an existential presupposition, the plain enriched meaning of (35) which is represented by the conjunction of its presuppositional and assertive meanings is given in (37).

(37)

!p(w) =: [Somex paper(x) & [D+∖ { Khālid } ∩ published(x) ≠ ∅)] &

[everyx paper(x) & [D+∖ { Khālid } ∩ published(x) ≠ ∅)] received_fund]

Let us see how syntactic exhaustification associated ʔilla _D+  results into contradictory truth conditions, which justifies the fact that the strong ʔilla _D+ is no longer acceptable in Strawson DE environments including presupposition triggers such as the left argument of the universal quantifier, as shown in (38).

(38)

It is clear that the outcome of the syntactic exhaustification in (38) which operated on the full meaning of the exceptive comprising its assertive and presuppositional components is contradictory truth conditions. Clearly enough, exhaustifying the existential presupposition with respect to domain alternatives contradict the plain meaning of the structure making the strengthened conjunctive meaning bad altogether. This example explains why the strong ʔilla _D+ is unacceptable in Strawson DE environements such as the left argument of universal quantifiers.

The second correct prediction concerns syntactic locality. As predicted, strong ʔilla _D+ is subject to syntactic locality just as any other strong NPI as shown in (39), repeated from (10′).

(39)

a.

*ma	ħakeet	ʔnnu	pro	ħadˤar	ʔilla	xa:lid
Neg	I said	that	3.SG.M	attended	except	Khālid
‘I did not say that anyone attended except Khālid.’

b.

*ma	ziʕil	laʔanu	pro	ħadˤar	ʔilla	xa:lid
Neg	get angry	because	3.SG.M	attended	except	Khālid
‘He did not get angry because anyone attended except Khālid.’

a′.

*I don’t travel in order to have seen him in years

b′.

*I don’t say that I have seen him in years

With the strong ʔilla _D+ and other strong NPIs such as ‘in years’ involving syntactic exhaustification based on a local Agree relation, the unacceptability of sentences like (39) is well-predicted.

Since Agree relation, just as movement, is subject to locality in such a way that syntactic Agree should take place within the local domain such as the finite embedded clause or the syntactic island; or if you like, within a syntactic phase where a phase is represented by CP or light vP (Polinsky and Potsdam 2001). It follows that syntactic exhaustification based on Agree should operate in the embedded clause. For the unacceptable ʔilla _D+  sentences in (38. a, a′), an instance of syntactic exhaustification applies in which a local Agree relation between the EXH+ operator and the domain variable D+ is established by virtue of features valuation. There are only two possibilities under which EXH+ applies to the structure. In Possibility 1, EXH+ is inserted locally at the level of embedded clause as represented in (40).

(40)

Syntactically, the parse in (40) is grammatical: the Agree relation between EXH _iσ+D and D+ is established locally within the local domain of the embedded clause. Semantically, the parse in (40) is ungrammatical since EXH+ operation on the positive ʔilla _D+  sentence gives rise to contradictory truth conditions. On sematic grounds, this possibility is excluded.

In possibility 2, EXH+ is inserted non-locally at the level of embedded clause taking the negative as its clausal argument as represented in (41).

(41)

Semantically, the parse in (41) is grammatical with EXH+ operation on negated form of embedded ʔilla _D+  yielding consistent truth conditions. Syntactically, the parse in (41) is bad given that the Agree relation between EXH _iσ+D and D+ does not apply locally with EXH+ being located outside embedded clause which contains the Agreeing scalar domain variable D+. Therefore, this possibility is excluded since the Agree relation in question violates syntactic locality. In strong ʔilla _D+  there is no EXH+ without either violating the locality condition on syntactic Agree or without yielding inconsistent truth conditions. Therefore, examples like (39) are unacceptable.

4 Conclusions

This paper addressed a puzzle involving an ambiguous NPI paradigm of exceptive ʔilla in Palestinian/Jordanian Arabic: exceptive ʔilla has a weak and strong NPI distribution depending on whether or not the exceptive phrase in question induces a domain broadening effect in the syntax. As a weak NPI- like expression, exceptive ʔilla combines with universally quantified expressions with no domain broadening effect in the syntax. In this way, weak ʔilla patterns with other weak NPIs and weak exceptive particles in other languages such ‘but’ or ‘except’ in English in being licensed under similar licensing conditions which license weak NPIs such as indefinite ‘any’; the so-called antitone or downward monotonic environments, (e.g., the restrictor of universal quantifiers). As a strong NPI-like expression, ʔilla _D+  induces a domain broadening effect which happens to occur in arbitrary pro-subject sentences. In this case ʔilla _D+  patterns with other strong NPIs such as ‘in week’ and ‘either’ and other strong NPI-like exceptives in other languages such as Japanese sika (Sauerland and Yatsushiro 2023) in being licensed under narrower licesnsing conditions, mainly the local scope of negation. This puzzling ambiguous NPI behavior of ʔilla raised the following theoretical question which calls for an answer: what is the connection between the presence and absence of the externally prosodic-grammatical factor of domain broadening based on Focus-marking and the strong/weak divide of exceptive ʔilla?

