## 1 Introduction

Within semantics and pragmatics, where the aim is to understand the inferences drawn from (uses of) sentences, this paper zooms in on a particular class of inferences: those drawn from sentences with a plural subject (such as Alice and Bob) about how each member of the subject participates in the predicate of the sentence (Bartsch 1973; Scha 1981; Link 1983; Roberts 1987); see Winter & Scha (2015); Nouwen (2015); de Vries (2017); Champollion (2019; 2020) for recent overviews.

(1) conveys that Alice and Bob each smiled. Smile is therefore distributive: inferred to be individually true of (to distribute down to) each member of the plural subject. (Distributivity applies to all sorts of plurals, but I focus on conjoined names for clarity.)

 (1) Alice and Bob smiled. (distributive) a. ✓Distributive: Alice smiled, Bob smiled. b. ✗Nondistributive: Alice and Bob smiled jointly but not individually.

In contrast, (2) does not convey that each person met – at least, not unless one imagines some sort of implicit object. Instead, meet is true of Alice and Bob together, not each one individually: nondistributive.1

 (2) Alice and Bob met. (nondistributive) a. ✗Distributive: Alice met, Bob met. b. ✓Nondistributive: Alice and Bob met jointly but not individually.

Whereas smile is distributive and meet is nondistributive, (3) can be interpreted in both ways: it can describe a situation in which Alice and Bob each opened the door (distributive); or a situation in which Alice and Bob did not technically each open the door, because they did so by working together (nondistributive).

 (3) Alice and Bob opened {the/a} door. (can be understood both ways) a. ✓Distributive: Alice opened {the/a} door, Bob opened {the/a} door. b. ✓Nondistributive: Alice and Bob opened {the/a} door jointly but not individually.

With an indefinite object (3), a predicate built from a transitive verb has the potential for covariation (Dotlačil 2010) – for the indefinite to covary with each member of the subject, as when (3) is interpreted to involve two different doors. In general, when a predicate can be interpreted as either distributive or nondistributive (3), and especially when its distributive interpretation would involve covariation, the nondistributive interpretation is favored even if both interpretations are available in principle (Brooks & Braine 1996; Frazier et al. 1999; Dotlačil 2010; Syrett & Musolino 2013; Dobrovie-Sorin et al. 2016).

This empirical picture raises two big questions, a formal semantics question which has been discussed widely, and a lexical semantics question which has largely remained open.

First, the widely discussed formal semantics question (Scha 1981; Link 1983; Dowty 1987; Roberts 1987; Landman 1989; Lasersohn 1995; Schwarzschild 1996; Winter 1997; Landman 2000; Winter 2002; Champollion 2010; de Vries 2015; Champollion 2016; 2017): How should sentences like (1)–(3) be represented formally? To what extent should the inferences drawn from these sentences manifest transparently in their semantic representation? In particular, how do we capture the two distinct interpretations available to (3) – in terms of a semantic ambiguity (Roberts 1987; Landman 1989; Lasersohn 1995; Champollion 2010), or in terms of an underspecified meaning compatible with multiple different situations (Schwarzschild 1996; Kratzer 2007)? If (3) is ambiguous, why are (1) and (2) unambiguous?

Second, the much less-discussed lexical semantics question: Which other predicates behave like smile, like meet, or like open the door – and why? Uncontroversially, the inferences drawn from these predicates are shaped by our knowledge about how events of smiling, meeting, and door-opening take place in the world (Dowty 1987; Roberts 1987; Winter 1997; 2000; Champollion 2010; de Vries 2015). Smile is distributive (1) because people have their own faces and thus cannot smile jointly without also doing so individually. Meet is nondistributive (2) because it describes an inherently social action that cannot be undertaken unilaterally. Open the door can be understood in both ways (3) because it can be carried out individually or jointly.

Prior work has illuminated various elements of the relation between lexical semantics and plural predication, including the interpretation of adjectives (Scontras & Goodman 2017; Glass 2018a), reciprocity (Kruitwagen et al. 2017; Poortman et al. 2018; Winter 2018), whether a predicate applied to a plural must apply to every single member of it (Yoon 1996), different types of non-distributive predicates (Corblin 2008; Kuhn 2020), interactions with negation (Löbner 2000; Križ 2016), and the distribution of the modifier all (Dowty 1987; Löbner 2000; Winter 2000; Brisson 2003). But there is still a need for a predictive theory of which predicates are interpreted as distributive and/or nondistributive and why, in view of lexical/world knowledge about the events that they describe.

