NPIs, intervention, and collectivity *

Negative polarity items are subject to so-called intervention effects (Linebarger 1980, 1987). Specifically, they are unacceptable in the immediate scope of certain non-downward-entailing operators, even if they occur in the scope of a (higher) downward-entailing operator. By studying the behavior of any in configurations with collective predicates, we provide new empirical arguments that the descriptive condition concerning intervention must be stated with reference to the content of the clausal constituents in which NPIs may occur, and not merely with reference to operators c-commanding them. This is in line with recent arguments for environment-based formulations of NPI licensing conditions (e.g., Homer 2008, Gajewski 2011). We conclude by discussing how the condition fits in with some recent theories of intervention (especially Guerzoni 2006, Chierchia 2013).


NPI Licensing Condition
An NPI is acceptable only if it is c-commanded by an operator that is downward-entailing.
The NPI Licensing Condition in (1) is stated merely as a necessary condition on the acceptability of NPIs due mainly to an observation by Linebarger (1980Linebarger ( , 1987 that occurrences of NPIs in the scope of a downward-entailing operator may be unacceptable -in particular, if they occur in the immediate scope of certain operators that are not downward-entailing, such as and. 3 These operators are then said to "intervene" in the licensing of the NPI and have been dubbed "interveners". An intervention configuration is exemplified in (2): in both cases, an NPI occurs in the scope of a downward-entailing operator -doubt and negation -and yet both sentences are unacceptable.
(2) a. *I doubt that Mary and any boy have blue eyes. b. *John didn't drink any whisky and the soda.
In order to have a more constrained characterization of the distribution of NPIs, Linebarger (1987: p. 338) suggested an additional restriction on their distribution, provided in (3). (3)

Additional Restriction
An NPI is unacceptable if it occurs in the immediate scope of an operator that is not downward-entailing.
This constraint has been further refined. It turns out, namely, that not all operators are interveners. In (4), we see that or does not intervene in the licensing of any, in contrast to and.
1 An operator is downward-entailing if and only if (iff ) it denotes a downward-entailing function. A function of type is downward-entailing iff for all and of type such that ⇒ , ( ) ⇒ ( ), where "⇒" is cross-categorial entailment. (See von Fintel 1999 for a qualification.) 2 Cross-categorial entailment, notated as "⇒", is defined recursively as follows. If and are of type , then ⇒ iff = F or = T. If and are of type , then ⇒ iff ( ) ⇒ ( ) for all of type . 3 occurs in the immediate scope of a logical operator iff c-commands (or m-commands) , and there are no other logical operators that c-command (or m-command) and are ccommanded (or m-commanded) by .

2:2
NPIs, intervention, and collectivity (4) a. I doubt that Mary or any boy has blue eyes. b. John didn't drink any whisky or the soda. Chierchia (2004Chierchia ( , 2013 notes that the property that appears to distinguish between interveners and non-interveners pertains to the relation the operators stand in with their scalar alternatives: "[i]nterveners are strong members of a scale; non-interveners are the weakest ones" (Chierchia 2004: p. 84) and "[w]hen a scalar item induces an intervention effect, what seems to be playing a role is not so much its intrinsic nature but rather its position in the scale" (Chierchia 2013: 378ff). A corresponding refinement of the Additional Restriction would be to restrict the class of intervening operators as stated in (5); the pertinent scales referred to in (5) are provided in (6). 4 (5)

Revised Additional Restriction
An NPI is unacceptable if it occurs in the immediate scope of an operator (i) that is not downward-entailing, and (ii) that does not occupy the lowest (logically weakest) position on its scale.
(6) Some example scales (e.g., Horn 1972, Sauerland 2004 a. ⟨or, and⟩ b. ⟨some, every⟩ c. ⟨one, two, three, …⟩ In the remainder of this remark, we present evidence that casts doubt on (5). We provide new arguments that the descriptive condition on NPI licensing, (1), must be environment-based (rather than operator-based), and must reference full sentential alternatives (rather than scalemates), thus replacing (5) (see, e.g., Kadmon & Landman 1993, Lahiri 1998, Homer 2008, Gajewski 2011, Chierchia 2004, 2013, Crnič 2014, 2019a,b, 2020, Buccola & Spector 2016 for further arguments). Specifically, we argue that the acceptability of a sentence instantiating an intervention configuration does not depend simply on the position that the relevant operator occupies in its scale, but rather depends on the logical relation that the pertinent constituent dominating the operator (i.e., the pertinent environment) bears to its alternatives.

