Distinguishing Scopal from Non-Scopal Semantic Arguments


We take it as given (for now) that certain predicates have scopal argument positions, i.e. contribute to the articulation of the scope tree. Examples are the sole arguments of seem and not and the second argument of deny in the examples below:

In calling these argument positions scopal, we believe we are making at least the following claims:

  1. Quantifiers may scope in between the predicate and its scopal argument.
    • The dog did not chase every cat.

    • Kim denied that every dog barked.

  2. A proposition embedded as a scopal argument is not necessarily (for the purposes of e.g. presupposition calculation) in the same context as the embedding predicate.
    • Kim believes that every dog barked.

Currently, in the English Resource Grammar (and DELPH-IN grammars more generally), we distinguish two types of elements which are adverbial modifiers syntactically and predicates (operators/scopal predicates or non-scopal predicates) semantically, which we call scopal and non-scopal modifiers. The former take the (semantics of the) syntactic head they combine with as a scopal argument:

While the latter instead are predicated of the event variable of the head they combine with:

While what we construct in the ERG are meaning representations (and not logical forms), for the subset of expressions which can be handled in some suitable object language, there is meant to be a mapping from each meaning representation produced by the ERG to one or more expressions in that object language. Assuming something like (a suitable variant of) higher-order predicate logic, we imagine that our non-scopal modifiers correspond to ordinary predicates while our scopal modifiers would likely have operator status.

Problem Statement

While we feel that some items are fairly clearly in one category (scopal modifiers) or the other, we find it difficult to categorize many other times. Accordingly, we have the following questions:

  1. Is this distinction in fact well-defined?
  2. If so, what tests can we use to classify particular predicates?
  3. If not, what representation should we use? (Underspecification; assimilating all modifiers to one type; others?)

Key Examples

The modifiers for a long time and deliberately seem like good candidates for non-scopal modifiers, but then it is not clear to us what it means for them to modify negated clauses:

Note also close semantic similarity between negation and fail, where we are more comfortable having non-scopal modification of failing events:

We can also pair likely non-scopal modifiers with verbs that seem to be close paraphrases, and which (as verbs) we expect to take verbal projections as clausal arguments:

What about when a (putative) scopal modifier appears to modify only a (putative) non-scopal modifier but not the head?

Possible Semantic Tests

Possible Syntactic Correlates

Notes from Discussion (2017/08/18)

Mary: Are these all of the places where quantifiers can scope? There are others.

Dan/Emily: Like what?

Mary: Restriction of a quantifier.

oe/Dan: That is another scopal argument in our framework.

Mary: If you have a relational noun.

Dan: Like belief?

Mary: Or friend of.

Dan: What about friend of?

Mary: You can scope a quantifier every friend of a student ... a student can scope around friend of. What's the predicate here?

Dan: friend of is a predicate, but not one that doesn't let things scope under it.

Mary: So you have other places where quantifiers can go and you're happy about that.

Dan: Correct.

Mary: We're just looking at things that are arguments of things for now.

Emily: You look skeptical of the claim that quickly is not scopal.

Mary: There are exmaples like he made the cakes slowly. You have to introduce event variables for these to make sense. Could mean: Each cake was made slowly, or he made each cake quickly but took a big rest in between. Scope ambiguity?

Dan: Collective/distributive is another dimension. Also need to worry about it in coordination. Maybe we're setting it aside too quickly. Maybe the availability of it will tell us something we didn't know before, but for the moment we're pretending we don't know about it.

oe: And yes, we are assuming a variant of a neo-Davidsonian event semantics, where we are relatively generous with our use of eventualities. I think Krifka has argued for at least some of them. For he baked the cakes slowly, we'd have one meaning representation, with bake(e,x,y) and essentially slow(e)

Emily: Actually slow(e',e), which is part of what Stephan meant by 'generous'...

oe: We don't want to ambiguate those two distinct readings or spell out subevents or ... we don't explicitly quantify our events, just assume appropriately scoped existential quantification.

Dag: So usually doesn't quantify over events?

Dan: We don't have any event quantifiers --- haven't tried to unpack always, never etc. We have left those event quantifying adverbs as opaque. And someone downstream could say I know how to interpret that, if they wanted to unpack. We're not particularly proud of that laziness...

oe: Frequently would be a candidate where we would have to ask. We picked not and quickly as scopal vs. non-scopal, respectively.

Dan: The distinction is difficult because we have a forced choice. Scopal or not, not possible to underspecify. Doesn't lend itself well to blurriness.