There is an ongoing “dictionary versus encyclopedia” debate about what knowledge should be tied to particular lexical items versus one’s extralinguistic knowledge of the world (Fillmore 1969; Pustejovsky 1995; Harley & Noyer 1999; Peeters 2000; McNally 2005). The noncommittal term lexical/world knowledge is intended to sidestep that issue. Here, the aim is to systematize the knowledge relevant for distributivity, without deciding whether that knowledge is lexical or encyclopedic or both.

This paper takes on the lexical semantics question. §2 motivates a series of predictions about the behavior of various types of predicates, generalizing the intuitive analysis of predicates such as smile and open the door to a larger scale. To preview:

 (4) Transitive/Intransitive Asymmetry: Predicates built from many intransitive verbs (smile, laugh, arrive, die) are only distributive, whereas predicates built from many transitive verbs (open a door, eat a pizza) can be nondistributive.
 (5) Mind Prediction: Because individuals have their own minds, predicates describing the subject’s mental processes (believe it, love a movie, meditate, see a photo, worry) are distributive.
 (6) Causative Prediction: Because the nature of causation allows that multiple individuals’ contributions may be jointly sufficient but individually insufficient to cause a result, predicates built from causative verbs (describing an event where the subject causes the object to change, such as annoy a neighbor, break a vase, destroy a family, open a door) can be nondistributive as well as distributive.

§3 presents distributivity judgments from online annotators for over one thousand English predicates (intransitive verbs, and transitive verbs with corpus-motivated objects). For each verb, the features predicted to shape its distributivity potential are labeled using FrameNet (Baker et al. 1998), a lexical database that records inferentially relevant features of events described by verbs. §4 presents a statistical analysis of those annotations, finding evidence consistent with (4)–(6). The observed asymmetry between transitive and intransitive verbs (4) is explained using the Causative Prediction (6): many transitive verbs (even, I argue, those not strictly categorized as “causative”) describe events in which the subject affects (causes a change upon an object), so that the structure of causation gives them a nondistributive interpretation.

Turning to the formal semantics question, §5 reviews the literature to emphasize that any semantic representation of distributivity must be complemented by a predictive analysis, like the one offered here, of which predicates are interpreted in which ways and why.

Broadly (§6), this paper aims to explore distributivity at a large scale; and to show that distributivity is productively handled not just as a formal semantics topic, but as a lexical semantics one.

## 2 Predicting distributivity across the lexicon

This section motivates a series of predictions about the types of predicates that are interpreted as distributive (like smile), nondistributive (like meet), or in both ways (like open the/a door).

In general, most predicates can be interpreted as distributive, because most predicates – all the ones that make sense with an atomic subject – describe actions that can be carried out by a single individual (Alice smiled, Alice opened the door). The only exceptions are (i) reciprocal predicates like meet, which describe inherently multilateral actions; and (ii) predicates with definite objects describing actions that cannot be repeated on the same object (break the vase; the same vase generally cannot be broken repeatedly). Because most predicates can be interpreted as distributive, it is most informative to distinguish between the predicates that can only be distributive (smile), versus those that allow a nondistributive interpretation in addition to a distributive one (open the/a door).

I focus on the predictions (§2.1–§2.3) that are supported in the annotation study reported below (§3, §4), before sketching (§2.4) some other predictions that did not reach statistical significance there.

### 2.1 The Transitive/Intransitive Asymmetry

Nearly forty years ago, Link (1983) observed that a predicate’s distributivity potential is related to its argument structure:

 (7) The Transitive/Intransitive Asymmetry: Predicates built from many intransitive verbs (smile, laugh, arrive, die) are only distributive, whereas predicates built from many transitive verbs (open a door, eat a pizza) can be nondistributive.

After observing that carry the piano (built from a transitive verb) can be both distributive and nondistributive, Link writes: “Common nouns and intransitive verbs like die, however, seem to admit only atoms in their extension. I call such predicates distributive” (Link 1983: 132). He reiterates (Link 1983: 141): “Most of the basic count nouns like child are taken as distributive, similarly IV [intransitive verb] phrases like die or see.”

