CAS LX 502 Semantics 5b. Pronouns, assignments, and quantifiers 5.7(.1), 6.1.

CAS LX 502CAS LX 502SemanticsSemantics

5b. Pronouns, 5b. Pronouns, assignments,assignments,

and quantifiersand quantifiers

5.7(.1), 6.15.7(.1), 6.1

Names and pronounsNames and pronouns We’re modeling names as referring to an We’re modeling names as referring to an individual in the universe of individual in the universe of individuals. We use names to refer to individuals. We use names to refer to individuals.individuals.

Pavarotti is boring Pavarotti is boring is true whenever is true whenever the individual that the name Pavarotti the individual that the name Pavarotti refers to is in the set of individuals refers to is in the set of individuals for which the property for which the property is boringis boring holds. holds.

Turning our attention to another class Turning our attention to another class of words, the of words, the pronounspronouns, they seem to be , they seem to be much like names in that they pick out much like names in that they pick out an individual in the world.an individual in the world.

Names and pronounsNames and pronouns

There is an additional dimension There is an additional dimension of complexity to pronouns—what of complexity to pronouns—what individual they pick out depends individual they pick out depends on who you are pointing at as the on who you are pointing at as the time.time. He is boring.He is boring. She is hungry. She is hungry.

In order to know the conditions In order to know the conditions under which under which he is boringhe is boring is true, is true, we need know who is being “pointed we need know who is being “pointed at.”at.”

Pronoun resolutionPronoun resolution Pronouns are a form of a more general Pronouns are a form of a more general class of nouns known as class of nouns known as anaphoraanaphora.. The primary characteristic of anaphora is The primary characteristic of anaphora is that they refer, but their referent is not that they refer, but their referent is not fixed intrinsically. They get their fixed intrinsically. They get their reference from somewhere else.reference from somewhere else.

Resolving pronouns is not a trivial Resolving pronouns is not a trivial matter, although we will not concern matter, although we will not concern ourselves really with how it happens.ourselves really with how it happens. Mary told Sue that she won first prize, and Mary told Sue that she won first prize, and then she congratulated her.then she congratulated her.

Rather, we will assume it Rather, we will assume it does does happen, happen, and take as given a list of “pointings” and take as given a list of “pointings” that go with the pronouns.that go with the pronouns.

Caution about the term Caution about the term “anaphora”“anaphora”

Pronouns are a form of anaphora.Pronouns are a form of anaphora. Other things are also anaphora.Other things are also anaphora. The most salient other type are the The most salient other type are the -self-self-type words (-type words (herself, himselfherself, himself).).

Very often (particularly in syntax), Very often (particularly in syntax), one uses the term “anaphor” to refer one uses the term “anaphor” to refer onlyonly to the to the self-self-anaphora. Pronouns anaphora. Pronouns are not called “anaphors” in those are not called “anaphors” in those situations, but rather just situations, but rather just “pronouns.” We will follow that “pronouns.” We will follow that practice here.practice here.

Shifty referenceShifty reference One of the interesting things about One of the interesting things about pronouns is that there is a kind of pronouns is that there is a kind of ambiguity with them.ambiguity with them.

A pronoun can refer to anyone you could A pronoun can refer to anyone you could (under the right circumstances) point at. (under the right circumstances) point at. This is always a possible meaning for This is always a possible meaning for pronoun.pronoun. John lost his keys.John lost his keys.

Pronouns can also “shift” in reference Pronouns can also “shift” in reference too:too: Every boy lost his keys.Every boy lost his keys.

There are two meanings here, a constant There are two meanings here, a constant one, and a “shifting” one.one, and a “shifting” one.

QuantifiersQuantifiers Quantifiers (Quantifiers (everyoneeveryone, , someonesomeone, , noonenoone) allow ) allow us to state generalizations.us to state generalizations. Someone is boring.Someone is boring. Everyone is hungry.Everyone is hungry.

When we say When we say everyone is hungryeveryone is hungry, we’re saying , we’re saying that that for each individual for each individual xx, , xx is hungry is hungry..

