Raising and Control Robert Levine Ohio State University - - PowerPoint PPT Presentation

Raising and Control

Robert Levine

Ohio State University levine.1@osu.edu

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Empty elements

(1)

• a. It’s raining.
• b. There is a lion in the garage.

◮ What semantic content do it and there contribute? ◮ How should we treat the semantics of empty elements? ◮ Since when they combine with the properties corresponding to

weather predicates they contribute nothing,

◮ we want some semantical operation allows a predicate to combine

with an argument to yield absolutely no effect.

◮ Does the λ-calculus give us a way to do that?.

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Vacuous abstraction

◮ There is no way to avoid treating rain, snow, hail, and sleet as VPs which require it

subjects.

◮ Each of these will combine with such a subject to yield S. ◮ Hence, they are functors on it arguments. ◮ It follows that the functions they correspond to combine with what it denotes to

yield a proposition.

◮ But it does not denote a potential member of a set, since there is no linguistic

expression specifying such a set element which can appear in place of it in such examples.

◮ Hence, in It rained, we do not want to say that rained has the semantics

λy.rain(y), since there is no denotation for it that can be a member of this set.

◮ In other words, we need a syntactic functor to apply to it that will not map any

defined object to t.

◮ How about λy.rain?

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◮ Remember that for any semantic terms φ which contains no variables,

λα[φ](β) = φ for any α, β.

◮ Hence, regardless of what it denotes—call it ξ— [

[It rained] ] = λy[rain](ξ) = rain.

◮ On this treatment, rain denotes a constant function to the proposition

rain, whose denotation is something like what is suggested by the phrasing, Rain is happening.

◮ This same treatment will work for dummy there, as in There is a

unicorn in the garden.

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Dummy subjects

◮ Let’s suppose that we have three subtypes of NPs:

NP normal there it

◮ Then we can force rain to combine with it as follows:

(2) rain; λx.rain; it\S allowing proofs such as (3): (3) rained; λx.rain; it\S it; ξ; it it • rained; λx[rain](ξ); S ................................ it • rained; rain; S

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Dummy subjects and auxiliaries

◮ What about (4) then?

(4) It was raining.

◮ What is the VP selecting it here? ◮ Where does the it\ valence requirement originate? ◮ So what can you conclude about is? ◮ Yes: is must adopt the subject type of its argument VP as its own. ◮ How can it do that?

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Revisiting VP

◮ We’ve used VP as a convenient symbol for NP\S and VP

α for NP\Sα

◮ But here we need to ensure that the subtype of the subject is shared between the

valent of the argument VP and the valent of the auxiliary functor VP.

◮ The VP symbol ‘conceals’ the properties of the argument, spotlighting only those

• f the output type.

◮ So it looks as though we are going to have to rethink the notation we’ve used

somewhat.

◮ Let’s say that is is actually (γ\Sfin)\(γ\Sprog). ◮ Then we can prove it is raining as follows:

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It is raining

is; λP.P; (γ\Sfin)\(γ\Sprog) raining; λx.[rain]; it\Sprog is • raining; λx.rain; it\Sfin it; ξ; it it • is • raining; λx[rain](ξ); Sfin ...................................... it • is • raining; rain; Sfin

◮ This sharing of subject arguments is required for all the auxiliaries:

(5)

• a. It had rained.
• b. It will rain.

◮ And we expect that this argument-sharing property will create ‘chains’ of

shared subject values: (6) It must have been raining.

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Raising predicates

◮ Should we add this subject-sharing property to the NICE properties as a diagnostic

for auxiliary status?

◮ That would be the right move if all predicates which structure-shared with their VP

argument also displayed the NICE properties.

◮ But that’s not the case:

(7)

• a. It began to rain./* Began it to rain?
• b. It seems to be raining./Seems it to be raining?
• c. It appears to have rained overnight./*Appears it to have rained overnight?
• d. It’s likely to rain tonight./*Likely it to rain?

◮ Adjectives such as (un)likely, certain and sure support this subject-sharing (=

raising) behavior,

◮ a sure sign that it’s not diagnostic for auxiliaryhood.

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Lexical entries for Raising predicates

◮ So how shall we characterize the Raising predicates? ◮ We already know a bit about that, since auxiliaries belong to the class. ◮ So seem will be (γ\S)/(γ\S). ◮ But what else? ◮ What did you notice about all the non-auxiliary Raising verbs we’ve

looked at?

◮ Yes: they’re followed by infinitival expressions. ◮ That means we need to determine the right way to characterize these

expressions, right now!.

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Capturing infinitives: what kind of subtype does it yield?

◮ You’ve already seen the critical data: to displays the ellipsis pattern. ◮ So that means. . . ? ◮ So as an auxiliary, it has the argument structure (γ\S)/(γ\S). ◮ What should the output S be?

◮ It can’t be Sfin or we’d get *John to go to the store. ◮ It can’t be Sbse or we’d get *John will to go to the store. ◮

. . . . . .

◮ and the same holds for Sprog, S perf , etc. ◮ Conclusion: we need a separate subtype for to + its arguments. ◮ How about inf ?

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Capturing infinitives: what kind of subtype does it combine with?