Of course, there are counter-examples: love a movie is built from a transitive verb and is only distributive (presumably because people have their own emotional attitudes); meet is intransitive and nondistributive. But as a tendency, (7) is plausible. To use introspective evidence, all the intransitive verbs in (8) behave like smile in that if Alice and Bob carry out these actions, then they each do so (distributive).

 (8) arrive, blush, die, disappear, faint, fall, laugh, meditate, pray, run, swim, walk, wink, … ✓distributive, ✗nondistributive

In contrast, all of the predicates built from transitive verbs in (9) behave like open the/a door in that if Alice and Bob carry out these actions, they may do so jointly rather than individually (nondistributive). (The predicates in (9) can also be interpreted as distributive, with or without covariation depending on whether the action described by the verb can be repeated on the same object; but the important point is that they can be interpreted as nondistributive.)

 (9) create a controversy, eat a pizza, score a point, send a letter, write a book, … (✓distributive), ✓nondistributive

Unlike the other predictions proposed below, (7) has no obvious theoretical motivation; if it is manifested, we face a deeper question of why it would be so. To preview, I suggest below that many transitive verbs describe events of causation, independently shown to favor nondistributivity.

### 2.2 The Mind Prediction

Love a movie is distributive because loving is a mental attitude, which people experience individually. The same reasoning should extend to other predicates describing the mental processes of an experiencer, such as perception, emotion, and thought. This intuition is inspired by Roberts (1987), who observes that predicates describing self-willed actions are inherently distributive:

“The fact that a particular lexical item is a group predicate or a distributive predicate doesn’t really need to be specified independently: it follows from the sense of the predicate itself. […] What is it to be a pop star or to walk or to die? The actions or states denoted by these verbs can generally only be performed or endured by an individual with a single will and consciousness. It is for this reason that we think of them as distributive.”—Roberts (1987): p. 124

In other words:

 (10) Mind Prediction: Because individuals have their own minds, predicates describing the subject’s mental or emotional processes (believe it, hear a sound, love a movie, worry) are distributive.

### 2.3 The Causative Prediction

It is less obvious why open the/a door prefers to be nondistributive, or which other predicates should pattern with it.

My proposal is that open is a causative verb (Smith 1970; Fillmore 1970; Dowty 1979), describing an event in which the subject causes the object to change in openness. By definition, causatives describe events of causation. I argue that this truism predicts the distributivity potential of such predicates: as a general fact about causation, captured by any adequate analysis of it (Swanson 2012; Menzies 2014; Copley & Wolff 2014), it is possible for the actions of multiple individuals to be jointly-but-not-individually sufficient (Mackie 1965) to bring about a result.

Illustrating with the influential counterfactual analysis of causation from Hume (1748), revitalized by Lewis (1973) and synthesized with distributivity by Dowty (1987), a sentence such as Alice and Bob opened the door is analyzed to mean that a and b (Alice’s action and Bob’s action) cause a result d (the opening of the door). Perhaps a caused d and b caused d (distributive), meaning that Alice’s action caused the door to open, and Bob’s action caused the door to open too (11a). But perhaps Alice’s action and Bob’s action (a and b) were jointly but not individually sufficient to cause the door to open: if Alice or Bob had acted alone, the door would still not be open (11b). Because two events may be jointly but not individually sufficient to cause a result, we predict that when a causative is predicated of a plural subject, the sentence may be interpreted as nondistributive (in addition to a distributive interpretation, which depends on the repeatability of the action and the definteness of the object). Perhaps Alice unlocks the door, and Bob pushes it open, so that the door would not have opened but for Alice’s action and Bob’s action together.

 (11) Alice and Bob opened {the/a} door. a. (✓Distributive: They each opened {the/a} door.) b. ✓Nondistributive: They opened {the/a} door jointly without each individually doing so. (Alice unlocks it, Bob pushes it open.)

To generalize, this discussion leads to a prediction:

 (12) Causative Prediction: Because the nature of causation allows that multiple individuals’ contributions may be jointly sufficient but individually insufficient to cause a result, predicates built from causative verbs (describing an event where the subject causes the object to change, such as annoy a neighbor, break a vase, destroy a family, open a door) should allow a nondistributive interpretation (in addition, perhaps, to a distributive one).