We can think of this as follows:We can think of this as follows: Run through Run through the universe of individuals (people at least), the universe of individuals (people at least), pointing at each one in turn, and evaluate pointing at each one in turn, and evaluate s/he is hungrys/he is hungry. If it is true for every . If it is true for every pointing, then pointing, then everyone is hungry everyone is hungry is true.is true. If it is true for at least one pointing, then If it is true for at least one pointing, then someone is hungry someone is hungry is true. If it is true for none of is true. If it is true for none of the pointings, then the pointings, then noone is hungry noone is hungry is true.is true.

What quantifiers tell What quantifiers tell us about pronounsus about pronouns

In a sentence like In a sentence like He is hungryHe is hungry, , the referent of the pronoun is the referent of the pronoun is just determined by the context. just determined by the context.

In a sentence like In a sentence like Every boy lost Every boy lost his keyshis keys, the referent of pointing , the referent of pointing doesn’t exactly come from the doesn’t exactly come from the context. There is something context. There is something grammatical going on that “points” grammatical going on that “points” to each individual in turn.to each individual in turn.

Interpreting Interpreting quantifiersquantifiers

Before we get to the technical details, Before we get to the technical details, we can think about what a quantifier we can think about what a quantifier like like only Johnonly John seems to do. seems to do. Only John is hungryOnly John is hungry

This is true when:This is true when: The property The property is hungry is hungry holds of holds of JohnJohn.. The property The property is hungryis hungry does not hold of does not hold of anyone who is not anyone who is not John.John.

So, it goes through the people, So, it goes through the people, “points” at each one, and checks to see “points” at each one, and checks to see if the property holds. And then sees if if the property holds. And then sees if the results match certain conditions.the results match certain conditions.

Quantifiers are not Quantifiers are not type <e>type <e>

Consider Consider everyone is hungryeveryone is hungry.. The property The property is hungryis hungry is true of is true of individuals—so it is initially tempting to individuals—so it is initially tempting to suppose that this is true if some suppose that this is true if some individual, referred to by individual, referred to by everyoneeveryone,, is is hungry.hungry.

This could be more or less like This could be more or less like the people the people are hungryare hungry.. We discussed how this would work already. If we We discussed how this would work already. If we suppose suppose peoplepeople is a plural, a collection of is a plural, a collection of collections, we can take collections, we can take thethe to pick the biggest to pick the biggest one, and then we attribute one, and then we attribute is hungryis hungry (or (or is is hungryhungry) to that collection. Interpreted ) to that collection. Interpreted distributively, this gets the meaning right.distributively, this gets the meaning right.

Quantifiers are not Quantifiers are not type <e>type <e>

But try as you might, finding But try as you might, finding such an individual (or such an individual (or group/collection) for other group/collection) for other quantifiers won’t lead to a quantifiers won’t lead to a satisfying conclusion.satisfying conclusion. Nobody is hungryNobody is hungry.. Two people are hungryTwo people are hungry.. Most people are hungryMost people are hungry..

This can’t be how it works.This can’t be how it works.

Quantifiers relate Quantifiers relate propertiesproperties

If we think about what If we think about what every person every person is hungryis hungry does, it seems to be the does, it seems to be the following:following:

Consider the individuals for which Consider the individuals for which personperson is true. is true.

Consider the individuals for which Consider the individuals for which is hungryis hungry is true. is true.

If you find an individual in the If you find an individual in the first set, that individual will be first set, that individual will be in the second set.in the second set.

Some logical notationSome logical notation We didn’t cover logic very systematically, We didn’t cover logic very systematically, but it is now going to start to be but it is now going to start to be relevant, so let’s work through it a bit relevant, so let’s work through it a bit as a reminder.as a reminder.

The relation of The relation of if…thenif…then is indicated with is indicated with the the symbol. symbol.

For any two propositions For any two propositions pp and and qq, the , the proposition proposition p p qq is true under the is true under the following conditions:following conditions: pp is false and is false and qq is anything. is anything. pp is true and is true and qq is also true. is also true.