The observation
We present a new observation: there are cases where and and an NPI stand in an intervention configuration -that is, their configuration violates the condition in (5) -but where the NPI is nevertheless systematically acceptable. This is the case in the following near-minimal pairs: the (a)-sentences are judged to be unacceptable, while the (b)-sentences are judged to be acceptable. In particular, (7b) conveys that I don't think Mary has ever collaborated with a boy, and (8b) conveys that John didn't mix the soda with any portion of whisky. ( A feature of the acceptable (b)-examples above that distinguishes them from the unacceptable (a)-examples is that the conjoined DPs combine with a collective predicate in the (b)-cases but not the (a)-cases (mix is collective with respect to its object argument). A collective predicate is one that may hold of a plurality without holding of any of the proper parts of that plurality. This observation is generalized in (9), which is stated as a necessary condition on the acceptability of conjunctions formed from any NP. 5,6 5 The constraint in (9) applies only to NPI occurrences of any NP, not to any NP in general. 6 A reviewer notes that if the conjunction that combines with a collective predicate were not scope-bearing, then it would not be subject to the (Revised) Additional Restriction (as defined in Linebarger 1980Linebarger , 1987. Following the reviewer's suggestion, we demonstrate its scope-bearing nature by means of an interaction with disjunction: sentence (i) has the two relevant readings described in (ia)-(ib), which depend on the scope of disjunction relative to conjunction. See Section 3 for definitions and related discussion.
(i) The physicists or the chemists and the biologist collaborated on a project. a.
[or > and]: the physicists collaborated ∨ the chemists collaborated with the biologist b.
[and > or]: the physicists collaborated with the biologist ∨ the chemists collaborated with the biologist 2:4 NPIs, intervention, and collectivity (9) Constraint on any NP conjunction Any NP conjoined with another DP is acceptable only if the conjunction combines with a collective predicate.
The collectivity of the predicates need not be lexical, but can be derived in syntax. It may spring from using expressions that require a plural argument in the sentence. These include a reciprocal anaphor, as in (10a), a so-called internal same, as in (10b), and a collectivizing adverbial like together, as in (10c).
(10) a. I don't think that Mary and any boy here have ever laughed at each other's jokes. b. The zookeeper didn't put any monkey and the lion into the same cage. c. John denies that Mary and any student of hers have ever written a paper together.
Relatedly, if a predicate is mixed (can in principle be interpreted either distributively or collectively), then the only interpretation that one may obtain with a conjoined any NP argument is the one that applies the predicate collectively to the conjoined plurality. For example, (11) can only mean that I doubt that any son of mine is such that my wife and 's combined weight is exactly 150 kg; it cannot mean that I doubt that my wife's weight is exactly 150 kg and that, at the same time, some son of mine's weight is exactly 150 kg. In the absence of an NPI, (12), both interpretations are in principle possible.
(11) I doubt that my wife and any son of mine weigh exactly 150 kg.
(12) I doubt that my wife and a son of mine weigh exactly 150 kg.

The puzzle
The observation summarized in (9) is puzzling on the formulation of the condition on interveners in (5), at least given the common approaches to 2:5 Brian Buccola and Luka Crnič conjoined DPs. Before revising the condition, we describe how the puzzle surfaces for three families of approaches to and.

A uniform boolean semantics of DP conjunction
If one assumes that the semantics of DP conjunction is derived from the basic meaning of conjunction in propositional logic by appropriately type-shifting it and its arguments (e.g., Partee & Rooth 1983, Keenan & Faltz 1985, Winter 2001, Champollion 2015, then one predicts that all occurrences of conjunction should qualify as interveners. Namely, propositional conjunction and its type-shifted counterparts on such an approach entail, respectively, propositional disjunction and its type-shifted counterparts, as illustrated in (13) and (14): for all arguments, the output of conjunction applied to them entails the output of disjunction applied to them. 7 (13) a. ⟦and⟧ ( ) = .
A simplified structure of sentence (15a) is provided in (15b) (the structure is simplified by dropping the attitude predicate). In addition to other operators, negation c-commands and, which in turn c-commands any boy in this representation (see Winter 2001, though his proposal differs in details). Accordingly, we are clearly dealing with an intervention configuration, as defined in (3) 7 More generally, for any boolean type , we have the following, where "⊓ " and "⊔ " denote the meet and join operators, respectively, defined over the domain associated with : For all and of type , ⟦and⟧ ( ) ( )( ) ⇒ ⟦or⟧ ( ) ( )( ).