Dan: And even worse there, that for might be semantically empty --- cf. Kim baked Sandy a cake. --- so then there's really nothing for probably to predicate itself off.

oe: But can you use the NP NP construction and then insert probably to mean it was only about the recipient?

Dan: No, but that could be a syntactic fact.

Dan: Maybe a little bit more about the background of the discussion: The really vexing thing is that as we run through the next 2000 adverbs, I have to for every one of them decide if they're scopal or not. When I run into frequently, usually, rarely, nearly... I have to decide. Kim nearly left doesn't entail Kim left. Does that mean it's scopal? Or is it something else about the rest of the meaning of nearly? And if rarely is non-scopal but never is scopal, what about rarely v. almost never? Shouldn't they mean the same thing?

oe: Non-scopal ones correspond to the vanilla, motivating cases in Davidson's presentation of events. Things you can predicate of the eventuality, that don't modulate veridicality, and don't require that we open a position for a quantifier to scope there. Then we're left with ... the other type.

Dan: We keep coming back to quantifiers, because at least for English we don't know of any other scopal operators that can float up and down the scope tree. But German is interestingly different in two respects. Some scopal operators can appear at the end of the VP (different from English) and we thought that maybe correlated with the observation that you can have partial scope constraints: I at least outscope these, but there might be things that happen in between. So one scopal operator to the left and one to the right fight it out (within just one syntactic structure). We don't have clear cases of that so far in English, though if we could find a post-VP convincingly scopal modifier, we could make construct similar motivation for the partial scope. That would make it easier to do some of these rescoping tests.

Dan: We hope to focus this discussion on adverbial guys --- the whole space of adjectives seems even more vexed. In the adnominal case, we've taken the not likely to be correct simplifying view that they're all non-scopal, including former, fake, probable.

oe: But you just said we're not having that discussion today...

Dan: But if someone had a brilliant idea? Though we hope to keep the discussion focused by just looking at the adverbial guys.

oe: One thing that pretty clearly drives us to making an argument position scopal is when the type of the argument corresponds to the semantics of a clause, as with We were happy to discuss scope. We assume that happy takes that thing that we sometimes call a proposition as its complement. Our main test there is that you can insert negation: We were happy not to discuss adnominal modifiers. Then the argument of happy would have to be not discussing.

Dag: Kim didn't speak for a long time. Do you have a distinction between the event and something like topic time that you could also modify?

Dan: Like Reichenbach? No---tried that once, but didn't keep it in the grammar. But if you think that more articulated representation of these elements in tense and aspect would give us an affordance for a sharper distinction, that could be fun.

Dag: Then you have two things it could modify: the event time, or the topic time (which under normal assumptions would be higher than the negation).

oe: Here's the meaning representation we currently provide.

neg[speak(e,Kim) ∧ for-a-long-time(e)]

Emily: Just the one?

Dan: Yeah, I don't know how to do the other.

Dag: If you put in an eventuality for the negation.

oe: We so far shy away from that...

Emily: It's there, we just don't expose it.

Dag: Having an eventuality for the negation would be like getting the topic time.

Dan: If I could explain it in terms of the tense semantics, maybe it would be less embarassing. We'd have to think about what we mean by that exposing of the negation event.

Dan: How much longer do you think we can get away without having quantification for events, if we were going to do things like rarely and frequently? Our observation so far is that we don't know of syntactic behavior that corresponds to/impinges on that. Assuming the mapping can be done after the fact from frequently(e) to many(e,body). Maybe worse if I have it as a non-scopal modifier. If I have it as scopal, then at least the scope tree would be the right shape.

Dag: You can get ambiguities there: Typhoons usually arise in the Pacific. Usually, if you're in the Pacific, there will be typhoons or if you're in the Pacific there will usually be typhoons.

Emily: But how does that relate to different scope trees?

Dan: Is there a puzzle for how I get that lowering of the effect of usually that is there whether or not it's scopal or non-scopal.

oe: If usually were scopal, doesn't that turn into parallel to Kim didn't speak for a long time, assuming that in the Pacific is ambiguous.

Emily: And we are maybe less embarassed about giving usually its own eventuality?

Dan: Still a little embarassed; we still want arise to give the main eventuality for

oe: Did you just make up that example?

Dag: No, it's from _The Generic Book_ (Krifka, ed).

Dag: But there are similar examples when there's no overt genericity operator: Ties must be worn (in a restaurant) v. Dogs must be carried (next to an elevator). Genericity is this weird operator that sometimes isn't overt but sometimes is.

Dan: It can be overt too: Dogs must always be carried (with implicit "if there is a dog")

Emily: Isn't it about the ambiguity between always and the generic operator?