Another way you can read Another way you can read is as is as “implies.”“implies.”

Every person is hungryEvery person is hungry

So, to say “if an individual So, to say “if an individual has the has the personperson property, it property, it also has the also has the is hungryis hungry property” we can write:property” we can write: person(person(xx) ) hungry( hungry(xx))

For this to be true, being a For this to be true, being a person must imply being hungry.person must imply being hungry.

Quantifiers in logicQuantifiers in logic There are two quantifiers in logic that we There are two quantifiers in logic that we will make use of in describing at least the will make use of in describing at least the parallel quantifiers in natural language.parallel quantifiers in natural language. : : universaluniversal quantifier (“for all”) quantifier (“for all”) : : existentialexistential quantifier (“there exists a”) quantifier (“there exists a”)

In action:In action: xx[person([person(xx)])] This is true if every individual you pick, and This is true if every individual you pick, and call “call “xx”, results in “person(”, results in “person(xx)” being true.)” being true.

Everything is a person.Everything is a person. xx[person([person(xx)])] This is true if there is some individual you This is true if there is some individual you could pick, call it “could pick, call it “xx”, that will result in ”, that will result in “person(“person(xx)” being true.)” being true.

Something is a person.Something is a person.

Every person is hungryEvery person is hungry To complete the example from before, to To complete the example from before, to say say every person is hungryevery person is hungry in the fancy- in the fancy-looking logic notation, we want to say looking logic notation, we want to say that “for every individual that “for every individual xx there is, there is, being a person implies being hungry.”being a person implies being hungry.”

xx[person([person(xx) ) hungry( hungry(xx)])]

The “syntax” of the logical The “syntax” of the logical and and is quite is quite like the “syntax” of like the “syntax” of ..

To be perhaps a bit more precise, we might To be perhaps a bit more precise, we might write this:write this:xxUU [person( [person(xx) ) hungry( hungry(xx)] ()] (UU being the being the universe of individuals). If not written, it’s universe of individuals). If not written, it’s implicit.implicit.

A person is hungryA person is hungry Likewise, to say Likewise, to say some person is some person is hungryhungry, we want to say that “there , we want to say that “there exists some individual exists some individual xx such that it such that it is both a person and hungry.”is both a person and hungry.”

x[person(x) x[person(x) hungry(x)] hungry(x)]

You can say You can say a persona person in a way that is in a way that is synonymous to synonymous to some personsome person. . This is what This is what we’ll usually talk about in the context of we’ll usually talk about in the context of quantifiers. Notice that quantifiers. Notice that thisthis version of version of aa is is notnot semantically “empty.” semantically “empty.”


For something likeFor something like Only John lost his keysOnly John lost his keys

We might continue to think of this We might continue to think of this as talking about a property that as talking about a property that John has and nobody else does. What John has and nobody else does. What is that property?is that property?

Well, it seems to be something like Well, it seems to be something like “having lost one’s own keys.”“having lost one’s own keys.”

True of x where x lost x’s keys:True of x where x lost x’s keys: xx [ [ xx lost lost xx’s keys in M]’s keys in M]


Only John lost his keysOnly John lost his keys xx [ [ xx lost lost xx’s keys in M]’s keys in M]

It appears that It appears that hishis is interpreted somehow is interpreted somehow as having the same value as the subject.as having the same value as the subject.

The reference of The reference of hishis depends entirely on depends entirely on the reference of the subject.the reference of the subject.

We check this by trying different values We check this by trying different values for the subject.for the subject.

This kind of This kind of dependentdependent reference is known reference is known as being as being boundbound. The reference of the . The reference of the pronoun is “tied” to the reference of the pronoun is “tied” to the reference of the subject. It is a subject. It is a bound pronounbound pronoun..