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NPIs, intervention, and collectivity For concreteness, we provide the computation of the meaning of (15) in (16). Lift lifts the denotation of Mary to a quantifier (Montague 1970). 8 Min takes a set of predicates that hold of, respectively, Mary and a boy, and returns the set of all the minimal subsets of that set -that is, the set of all subsets consisting of Mary and a boy (Winter 2001). 9 ∃ stands for existential closure over sets of individuals. Accordingly, if we treat pluralities as sets of individuals, which we do for expository reasons, then the meaning of the sentence is that none of these minimal sets consisting of Mary and a boy is in the denotation of collaborate. 10 To summarize, an appropriately type-shifted conjunction counts as an intervener on the condition in (5). Thus, the condition, coupled with this approach to and (and or), undergenerates -it does not admit examples of conjoined NPIs that combine with a collective predicate.

A uniform non-boolean semantics of DP conjunction
An alternative approach assumes that DP conjunction effectively takes individuals as arguments and returns sets of them -that is, pluralities of them (e.g., Hoeksema 1988, Krifka 1990, Lasersohn 1995. On this kind of approach, the semantics of and that combines quantifiers can be stated as in (17), where it effectively corresponds to pointwise set union.
A simplified structure of sentence (18a) is provided in (18b), and its interpretation is provided in (19). Lift again lifts the denotation of Mary to a quantifier, to which the first occurrence of Min applies, yielding the singleton containing the singleton containing Mary. The second occurrence of Min takes a set of sets containing a boy, and returns the set of all minimal 8 ⟦Lift⟧ (( ) ) = . .
, for any type . 10 The reason we need Min is that we want a sentence like Mary and John lifted the piano together to be true only if Mary and John did it as a two-person group; without Min, the sentence would mean merely that a group containing John and Mary (and possibly others) lifted the piano (see Winter 2001, Champollion 2015 for discussion).

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Brian Buccola and Luka Crnič subsets of that set -that is, the set of all singletons containing a boy. The conjunction and now pointwise-unions these two quantifiers, yielding the set of all sets consisting of Mary and a boy. The meaning of the sentence, then, is that none of these sets consisting of Mary and a boy is in the denotation of collaborate, just as we derived above. Furthermore, just as above, negation c-commands and, which in turn ccommands any boy. (18b) thus looks, at first glance, like another intervention configuration.
In this case, however, there is no sensible definition of disjunction that would stand in an entailment relation with (19) -that is, we lack a sensible non-boolean definition of disjunction. Accordingly, the restriction in (5) does not apply to the conjunction (namely, this version of and does not form an entailment scale with or), thus potentially capturing the acceptability of (18). An unfortunate consequence of this logic, however, is that occurrences of any NP in conjunction would be predicted to be acceptable even when they combine with distributive predicates. This is illustrated in (20), where for simplicity we assume that the distributive predicate is cumulative (which we mark with a *-operator; see Kratzer 2007 Accordingly, the condition in (5), coupled with a non-boolean approach to and, overgenerates -it admits infelicitous examples of conjoined NPIs that combine with a distributive predicate.

Ambiguity of DP conjunction
An approach that takes DP conjunction to be ambiguous -that is, an approach that assumes that there are boolean and non-boolean lexical entries 2:8 NPIs, intervention, and collectivity for and -initially appears to be better off than its alternatives discussed above. Namely, if a non-boolean lexical entry is used, as may be necessary with collective predication, then one would correctly predict no intervention effects given the condition in (5). However, an issue of overgeneration still arises: as it stands, nothing would prevent one from using non-boolean conjunction also with distributive predicates (e.g., Hoeksema (1988), Krifka (1990), and Lasersohn (1995) carefully demonstrate this), thus incorrectly allowing for obviation of intervention effects in those cases as well. While a theory that would force different derivations with collective vs. distributive predicates can be devised, we refrain from exploring this possibility here, not least because there may be good independent reasons to avoid an ambiguity approach to conjunction (see especially Winter 2001, Champollion 2015, Schein 2017. Rather, we take the patterns in Section 2 to support a revision of the condition in (5). The revision that we end up with is agnostic with respect to the details of the analysis of conjunction (and disjunction).