To address this question, the paper extends a unified exhaustification analysis to the NPI paradigm of ʔilla based on a theory of NPIs licensing which assigns different types of exhaustification to the strong and weak uses of NPIs: namely pragmatic versus syntactic exhaustification for the weak and strong NPIs as proposed in Zeijlstra (2022), who built into the multi-dimensional analyses of Gajewski 2011; Chierchia 2013). In a nutshell, our unified account went as follows. First, exceptive ʔilla carries the plain subtractive meaning p(w) which undergoes exhaustification with the two semantic inferences of subtraction and unique minimality being derived in grammar. The plain subtractive meaning introduces the set of scalar alternatives σ which comprises all relevant pragmatically-open, non-weaker propositions ALT_σ (p(w)) representing the alternative denotations to p(w) with the complement of the exceptive phrase XP [ʔilla XP] being replaced with the denotations of the XP’s subsets. The scalar alternatives induced stand in no syntactic Agree relation with the exceptive phrase [ʔilla XP]. With no syntactic agreement in place, an instance of pragmatic exhaustification applies as a last resort operation with the exhaustivity operator EXH quantifying over ALT_σ (p(w)). As assumed under Zeijlstra (2022), pragmatic exhaustification applies non locally as operating on the assertive dimension of the structure from its highest clausal location with no locality requirement imposed. This explains the default weak NPI-distribution of exceptive ʔilla _.

As for strong ʔilla _D+ , because ʔillaD ₊  induces a domain broadening effect which happens to occur in existentially-interpreted arbitrary pro-subject sentences. As a domain broadening scalar item, ʔilla _D+  involves a Focus-marked quantificational domain variable of discourse D+ which triggers a set of subdomain alternatives in the syntax. The domain alternatives induced are not an inherent component of the exceptive meaning of the exceptive but it is a prosodically added value. As a result, an Agree relation is established between the Focus-marked D+ and a focus-sensitive operator in the syntax. The focus-sensitive operator in question is EXH+ which carries on the type of exhaustification that Zeijlstra (2022) labelled syntactic exhaustification. Syntactically, EXH+ establishes an Agree relation with the D+ as carrying the interpretable [iD] that checks or values the uninterpretable feature [uD] of by D+ variable. Following Zeijlstra (2022), we assume that EXH+ is smart operator that operates on both domain and scalar alternatives ALT_D+σ (p(w)) and it looks into both assertive and non-assertive (e.g., presuppositional) dimensions of meaning. With syntactic exhaustification in effect, we can easily and straightforwardly account for two facts about the strong NPI-like ʔilla _D+  under a unified exceptive semantics for ʔilla: (i) the strong NPI distribution of ʔilla _D+ (ii) ʔilla _D+ ’s sensitivity to syntactic locality _.

The analysis just presented, which draws on a syntactic version of the multi-dimensional exhaustification analysis of weak/strong NPIs in terms of Zeijlstra (2022) has the following empirical and theoretical advantages. Empirically, the analysis captures the weak and strong NPI-behavior of exceptive ʔilla under a unified exceptive semantics based on exhaustification with the intuitive connection between the absence/presence of domain broadening effect, on one hand, and the weak/strong NPI-behavior of the exceptive, on the other hand being understood. Theoretically, the analysis contributes a case study which contributes further support to the distributed semantics of exceptives based on exhaustification (Crnič 2018; Gajewski 2008, 2013; Hirsch 2016; Sauerland and Yatsushiro 2023; Spector 2014), which receives more support to the exclusion of an intergrated semantics of the exceptives which rely on no exhaustification in grammar (see Crnič 2018 for a set of arguments supporting the distributed exhaustification approach). Just as weak and strong NPIs which vary with respect to the type of exhaustification involved (e.g., Chierchia 2013; Gajewski 2011; Zeijlstra 2022), exceptive ʔilla, which shows both weak and strong NPI-behavior, is also subject not only to an application of grammatical exhaustification deriving its subtraction and unique minimality inferences but also it is sensitive to the type of exhustification involved which gives rise to a weak and strong variant of the exceptive in question.