Only John lost his keysOnly John lost his keys xx [ [ xx lost lost xx’s keys in M]’s keys in M]

How do we get this to come out?How do we get this to come out? The basic idea goes like this: When you have a The basic idea goes like this: When you have a

quantifier, you “shift” it out of the sentence in quantifier, you “shift” it out of the sentence in order to form the property.order to form the property. Take Take only Johnonly John out and put it at the beginning. out and put it at the beginning. Add Add xx and brackets around the sentence. and brackets around the sentence. Put Put xx where the quantifier was. where the quantifier was. For any pronouns interpreted as bound, replace them with For any pronouns interpreted as bound, replace them with

xx.. Every girl finished her sandwich.Every girl finished her sandwich. Every girl Every girl xx [ [ xx finished finished xx’s sandwich in M]’s sandwich in M]

Combining these is the next task. This recipe above Combining these is the next task. This recipe above is what we will come to call “quantifier raising.”is what we will come to call “quantifier raising.”


No girl finished her sandwich.No girl finished her sandwich. No girl No girl xx [ [ xx finished finished xx’s sandwich in M]’s sandwich in M]

We have here a quantifier (We have here a quantifier (no girlno girl) and a ) and a property (property (to have finished one’s own to have finished one’s own sandwichsandwich).).

We need to check to see if everyone (among the We need to check to see if everyone (among the girls) has this property.girls) has this property.

Is Is no girlno girl the argument of the property (like the argument of the property (like it would be in it would be in John finished a sandwichJohn finished a sandwich)?)?

Well, no, that won’t work. (Cf. earlier, not Well, no, that won’t work. (Cf. earlier, not type <e>).type <e>).

It must be that the property is taken as an It must be that the property is taken as an argument to the quantifier, actually.argument to the quantifier, actually.


And it makes sense for the quantifier to And it makes sense for the quantifier to take a property.take a property.

No girlNo girl takes a property P. takes a property P. It is true if, when you have checked all It is true if, when you have checked all of the individuals (among the girls), of the individuals (among the girls), none of them had the property P.none of them had the property P. No girl (No girl ( xx [ [ xx finished finished xx’s sandwich in ’s sandwich in M])M])

PP [ for no girl, [ for no girl, xx:: P P((xx)])] PP [ for every girl, [ for every girl, xx:: PP((xx)])]

Now, let’s make these ideas more Now, let’s make these ideas more precise…precise…

Bond is Bond is hungryhungry

[N][N]MM = = FF((BondBond) = BOND) = BOND [VP][VP]MM = [Vi] = [Vi]MM = =

xx [ [ xx is hungry in M] is hungry in M] [S][S]MM = [VP] = [VP]MM ( [N] ( [N]MM ) = ) =

xx [ [xx is hungry in M] is hungry in M] (BOND) =(BOND) =BOND is hungry in MBOND is hungry in M

U

S

N VP

Vi

is hungry

Bond

…is hungry…BondLorenPavarotti…

F

For now,going backto is hungryas a Vi, forsimplicity

Bond is Bond is hungryhungry

[S][S]MM11 = = BOND is hungry in MBOND is hungry in M11 = =true in the specific true in the specific situation Msituation M11..

U1

S

N VP

Vi

is hungry

Bond


F1

He is hungryHe is hungry

We don’t have We don’t have hehe in our lexicon yet, in our lexicon yet, but if we did, how should we but if we did, how should we interpret it?interpret it?

This sentence could mean different This sentence could mean different things (have different truth things (have different truth conditions), in the same situation, conditions), in the same situation, depending on who we’re pointing at.depending on who we’re pointing at.

U

S

N VP

Vi

is hungry

He


F

HeHe11 is hungry is hungry

When writing a sentence like When writing a sentence like he is he is hungryhungry, the standard practice is to , the standard practice is to indicate the “pointing” relation by indicate the “pointing” relation by using a subscript on using a subscript on hehe::

HeHe11 is hungry is hungry.. The idea here is that this is The idea here is that this is

interpreted in conjunction with a interpreted in conjunction with a “pointing function” that tells us who “pointing function” that tells us who ““11” points to.” points to.