The revision
We concluded that the facts described in Section 2, and the generalization/ constraint stated in (9), contradict the refined characterization of interveners in the Revised Additional Restriction in (5). We propose that the key to understanding the source of (9) involves understanding how the semantic difference between distributive and collective predicates affects the relation between the sentence containing the NPIs and their alternatives, which includes alternatives in which conjunction is replaced by disjunction. We expose this relationship in terms of the semantic property in (22) (focusing here just on subject-collective predicates for simplicity). 11 (22) a. For distributive VP: ¬( or VP) ⇒ ¬( and VP). b. For collective VP: ¬( or VP) ⇏ ¬( and VP).
11 This property may need to be qualified for some collective predicates, for which the entailment pattern in (22b) may hold (Križ 2015, Bar-Lev 2018. To the extent that such predicates exist, and obligatorily validate the entailment pattern in (22b), we expect them to pattern with distributive predicates in creating intervention effects with conjoined any NP. On the other hand, if the validation is only optional (e.g., the predicates allow for multiple construals), then, in the presence of an NPI, we expect a disambiguation to a construal that does not validate (22b).

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Brian Buccola and Luka Crnič (23) a. It's not the case that the girls or the boys have blue eyes. b. ⇒ It's not the case that the girls and the boys have blue eyes.
However, (24a) does not entail (24b) (on its collective reading). Consider a scenario in which the girls and the boys all wrote a paper together, but no group of girls wrote a paper together, nor did any group of boys. In this scenario, the or-sentence is true, while the and-sentence (on its collective reading) is false.
It's not the case that the girls or the boys wrote a paper together. b. ⇏ It's not the case that the girls and the boys wrote a paper together.
In light of this observation, we suggest that, rather than checking whether a potential intervener cross-categorially entails some alternative operator, one must evaluate whether a pertinent sentence containing the NPI and the operator is entailed by its alternatives (which are induced by the operator). A pertinent sentence is one that is downward-entailing with respect to the NPI -that is, one in which replacing the NPI with a stronger expression results in a weaker meaning overall (see, e.g., Kadmon & Landman 1993, Gajewski 2005, Homer 2008, Chierchia 2004, 2013, Buccola & Spector 2016, Crnič 2014, 2019a,b for further arguments for such a switch). 12, 13 This leads us to the Revised NPI Licensing Condition in (25), which replaces both the original NPI Licensing Condition in (1) and the Revised Additional Restriction in (5). (The latter, which was previously split off from the NPI Licensing Con-12 A sentence is downward-entailing with respect to (an occurrence of) iff (i) dominates , and (ii) for any such that ⇒ , ⇒ → , where → is the result of replacing (the occurrence of) with in . See Gajewski 2005, Homer 2008 for slightly different formulations. 13 Clause (ii) of the constraint needs to be further constrained in order to deal with sentences like (ia), which is entailed by its alternative in (ib). A proper statement would restrict the pertinent alternatives to those that are induced by the material that is appropriately local to the NPI (see Chierchia 2013 for a proposal).
(i) a. Few students read any book. b.
No students read any book.
In addition, clause (i) of the constraint needs to be further revised to deal with acceptable cases of any NP in presuppositional, modal, and non-monotonic environments (Kadmon & Landman 1993, Gajewski 2011, Crnič 2014, 2019a.

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NPIs, intervention, and collectivity dition, is now crucially encoded as a part of the licensing condition because recourse to the constituent in which the NPI would be otherwise acceptable is required.)

Revised NPI Licensing Condition
An NPI is acceptable only if it occurs in a sentence (i) that is downwardentailing with respect to the NPI, and (ii) whose scalar alternatives do not entail the sentence.
The condition in (25) has the generalization in (9) as an immediate consequence. Consider, for example, the unacceptable sentence in (26).
(26) *I don't think that the girls and any boys have blue eyes.
Here, and is dominated by a sentence that is downward-entailing with respect to the NPI -this is illustrated in (27); but at the same time, is entailed by the or-alternative of -this is illustrated in (28) (see also (23)). Thus, the sentence violates the Revised NPI Licensing Condition, yielding unacceptability.
(27) a. I don't think that the girls and some boys have blues. b. ⇒ I don't think that the girls and some tall boys have blue eyes.
[satisfies condition (i) of (25) ] a. I don't think that the girls or some boys have blue eyes. b. ⇒ I don't think that the girls and some boys have blue eyes.
(29) I don't think that the girls and any boys have ever written a paper together.
Here, and is again dominated by a sentence that is downward-entailing with respect to the NPI -this is illustrated in (30); but now is not entailed by the or-alternative of -this is illustrated in (31) (see also (24)). Thus, the sentence respects the Revised NPI Licensing Condition, yielding acceptability. 14 14 If the alternatives involve singular DPs, then the or-alternative is ill-formed, and thus perhaps does not count as an alternative. The sentence would thus vacuously satisfy the condition.