### 2.4 Other predictions (which turned out not significant)

I turn to some other predictions which, while intuitively motivated, did not reach statistical significance in the annotation study (§3) reported below.

Smile is distributive because it describes a facial action which people can only carry out individually. The same reasoning should extend to other predicates describing the actions of an individual body, including actions of the face, voice, and self-propelled motion (Roberts 1987; de Vries 2015). Thus:

 (13) Body Prediction: Because individuals have their own bodies, predicates describing the actions of an individual body (chew, faint, jump, laugh, sing, smile, shrug, walk) are distributive.

Some predicates describe an event where an object, called an incremental theme (Dowty 1991), is affected in tandem with the progress of the event of affecting it (Tenny 1987; Krifka 1992). Eat a pizza describes an event that is half over when a pizza is half-eaten, and fully over when it is fully eaten. Such events are not necessarily causative; the progress of a read a book event maps incrementally to the parts of the book, but does not describe a caused change therein (Rappaport Hovav 2008).

If two people eat a pizza, perhaps they each eat one (distributive), or perhaps they each eat a different portion of a single pizza, adding up to a whole pizza between them (nondistributive). Informally, it is always possible for multiple individuals to each carry out the event described by the verb on a different portion of an incremental object, only jointly adding up to the whole. To generalize:2

 (14) Incremental Prediction: Because individuals may each affect a different portion of an incremental object, only jointly affecting the whole, predicates with incremental objects (build a house, eat a pizza, paint a wall, read the book, write a letter) are predicted to allow a nondistributive interpretation (in addition, perhaps, to a distributive one).

(15) can be understood in both ways (distributive and nondistributive), presumably because buying is a commercial transaction that can involve both individuals and larger parties.

 (15) Alice and Bob bought a car. (can be understood both ways) a. ✓Distributive: Alice bought a car, Bob bought a car. b. ✓Nondistributive: Alice and Bob bought a car jointly but not individually.

The modern legal system allows property and commercial transactions to be shared as well as individualized. Thus:

 (16) Commercial Prediction: Because money and property can be possessed collectively, predicates describing commercial transactions (buy/sell a car, lease/rent a room, pay a bill, owe a debt, donate a library, own a boat) are predicted to allow a nondistributive interpretation (in addition to a distributive one).

Intuitively, meet is nondistributive because it describes an inherently multilateral action which individuals cannot carry out alone. If an action requires multiple participants, then an individual person (Alice) cannot carry out that action alone (Carlson 1998; Siloni 2012). Therefore, predicates describing such actions cannot be distributive, but can only be nondistributive.3 To generalize:

 (17) Multilateral Prediction: Because individuals cannot carry out inherently multilateral actions alone, predicates describing such actions (coexist, collaborate, cooperate, meet, share a pizza, tango) are predicted to be nondistributive.

Note that (17) is the only prediction about when nondistributivity is required; all the others predict when it is allowed.

### 2.5 Section summary

For certain predicates, one can identify an intuitive explanation for how they are understood (as distributive, nondistributive, or in both ways) when applied to a plural subject, based on the real-world event described by the predicate. This section has expanded such intuitive explanations into a series of predictions about the distributivity potential of various classes of predicates.

## 3 Distributivity annotations

To test these predictions, this section presents a dataset of 1020 predicates (intransitive verbs, and transitive verbs with corpus-motivated objects), annotated for distributivity using Amazon’s Mechanical Turk service.

### 3.1 Study design

Annotators encountered past-tense predicates applied to two conjoined human names, and answered questions such as (18)–(19) – thus annotating the predicate as either distributive (“technically each PRED”) or nondistributive (“jointly PRED without technically each doing so”).

 (18) Nora and Ralph walked. From this sentence, one most likely infers that Nora and Ralph …
 (19) Kendall and Taylor reduced a risk. From this sentence, one most likely infers that Kendall and Taylor …

For each predicate, the FrameNet database is used to label features of the event predicted (§2) to shape its distributivity potential.