Dag: The assumption is that the generic operators, there's a restrictor, so the ambiguity has to do with whether or not the subject (dogs, ties) is in the restrictor.

Dan: Would that work for usually, rarely, frequently?

Dag: Yes.

Dan: Would that give me a way to pull together rarely and never? Rarely seems to be the limiting case of never: very very rarely seems to go to never in the limit. But maybe there's something not quite linguistic coing on there.

Dan: What if we took the strong Occam's Razor view and said there isn't a disticntion at the level of composition. Adverbials are slippery and to pretend that loudly is different in kind from never is maybe a mistake. What would I lose if I made them all scopal, but lots of the scopes just never amounted to much.

Mary: Does that mean you'd get two representations for every sentence with an adverb in it?

Dan: No, for every dog happily chased a cat, I'd get happily as the outermost quantification, taking chase as its argument. But that seems to predict more possible scopings for the quantifiers.

oe: If happily were scopal, on our current standard assumptions about where quantifiers go, you'd get some more.

Dan: I get more than two already with Every dog didn't chase a cat.

Emily: Yes, six.

Dan: So the question is do I want six with happily? How about with frequently?

Mary: happily has to be relative to some individual that's happy. So happy has to take not just the situation that the individual is happy about, but also the individual who is happy about it: every(happy(some or every(some(happy both okay --- these seem different, is there some particular cat that the dog is happy about chasing. For frequently it's even clearer.

Dan: With every always.

Emily: That's forced (for happy) because of variable binding, like Mary said.

Mary: But not for frequently --- and the six seem okay.

Dan: So you're saying that the fact that happy takes that variable would rule out some.

Emily: Did you convince yourself of all six of those?s

Mary: There's a poor cat that gets chased every hour by all of the dogs all at once or there's a poor cat that each of the dogs likes to chase, but not necessarily all at once.

Emily: But then here's where I fail as a semanticist: we have to next hold those scenes in our minds and see if the sentence can be used to describe them.

Dag: But we only need one quantifier: Every dog frequently barks.

Mary: Seems different from Frequently, every dog barks.

[ group lays out readings ]

Dan: Can I get both of those as readings for every dog frequently barks

Mary: There are strong preferences for scoping from word order; have to do things with the intonation.

Dag: So just one of each is enough, right?

Emily: But we'd have other problems if the order pins it down.

Mary: Really just tendencies ... if someone says you can't get that reading

Dan: ... they probably aren't trying hard enough.

Dag: German is supposed to be scope rigid.

Mary: Yeah, because of free word order.

Dag: When it's fronted, can you still get the low scope reading? Frequently, every dog barks.

Dan: I get both of them, I think. I can picture both of those scenes, and I think the sentence works for both of them.

Emily: I'm having a hard time getting the low reading, but I'm bad at these.

Mary: I think they're both there.

oe: So we've made a good case for frequently, but what about happily?

Mary: Happy about different things?

oe: I wanted to get back to that, because we haven't explicitly discussed that property of happily. You seem to be assuming that if it's attaching as a modifier, it's also predicated of the subject or maybe agent.

Mary: The horrible man happily beats his dog. --- it's the subject.

oe: Is it also the subject, or always the subject?

Mary: Would be easier if it's the subject, but probably not necessarily.

Dan: The cookie was happily eaten by the kid.

Emily: There's happily lots of cookies.

Dan/Mary: That's the discourse happily.

oe: We can't pin it down in the syntax.

Dag: A bit like depictives, oriented towards one of the participants.

Emily: I think we can handle this by marking that argument as an anaphor that needs an antecedent in the same clause, and once we pin that down it reduces the possible scope readings.

Mary: nods

oe: So happily is two-place?

Dan: It already is ... it's the same predicate as for the adjective happy.

Mary: What about deliberately?

Dan: You can get The cookie was deliberately eaten by the kid?

Mary: Yes.

Emily/Dag: Deliberately is agent-oriented, not subject oriented. (This has been widely studied.)

Emily: Back to happy/happily --- same predicate, but different argument type for ARG2?

Dan: [Tests and finds that in adverbial use _happy_a_with only takes ARG1 which takes the event as ARG1.] Can fix that.

Dan: But now you're asking me to make another distinction, because you don't want slow to take two arguments do you?

oe: What about The child slowly ate the apple/The child was slow to eat the apple/My daughter is slow to eat dinner

Dan: Not clearly the same sense --- VP[to] complement taking slow seems to mean something like "hesitant".

oe: But you were getting around to improving the grammar by making happily like happy.

Dan: I'm not yet sure I want the ARG2 to be the proposition rather than the eventuality.

Dag: There's literature on this type of participant-oriented adverbials.