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(30) a. I don't think that the girls and some boys have written a paper together. b. ⇒ I don't think that the girls and some tall boys have written a paper together.
[satisfies condition (i) of (25) ] (31) a. I don't think that the girls or some boys have written a paper together. b. ⇏ I don't think that the girls and some boys have written a paper together.

Two predictions
Importantly, the Revised NPI Licensing Condition makes predictions about "inteveners" beyond just conjunction. Here we discuss several other such cases.

Numeral intervention
Numerals above one (e.g., four), like and, are considered "strong", and hence interveners, in Chierchia 2013. For instance, (32a) and (32b), which both include the distributive predicate read any paper of mine, exhibit an acceptability contrast between one, which is acceptable, vs. four, which is unacceptable. However, we observe that when the predicate is collective (write any paper together), four is acceptable. 15 Do these observations follow from the Revised NPI Licensing Condition?
(32) a. I don't have one colleague who has read any paper of mine. b. *I don't have four colleagues who have read any paper of mine. c. I don't have four colleagues who have written any paper together.
Consider first the matrix sentence in (32b). It is downward-entailing with respect to any paper of mine, as illustrated in (33). However, it also holds that the alternative obtained by replacing four with, say, three entails the sentence, as illustrated in (34) [satisfies condition (i) of (25) ] (34) a. I don't have three colleagues who have read a paper of mine. b. ⇒ I don't have four colleagues who have read a paper of mine.
[violates condition (ii) of (25) ] In contrast, the sentence in (32c) is downward-entailing with respect to the NPI, but it is not entailed by the alternatives obtained by replacing four with other numerals. This is illustrated with three in (36): there may well not be (a group of) three colleagues who wrote a paper together, while there is (a group of) four colleagues who wrote a paper together (see fn. 16 for more details).
(35) a. I don't have four colleagues who have written a paper together. b. ⇒ I don't have four colleagues who have written a long paper together.
[satisfies condition (i) of (25) ] (36) a. I don't have three colleagues who have written a paper together. b. ⇏ I don't have four colleagues who have written a paper together.
[satisfies condition (ii) of (25) ] 16 Slightly more formal representations of the meanings of the sentences discussed in this subsection are provided in the following. The crucial difference between them pertains to the distributivity of read vs. the non-distributivity of write together. See Buccola & Spector 2016 for evidence for this analysis. The condition in (25) predicts these contrasts: substituting the numeral with a smaller numeral yields a logically stronger sentence in the cases with distributive predicates, hence the intervention effect, whereas in the case of collective predicates, there is no logical relation between the various numerical alternatives, hence the lack of an intervention effect.

Other interveners
We have shown that conjunction and numerical phrases are not interveners simpliciter; in particular, they do not induce intervention in configurations with collective predicates. Can similar configurations be constructed with other potential interveners? It turns out that conjunction and numerical phrases may be uniquely able to avoid inducing intervention effects in a way that obeys the condition in (25). Consider every, all, and always, which tend to give rise to intervention effects.
(37) a. *Not all students did any homework. b. *Mary doesn't always read any books.
In order not to violate the condition in (25), one would need to find a configuration in which the alternative with some, Not some (= No) NP VP, does not entail the sentence with all, Not all NP VP. But this entailment always holds: to the extent that universal quantifiers are acceptable with collective predicates, the negation of such predication will be entailed by the negation of their counterparts with some. This is exemplified in (38) and stated more generally in (39) (on the assumption that every/all entails existence). (Similar considerations extend to always and sometimes).
No students met/collaborated. b. ⇒ Not all students met/collaborated.
Accordingly, configurations in which NPIs occur in the immediate scope of every NP or always cannot satisfy the Revised NPI Licensing Condition, resulting in their unacceptability.

Towards an explanation
We have provided a descriptive condition, (25), for what constitutes an intervention configuration as part of the NPI Licensing Condition. We conclude this remark by briefly discussing how (25) relates to two families of recent theories of NPI licensing and intervention. The first is tied to operators, while the second is not.