U

S

N VP

Vi

is hungry

He1


F

123…

g


Where different people are being Where different people are being pointed to, we use different pointed to, we use different subscripts:subscripts:

HeHe11 likes her likes her22, but he, but he33 hasn’t noticed. hasn’t noticed.

The “pointing function” goes by the The “pointing function” goes by the more official name more official name assignment functionassignment function, , and is generally referred to as and is generally referred to as gg..

U

S

N VP

Vi

is hungry

He1


F

123…

g1


The assignment function The assignment function gg fits into fits into the system much like the valuation the system much like the valuation function function FF does. does. FF maps maps lexical itemslexical items into the universe of individuals, into the universe of individuals, gg maps maps subscriptssubscripts into the universe of into the universe of individuals.individuals.

[[nn]]MM,,gg = = gg((nn))

U

S

N VP

Vi

is hungry

He1


F

123…

g1


[[nn]]MM,,gg = = gg((nn))

[S][S]MM1,1,gg11 = = gg11(1(1)) is hungry in M1 = is hungry in M1 =BOND is hungry in M1 =BOND is hungry in M1 =true in the specific model M1true in the specific model M1

U1

S

N VP

Vi

is hungry

He1


F1

123…

g1

Bond likes everyoneBond likes everyone So, what we’re after is something like So, what we’re after is something like this:this:

xxUU [Bond likes [Bond likes xx in in MM]]

That is, we have to convert That is, we have to convert everyoneeveryone into a into a pronoun and interpret the S, with a pronoun pronoun and interpret the S, with a pronoun in it, with every “pointing” that we can in it, with every “pointing” that we can do.do.

To do this, we will introduce a rule called To do this, we will introduce a rule called Quantifier RaisingQuantifier Raising for sentences with for sentences with quantifiers in them that will accomplish quantifiers in them that will accomplish just that.just that.

Bond likes every fishBond likes every fish Add a few Add a few (obvious things), (obvious things), so we can make so we can make better sentences.better sentences.

Not much new Not much new here, except that here, except that we’ve added some we’ve added some words we can play words we can play with, including with, including some common some common nouns, and some nouns, and some determiners (Det) determiners (Det) to use to build to use to build quantifiers.quantifiers.

S

DP VP

Vt

likes

Bond DP

Det

every

N

fish

Bond likes every fishBond likes every fish Back to the problem of quantifiers.Back to the problem of quantifiers. Consider the meaning of Consider the meaning of Bond likes Bond likes every fishevery fish. It should be something . It should be something like:like:

For every For every xx in in UU that is a fish, Bond that is a fish, Bond likes likes xx..

Or:Or:

xxUU [ [xx is a fish in is a fish in MM Bond likes Bond likes xx in in MM]]

Bond likes every fishBond likes every fish xxUU [ [xx is a fish in is a fish in MM Bond likes Bond likes xx in in MM]]

Notice that our sentence is basically Notice that our sentence is basically here, but with here, but with xx instead of instead of every fishevery fish. . The meaning of The meaning of every fishevery fish is kind of is kind of “factored out” of the sentence and used “factored out” of the sentence and used to set the value of to set the value of xx..

In order to get this interpretation, In order to get this interpretation, we’re going to introduce a we’re going to introduce a transformationtransformation. A new kind of rule. . A new kind of rule.

TransformationsTransformations The The syntactic base rulessyntactic base rules that we have that we have allow us to construct trees.allow us to construct trees.

A A transformationtransformation takes a tree and alters takes a tree and alters it, resulting in a new tree.it, resulting in a new tree.

The particular transformation we are going The particular transformation we are going to adopt here (to adopt here (Quantifier RaisingQuantifier Raising) takes ) takes an NP like an NP like every fishevery fish and attaches it to and attaches it to the top of the tree, leaving an abstract the top of the tree, leaving an abstract pronoun behind. Then we will write our pronoun behind. Then we will write our semantic rules to interpret that semantic rules to interpret that structure.structure.