The questions (18)–(19) elicit a binary judgment about whether to interpret the predicate as distributive (each) or nondistributive (jointly). For predicates where only one interpretation makes sense (walk, smile), annotators are expected to choose the only sensible answer. For predicates where both interpretations make sense in principle (reduce a risk, open a door), annotators are expected to choose either answer, but with a bias towards the nondistributive interpretation in light of the finding (Brooks & Braine 1996; Frazier et al. 1999; Dotlačil 2010; Syrett & Musolino 2013; Dobrovie-Sorin et al. 2016) that nondistributive interpretations are preferred when they are available. Thus, predicates that only make sense as distributive (smile) should be annotated as distributive; predicates that only make sense as nondistributive (meet; by far the smallest class) should be annotated as nondistributive; and predicates that can receive both interpretations (open a door) should tend to be annotated as nondistributive. Of course, the task is rather abstruse and annotators may interpret it in idiosyncratic ways, so we should realistically expect these predictions to manifest as tendencies rather than absolutes.

While (18)–(19) elicit a single binary judgment about how annotators actually interpret the sentence, prior work (Glass 2018b) asked two hypothetical questions, using a five-point Likert scale, about how annotators could interpret it: (a) “Does it follow that Nora and Ralph each walked?” and (b) “Could it be that Nora and Ralph didn’t technically each walk, because they did so together?” The current formulation was chosen because it is simpler (asking about one’s actual interpretation rather than hypothetical ones, using a binary scale rather than a Likert scale for what is really a binary distinction); it eliminates the confusing redundancy of asking two inversely related questions; and it avoids the notoriously polysemous word together, which can evoke both nondistributivity and socio-spatial coordination (Moltmann 2004). But, as expected, the 2018 data are strongly correlated with the new data reported here,4 meaning that both formats probe the same phenomenon.

### 3.2 Choosing corpus-motivated verbs

The verbs to be annotated were chosen using a corpus of comments from Reddit, a United States-based online discussion platform. Reddit is organized into sub-communities with more or less specialized interests (r/bicycling, r/movies); here, comments were taken only from r/AskReddit, one of the largest communities, dedicated to general-interest topics (recently popular: What is something about yourself that sounds totally made up but is 100% real?, and: People who shoved their school papers in their backpack with no binder/folder etc, where are you now?). Reddit is a massive, freely available dataset of contemporary English, using fairly standard orthography but with a register close to that of spoken English (Herring et al. 2013).

Next, the comments were run through SpaCy (Honnibal & Johnson 2015), a natural language processing pipeline which tokenizes sentences, lemmatizes words, tags parts-of-speech, and parses the syntactic dependencies of each sentence. I counted all occurrences of each part-of-speech-tagged verb lemma in the data, and kept the verbs (excluding crude ones) with a per-million-word frequency of 2 or more. (Some of the least-frequent verbs in the data, with a per-million-word frequency of 2, include assist, await, bolt, and chuck; the most-frequent include get, make, say, want, and know, each with a per-million-word frequency of over 2000).

To create sentences such as (18)–(19) to be annotated, each verb also has to be classified as transitive (in which case it is given an object, using a process described below), or intransitive. Although many verbs can appear in both transitive and intransitive argument structures (I ate lunch; I ate; see, e.g., Levin 1993), this dataset annotates each verb only once, as either transitive or intransitive. Using the dependency parse from SpaCy, I computed the percent of the time that the verb appeared with a “dobj” (direct object) dependency, as a fraction of its overall occurrences. As a general rule, verbs were classified as transitive if they have a direct object more than 30% of the time, intransitive otherwise.6

### 3.3 Choosing corpus-motivated objects for transitive verbs

To create sentences to be annotated as in (19), each transitive verb must be given an object. The object of a transitive verb – both its grammatical properties and its referent – plays an important role in shaping the distributivity potential of a full predicate.

Grammatically, it matters whether the object is singular or plural. A predicate with a plural object can always be interpreted as nondistributive (“cumulative”; Scha 1981): if two people open two doors or see two photos, perhaps they do so by each opening/seeing one, adding up to two doors/photos between them (Krifka 1992; Champollion 2010). Singular objects were used to avoid that confound.

As previewed above (§1), a predicate’s potential for distributivity also depends on whether the object is definite or indefinite, which in turn interacts with whether the action described by the verb can be repeated on the same object (Champollion 2020).