Movement-based approaches
One family of approaches to intervention with NPIs can be stated as requiring the relation between the NPI and its putative "licensing" operator to involve a syntactic dependency, for example formed by covert phrasal movement (Progovac 1994, Giannakidou 1997. This means that the sentence in (40) would be acceptable if the NPI could move to its licensing operator (negation), but this is not possible in (40): any boy cannot extract out of the conjoined phrase, which is an island for (covert) phrasal movement. This is demonstrated by the unavailability of wh-movement in (41a), and the impossibility of QR of every boy above a different person in (41b). Another movement-based theory, potentially better poised to capture the data, comes from Guerzoni (2006), who argues that NPIs can be licensed in either of two ways: by phrasal movement (p-movement) or by feature movement (f-movement). As just discussed, the acceptable NPIs in conjunctions like (40) cannot be captured by p-movement, since the conjunctions are islands that block p-movement. But can the NPI be licensed by f-movement? Guerzoni, building on Pesetsky 2000, argues that f-movement is not subject to the same constraints on movement as p-movement, but is instead blocked by "interveners". On her theory, whether or not an expression is an "intervener" is diagnosed by whether or not it creates wh-intervention effects. If it can be shown that and is an intervener in (40), but not in (42), then we may get some insight into why (42) is acceptable, but not (40). The pertinent data are in (44) (judgment marks omitted): (44) a. Which student thinks that Mary and which boy have laughed at my jokes? b. Which student thinks that Mary and which boy have collaborated?
For the f-movement account to capture the NPI facts, there would need to be a contrast in acceptability between the two sentences in (44): (44a) should be unacceptable, and (44b) acceptable. We found it hard to elicit this contrast. However, we note that the judgments are subtle and thus mandate further testing.
Furthermore, some general issues arise for the movement approaches to intervention in view of being tied to an operator-based characterization of NPI licensing. One set of issues is theoretical in nature. For example, even if the approaches captured the data, they seem to us to provide little insight into why the two occurrences of and in (40) and (42) differ in terms of intervention effects. This is different from the environment-based approach discussed in the upcoming section, on which the intervention effects are explained by how they affect interpretation.
The other set of issues is empirical in nature. On the one hand, due to being operator-based, the movement approaches face an issue with the arguments for the environment-based approach to NPI licensing. This is illustrated by the sensitivity of NPIs to the collectivity of the main predicate in (45) (see Buccola & Spector 2016 for further arguments).
(45) a. #Fewer than ten soldiers surrounded any castle. b. Fewer than ten soldiers visited any castle.

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NPIs, intervention, and collectivity On the other hand, the approaches also face an issue with certain configurations that do not exhibit intervention for f-movement. For example, given the felicity of (46), which would be accounted for by f-movement of which philosopher to the matrix clause, we would expect that (47) should be acceptable as well (namely, the pertinent NPI feature could f-move out of the singular definite description and be checked by negation), contrary to fact (see Crnič & Buccola 2019 for exceptions).
(46) Which student read the book that praised which philosopher?
(47) #Mary didn't read the book that praised any philosopher.

Exhaustification-based approaches
A second family of approaches to intervention arises from the work of Chierchia (2004Chierchia ( , 2013 and Gajewski (2011). On such approaches, the alternatives induced by operators that c-command NPIs and that occur in constituents that are downward-entailing with respect to the NPIs obligatorily enter into determining the acceptability of the NPIs. These alternatives are, then, responsible for the unacceptability of the sentences because their incorporation into subsequent computations results in semantic anomaly -at least if these alternatives are stronger than the sentence. Chierchia's (2004) core idea is that intervention effects are the result of implicatures triggered by an exhaustification operator that associates with the NPI -and all the intervening scalar items. For instance, in *John didn't drink the soda and any whisky, the occurrence of and leads to the implicature that the or-alternative (John didn't drink the soda or any whisky) is false. Overall, then, the sentence conveys that John didn't drink both the soda and a portion of whisky, but he did drink one or the other. The implicature ends up destroying the downward-entailingness of the NPI's environment, hence is responsible for the unacceptability of the NPI, as illustrated in (48). What about acceptable sentences with collective predicates, discussed above, such as John didn't mix the soda and any whisky? The same interference also arises for them, as shown in (49).