Emily/Dan: That's a good search term?

Dag: Yes.

Dan: Would that literature help me see that slowly or maybe others that aren't.

Emily: My guess is that scopal v. non-scopal and participant-oriented v. not might be different dimensions.

Dan: That makes the problem of adding adverbs harder. Slows the pace of lexical acquisition, especially without adequate tests.

Dan: What's a crystal clear case of non-participant-oriented, aside from not, never, or probably?

Dag: Degree adverbials, like deeply: He loves her deeply.

oe: Manner adverbials, like heavily.

Dan: He heavily dropped the box on the floor. Yeah, the guy's not heavy.

oe: So far we aren't seeing any reason to make heavily scopal. If we try to apply what we did for frequently, Every athelete breathed heavily: Is that ambiguous?

Dan: If I make them all scopal, can I find another way to differentiate heavily from happily? Mary's observation about the participant-oriented ones taking another argument reducing the readings is quite tempting.

Emily: But that's not going to help you with heavily.

Dan: I want to know if I can play that game one more time.

oe: And furthermore, you'll be able to take advantage of similarity to happy the adjective.

Dan: Yes.

oe: So what I thought was a challenging example... the challenge dissipates.

Dan: Tell me about merely. Every dog merely barked. How many readings?

Emily: The two readings would have to be each dog only barked, or all that happened was that all the dogs barked. But I don't think that sentence can have the second reading.

oe: So would that second reading also be the meaning of Merely, every dog barked.?

Dan/Emily: Star.

oe: And what would it mean if grammatical?

Emily: I'm a scientist!

oe: So making merely scopal would overpredict scope ambiguities. Also, making everything scopal would undermine our reason for having Davidsonian events.

Dan: But we also need to be able to count them (quantification over events).

oe: What about Every dog barked on Tuesday.?

Emily: Yes! I can at least come up with the two situations, and I think the sentence works for both of them, but maybe that doesn't require two different readigs. What was the day that the all the dogs barked? Every dog barked on Tuesday.

Mary: Cumulative event v. separate ones.

Dag: With The dog barked on Tuesday, there's a containment relation between event and topic time. You see it much more clearly with negation.

Dan: Every dog didn't bark on Tuesday

Emily: All were quiet, vs. Fido was quiet. Oh, but that's just every/neg. Do we really need the every?

Mary: The dog didn't bark on Tuesday.

Dag: I think on Tuesday has to take wide scope.

Emily/Dag: But then we have the problem of focus of negation coming in, which muddles these ones.

Emily: What about The dog always barks on Tuesdays?

Mary: That's kind of the habitual thing, which is a whole can of worms in itself.

Dan: So it may again not be about a scope difference, but rather about generics.

oe: Can we try probably? Steering clear of negation, but picking something we're pretty confident is scopal.

Dan: The dog probably barked on Tuesday. There was a barking event and I think it was on Tuesday, or there was probably a barking event, and if so, it was on Tuesday.

Mary: It's probably the case that my dog barked on Tuesday. What's the other one?

Dan: It was actually Wednesdasy.

Mary: Oh, yeah -- these things sometimes act like focus operators.

Emily: There's too many moving parts.

oe: So that focus of negation problem isn't limited to negation.

Dan: My dishwasher probably died last week. Last week, something terrible happened. It seems probable that what my renters were complaining at me about was the dishwasher dying. Seems convenient to hang that on what probably is predicated of.

Dan: What do normal people do with this? Do they make a two-ways distinction or not?

Mary: I think adverbs are hard.

Dan: But what would someone like Krifka say --- two kinds, maybe not these two kinds?

Mary: So you're starting from the assumption that all of these are one-place?

Dan: No -- things like if-then can be two place.

Emily: And we were happy to be convinced that happily is two-place. (Pun not intended.)

oe: So were we about to decide that on Tuesday is scopal?

Dan: No.

Dan: We've used up the hour and a half we asked you for, and I can't do semantics for more than 90 minutes. Any last words? Any references we should look into?

Dag: There's lots of stuff on adverbials...

oe: We don't want to read lots of stuff. We want to read the thing. We're lazy.

Dan: Did Davidson have anything to say about this? He knew about scope. Did he say how his events fit into the scopal universe?

Dag: No, he was a philosopher.

oe: Parsons-style would be that on Tuesday is an event modifier.

Dag: Because he doesn't have topic times?

oe: He would kind of have to eventually, but he doesn't initially. It's a very clean story initially.

Emily: He's not broad coverage.

SynSem/Problems/ScopalNonScopal (last edited 2017-08-29 09:56:21 by StephanOepen)

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