 (20) Alice and Bob opened {the/a} door. a. ✓Distributive: They each opened {the same, a different} door. b. ✓Nondistributive: They opened {the/a} (single) door jointly without each individually doing so.
 (21) Alice and Bob broke {the, a} vase. a. {???/✓} Distributive: They each broke {??the same, a different} vase. b. ✓Nondistributive: They broke {the/a} (single) vase jointly without each individually doing so.

Because the same door can be opened more than once, (20) allows both interpretations regardless of whether its object is indefinite or definite. But because the same vase normally cannot be broken more than once, an indefinite object allows break a vase (21) to have a (covarying) distributive interpretation which is unavailable with a definite object. Thus, indefinite objects were used to abstract away from whether the action described by the verb can be repeated on the same object.

A predicate’s distributivity potential is also affected by the referent of its object. Open an eye is distributive, based on the knowledge that people have their own eyes. Open a book and open a vault can both go both ways, but may differ because it is easier to open books than vaults.

For this study, it is important to choose objects for verbs using a method that systematically controls for these issues. Particularly if the focus is verbs, we do not want the choice of object to confound the data. But we cannot give every verb the same object (open a door vs. #eat a door); and a generic object such as thing would be unnatural. Instead, the AskReddit corpus data were used to find, for each transitive verb, a list of its most-frequent lemmatized direct objects according to SpaCy’s dependency parse. (The list automatically excludes pronouns; demonstratives such as this; wh-words such as who and whatever; quantifiers such as anyone; partitives such as piece and lot; the highly bleached words other, way, and thing; and all vulgar words). By default, each transitive verb was given its most common lemmatized object, as a singular indefinite. I then went through by hand and identified any objects that did not make sense as a singular indefinite (mass nouns such as water, intensifiers such as hell, relational nouns such as end). In such cases, one of the next-most-common objects was chosen; for reduce, the object risk was chosen, because the more-common objects (amount, chance, number) would need further context to make sense.

 (22) Most common lemmatized objects for the verb reduce, and their counts. amount(64), chance(48), number(41), risk(37), cost(32), rate(29), stress(19), level(15), price(13), pain(12)

The noun person was the most-common object for so many verbs that the next-most-common object, if it made sense as a singular indefinite, was chosen for balance.

This process yields objects that are naturalistically motivated, minimally shaped by researcher bias, and sensible as singular indefinites.

### 3.4 Labeling predicate features with FrameNet

Each predicate must also be labeled for the features predicted (§2) to shape its potential for distributivity. Of course, if the researcher labeled these features, the study might be vulnerable to confirmation bias – the researcher might choose labels consistent with their own beliefs about the predicate’s potential for distributivity, and then circularly use these labels to predict distributivity.

Therefore, labels were chosen in an automatic manner using the FrameNet database7 (Baker et al. 1998), which is built upon the theory of Frame Semantics from Fillmore (1976). Frame Semantics brings together the idea of thematic roles (the roles played by each argument of a verb in the event that it describes; Gruber 1965) with the idea that humans understand language using rich background knowledge – called frames, scripts, or schemas (Schank & Abelson 1977) – about stereotypical events.

FrameNet is a machine-readable database of such frames, built by semanticists and lexicographers. The lexical unit walk.v evokes the SELF-MOTION frame:

 (23) SELF-MOTION: “The Self-Mover, a living being, moves under its own direction along a Path. Alternatively or in addition to Path, an Area, Direction, Source, or Goal for the movement may be mentioned.”

Each underlined word constitutes a Frame Element, to which each argument of the verb walk can be mapped. Reduce.v evokes the CAUSE-CHANGE-OF-POSITION-ON-A-SCALE frame:

 (24) CAUSE-CHANGE-POSITION-ON-A-SCALE: “An Agent or a Cause affects the position of an Item on some scale (the Attribute) to change it from an initial value (Value1) to an end value (Value2). The direction of the change (Path) can be encoded as well as the magnitude of the change (Difference).”

Frames are related to other frames through various Frame-Frame relations. The SELF-MOTION frame “inherits” (is a more specific instance of) the MOTION frame. The CAUSE-CHANGE-POSITION-ON-A-SCALE frame (also evoked by related verbs such as add, double, and raise) serves as the “causative-of” the CHANGE-POSITION-ON-A-SCALE frame (which, in turn, is the “inchoative-of” the CAUSE-CHANGE-POSITION-ON-A-SCALE frame).