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Brian Buccola and Luka Crnič (49) a. ¬(John mixed the soda and some whisky) ∧ (John mixed the soda or some whisky) b. ⇏ ¬(John mixed the soda and some Irish whisky) ∧ (John mixed the soda or some Irish whisky) However, sentences with collective predicates differ from those with distributive predicates in one important respect, which can be capitalized on in the full system of Chierchia 2013. Specifically, in this system, the sentence with the distributive predicate (drink) ends up having the interpretation in (50), which is inconsistent and thus reason for the sentence to be unacceptable (see Chierchia 2013: ch. 7, for details). On the other hand, the sentence with the collective predicate has the interpretation in (51), which is consistent and should thus be acceptable. The consistency of this meaning is a consequence of the pertinent scalar alternatives (including subdomain alternatives in Chierchia 2013) not entailing the sentence with the NPI. 18 18 Here we provide the derivations in a simplified form.
refers to the domain of discourse, over which portions of whisky (etc.) are quantified. The distributive sentence (with drink) asserts the proposition in (ia) and has the scalar alternatives in (ib) and the subdomain alternatives in (ic) (we omit the assertion itself from these sets). Within the system of Chierchia 2013, these alternatives get negated, yielding the contradictory overall meaning in (id). The collective sentence (with mix), by contrast, works as in (ii), whose overall meaning is non-contradictory.
(ii) John didn't mix the soda and any whisky. While it seems that the data we discussed fits with proposals like that of Chierchia, the approach does predict non-trivial inferences for sentences like John didn't mix the soda and any whisky. Specifically, John didn't mix the soda and any whisky is, all else being equal, predicted to convey that John mixed the soda and that he mixed (all portions of) the whisky, as provided in (51). Since this inference does not seem to necessarily accompany such sentences, the question arises what its absence may be due to in Chierchia's system. We point to two possibilities.

Constraint on pruning.
The logical properties holding between the sentence and its alternatives point to one possible direction of answering this question. Chierchia assumes in his system that all the scalar and subdomain alternatives induced by a constituent in the scope of an exhaustification operator are relevant. This is necessary in order to derive intervention effects. Crucially, the scalar alternatives whose exhaustification yields ungrammaticality are stronger than the respective constituent itself, as in (52a)-(52b). As we rehearsed above, this is crucially not the case for the alternative to conjunction with a collective predicate, as in (53). Accordingly, if the absolute constraint on pruning of alternatives is replaced by a constraint against the pruning of stronger alternatives, then we may account for the absence of the inference under discussion -in the case of pruning of logically independent alternatives, the problematic inference disappears.
Timing of pruning. An alternative explanation relies on an architectural underpinning of Chierchia's system (cf. Gajewski 2003, Fox & Hackl 2006: the acceptability of NPIs is effectively determined at a level that is blind to non-logical content (in the so-called "deductive system", Fox & Hackl 2006). Accordingly, if one obtains a consistent meaning at that level, as is the case of exhaustification with collective conjunction, the NPI is licensed. It is possible that contentful considerations, including the pruning of certain alternatives, are effected later. We have to leave it open here which of these two options, if either, is on the right track. 19

Conclusion
NPI intervention effects with conjunction are sensitive to the collectivity of the predicate that combines with the conjunction: an NPI conjoined with another DP is acceptable only if the conjunction combines with a collective predicate. We proposed to capture this distribution by imposing a constraint on the pertinent constituent that is downward-entailing with respect to the NPI: it must not be entailed by its scalar alternatives. This distribution of NPI intervention effects provides further support for an environment-based statement of the condition on NPI licensing (see Heim 1984, Gajewski 2005, 2011, Homer 2008, Chierchia 2004, 2013, Crnič 2019a for further discussion).
19 A similar state of affairs with (non-)intervention may obtain also on other alternativesensitive approaches to NPI licensing, in particular the approach that takes the licensing of any to involve a covert even operator that associates with any NP (see, e.g., Lahiri 1998, Crnič 2014, 2019a. If we adopt the assumption that even must associate with all the alternatives induced in its scope (following Chierchia 2013), then we obtain the following predictions: (i) in the case of conjoined NPIs with distributive predicates, the pertinent disjunctive alternatives will entail the sentence, and so the sentence will end up having a contradictory presupposition; and (ii) in the case of conjoined NPIs with collective predicates, the disjunctive alternatives will not entail the sentence, and so the presupposition of even will be consistent. As in the case with the exhaustification-based approach, many questions arise and further study is mandated.