◮ So now we have (γ\Sinf )/(γ\S). ◮ But what about the input? What subtype of S is involved there? ◮ In other words, what kind of VP (or whatever) does to combine with? ◮ You know how to figure that one out.

(8)

• a. Mary seems to be worried about something.
• b. John began to be worried about the job offer.
• c. For John to be awarded the contract, a lot would have to

change.

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Wrapping up

◮ So, the specification (γ\Snonaux)/(γ\Sinf ) defines the class of raising verbs ◮ What about raising adjectives such as likely?

(9) John likely to change his mind? You can’t be serious.

◮ So (γ\Snonaux)/(γ\Sinf ) looks good here too. ◮ Things are a little more complicated than this. . . ◮ but basically, that’s the story on the syntax of raising verbs. ◮ What about their semantics? ◮ In particular, what about (10)?

(10) It began to rain.

◮ Does it make sense to say that began denotes a relation between an individual and

a property?

◮ So if not, what does it actually denote?

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Semantics of raising verbs

◮ How about the following: ◮ Begin is defined with respect to some some contextually determined time interval

∆t0,

◮ and applies to an event which has been asserted via the proposition

expressed by the sentence

◮ with the semantic action of identifying the first interval ∆teφ of that

event’s temporal duration with ∆t0.

◮ In other words, [

[begin(φ)] ]∆t0 = 1 iff ∆t0 = ∆teφ

◮ So begin actually denotes an operator which applies to propositions and imposes an

identity between a certain background interval on the one hand and the initial interval of a specific event which is a guarantor of the proposition’s truth,

◮ the point being that it is an operator on propositions, not a relationship between

properties on the one hand and individuals on the other,

◮ making it very much like the denotation of a modal auxiliary.

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More on raising semantics

◮ Likewise, for It seems to be raining, ◮ which we can characterize informally as assertion that the proposition

expressed by it is raining has a greater than random chance of being true based on evidence that the speaker takes to be generally relevant.

◮ Here again, the semantic action of seem is an operator which takes a

proposition as its argument (in this case, mapping it to a certain level

• f confidence in accepting the truth of the proposition).

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Control verbs

◮ Consider the two cases in (11):

(11) John

• a. began
• b. tried
• to play the piano.

◮ These seem very similar in form. ◮ But do they behave in the same way?

(12)

• a. It
• i. began
• ii. *tried
• to rain.
• b. There
• i. began
• ii. *tried
• to be some indication that a verdict had

been reached.

• c. Some headway
• i. began
• ii. *tried
• to be made on the project.

◮ Conclusion: meaningless material cannot be the subject of try

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Control vs. Raising

◮ Raising verbs don’t care about the meaning (or lack of it) of their subjects ◮ because they don’t posit a relationship between those subjects and anything

else.

◮ They are predicates on propositions, just as auxiliaries are. ◮ Evidently, control verbs do establish such a relationship, which accounts for

the difference.

◮ in (11a), if we ask what John did, ◮ we see that it’s two things.

◮ John made an effort, ◮ and the nature of the effort involved piano-playing.

◮ In contrast, The story began to worry me isn’t about the story beginning. . .

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Control vs. Raising, cont’d

◮ But it’s true that both begin and try combine with an infinitive VP to

yield a VP.

◮ So they have the same syntactic type. ◮ So the difference must be a matter of their semantics. ◮ How can we capture it? What should we write as the sign for try? ◮ How about (13)?

(13) try; λPλy.try(y)(P(y)); VP/VP

inf

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Control vs. Raising, cont’d

◮ Then we’d have:

play; play; VPbse/NP the • piano; ι(piano); NP play • the • piano; play(ι(piano)); VPbse to; λQ.Q; VP

inf /VPbse

to • play • the • piano; play(ι(piano)); VP

inf

tried; λPλy.try(y)(P(y)); VP

fin/VP inf

tried • to • play • the • piano; λy.try(y)(play(ι(piano))(y)); VP

fin

john; j; NP john • tried • to • play • the • piano; try(j)(play(ι(piano))(j)); Sfin

◮ This looks like the result we want. ◮ But it’s not the end of the story. . .

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Object control

◮ We can exhibit a parallel set of data for objects as well.

(14) John  believed convinced ff Bill to be a candidate for mayor. (15) John  believed *convinced ff  there to be a problem it to be raining ff .

◮ Again, the difference seems to be in the semantic possibilities:

◮ When the direct object is referential, both believe and convince can

appear;

◮ but when the direct object is a dummy, only believe is legal.

◮ We can make the same judgment as with the subject control verbs: ◮ convince imposes an interpretation in which the direct object has a semantic

relationship

◮ not only to the infinitive VP argument, ◮ but to the selecting verb as well.

◮ whereas believe does not.

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Object control, cont’d

◮ Let’s write out a lexical entry for convince which mirrors this property.

(16) convince; λzλPλy.convince(z)(P(z))(y); VP/VP

inf /normal

◮ Here’s an exercise: using this entry, write out a proof for John convinced Bill

to testify.

◮ It’s a direct result of this treatment that referentially empty elements may

not appear,

◮ since we will wind up with failed derivations of the following sort:

convince; λzλPλy.convince(z)(P(z))(y); VP/VP

inf /normal

there; ξ; there

⊥

◮ given the mismatch between functor and argument types.

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