FrameNet was used – specifically, the version integrated into the Natural Language Toolkit (NLTK; Loper & Bird 2002) by Schneider & Wooters (2017) – to label predicates for the features predicted (§2) to shape their distributivity potential.

A predicate was labeled as a “mind” predicate if it evokes or inherits the frames EXPERIENCER-FOCUS (for verbs with experiencer subjects, such as love); PERCEPTION, EMOTIONS-OF-MENTAL-ACTIVITY, COGITATION, AWARENESS, MEMORY, and MENTAL-ACTIVITY; and/or if it requires a COGNIZER among its core Frame Elements. Because the prediction is about the subjects of mind verbs rather than their objects, verbs were excluded from this classification if they evoke the EXPERIENCER-OBJECT frame, describing the mental experience of the syntactic object (astonish; Grafmiller 2013) rather than the subject. In total, 127 predicates were labeled as “mind” predicates (112 transitives, 15 intransitives), including:

 (25) admire a person, believe a story, care, crave a cigarette, dread a class, dislike a movie, feel a pain, grieve, hear a story, find a job, expect a tip, imagine a scenario, envy a friend, listen, perceive a threat, pity a fool, …

A predicate was labeled as “causative” if it involves a transitive verb (because causatives, as defined here, describe events in which a subject causes a change upon an object) and evokes or inherits the frames EXPERIENCER-OBJ (for “psych” verbs such as annoy, describing events in which a stimulus subject causes an emotion in an experiencer object); CAUSATION, or KILLING; if it evokes or inherits any frame with the CAUSE- prefix; if is related to any other frame through the “causative-of” frame relation; or if it requires a CAUSE among its core Frame Elements. In total, 314 predicates were labeled as causative (all transitive), including:

 (26) activate a card, annoy a friend, arrest a person, baffle a doctor, bake a cake, butcher an animal, cast a spell, chill a drink, calm a child, develop a skill, dissolve a plastic, discourage a child, fry a chicken, melt a cheese, plant a seed, reduce a risk, rip a shirt, …

Any predicate was excluded from the study if its verb is absent from FrameNet (which has some odd gaps; blush, dream, edit, greet, and relax are absent). Even among the predicates that appear in FrameNet, quite a few of them do not receive any of the labels just described; for example, refuse an offer is labeled as neither “mind” nor “causative” nor any other label.8

Predicates were labeled before gathering any distributivity annotations, and the data to be annotated were pre-registered through the Open Science Framework (https://osf.io/ena5r/).

### 3.5 Data collection

In total, 1020 predicates were assembled, 161 intransitive verbs and 859 transitive verbs with objects, all labeled using FrameNet for the features predicted to shape their distributivity potential. These 1020 predicates were randomly split into 20 lists of about 50 predicates each.9 Each list of about 50 predicates was used to generate an annotation survey on the Qualtrics platform (using the “Loop and Merge” function to iterate over a list of predicates). Each predicate, in the past tense, was combined with a random conjunction of two names and placed in a question modeled after (18)–(19).

## Acknowledgements

For constructive feedback and inspiring conversations, I am very grateful to the advisors of my 2018 Stanford dissertation, the antecedent of this work: Beth Levin, Christopher Potts, Cleo Condoravdi, and Daniel Lassiter; to the Editor (Min-Joo Kim) and three anonymous reviewers at Glossa as well as to three earlier reviewers at Journal of Linguistics; and to Lucas Champollion, Yoad Winter, and Hanna de Vries. I thank Aaron Steven White and Will Gantt for conversations which helped me to redesign the annotation study, and Kathy Dahlgren and Karen Wallace at Nuance Communications for first inspiring me to work on distributivity. I am also indebted to all the audiences before whom the work has been presented. Errors are mine.

## Funding information

This work was partially supported by awards from the American Council for Learned Societies Mellon Dissertation Fellowship, Phi Beta Kappa of California, and the Vice Provost for Graduate Education at Stanford University, as well as by research funding from the School of Modern Languages at Georgia Institute of Technology. The support is gratefully acknowledged.

## Competing interests

The author has no competing interests to declare.

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