Quantifier RaisingQuantifier Raising

S

DP VP

Vt

likes

Bond DP

Det

every

N

fish

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S

Quantifier RaisingQuantifier Raising

Quantifier RaisingQuantifier Raising[[SS XX DP DP YY ] ] [ [SS DP [ DP [SS i [ i [SS XX ttii YY ] ] ] ] ] ]

That is:That is:S

… DP … S

… ti …

i

S

S

DP


Now comes the tricky part: How do we Now comes the tricky part: How do we assign a semantic interpretation to the assign a semantic interpretation to the structure? (It structure? (It isis easier—nay, possible—now easier—nay, possible—now that we have the QR rule, but let’s see that we have the QR rule, but let’s see why).why).

Remember, what we’re after is:Remember, what we’re after is:xxUU [ [xx is a fish in is a fish in MM Bond likes Bond likes xx in in MM]]


Let’s start with theLet’s start with thelower S. We knowlower S. We knowhow to interprethow to interpretthat, it is that, it is essentiallyessentiallyjust just Bond likes itBond likes it11..

True if BOND likes True if BOND likes gg(1) (1) in Min M

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


The purpose of the The purpose of the 11node is to make anode is to make apropertyproperty out of this out of thissentence.sentence.

The property willThe property willbe, in effect,be, in effect,things Bond likesthings Bond likes..

Goal:Goal:1 [BOND likes 1 [BOND likes gg(1) in (1) in M]M]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


The interpretation of The interpretation of [[11]]M,gM,g,,then, will be a functionthen, will be a functionthat takes a sentencethat takes a sentence(type (type <t><t>) and returns a) and returns apredicate (type predicate (type <e,t><e,t>).).

[[11]]M,gM,g is type is type <t,<e,t>><t,<e,t>>..

[1][1]M,gM,g = =S [S [xx [ [S] [ [S]MM,,gg[1/[1/xx] ] ] ]] ]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S

[ ][ ]MM,,gg[1/[1/xx]]

To understand what is going to happen To understand what is going to happen here, we need to introduce one more here, we need to introduce one more concept, the concept, the modified assignment function modified assignment function gg[1/[1/xx].].

Remember that the assignment function maps Remember that the assignment function maps subscripts to individuals, so that we can subscripts to individuals, so that we can interpret pronouns like interpret pronouns like hehe22..

So, So, gg11 (an assignment function for a (an assignment function for a particular pointing situation) might map particular pointing situation) might map 11 to to PavarottiPavarotti, , 22 to to NemoNemo, , 33 to to LorenLoren, and , and so forth.so forth.

[ ][ ]MM,,gg[1/[1/xx]]

gg11 maps maps 11 to to PavarottiPavarotti, , 22 to to NemoNemo, , 33 to to LorenLoren, …, …

A modified assignment function A modified assignment function gg[[ii//xx] is ] is an assignment function that is an assignment function that is just likejust like the original assignment function except the original assignment function except that instead of whatever that instead of whatever g g mapped mapped ii to, to, gg[[ii//xx] maps ] maps ii to to x x instead. That is:instead. That is:

gg11(1) (1) = = PavarottiPavarotti, g, g11(2) = (2) = NemoNemo gg11[2/[2/BondBond](1) = ](1) = PavarottiPavarotti, , gg11[2/[2/BondBond](2) = ](2) = BondBond

[ ][ ]MM,,gg[1/[1/xx]]

gg11(1) (1) = = PavarottiPavarotti, g, g11(2) = (2) = NemoNemo gg11[2/[2/BondBond](1) = ](1) = PavarottiPavarotti, , gg11[2/[2/BondBond](2) = ](2) = BondBond

The reason that this is useful is that to The reason that this is useful is that to interpret interpret every fishevery fish, we want to go through , we want to go through all of the fish, and check whether all of the fish, and check whether Bond likes Bond likes itit is true when we point to each fish. is true when we point to each fish.

ItIt is a pronoun, whose interpretation is is a pronoun, whose interpretation is dependent on who we are pointing to, so we dependent on who we are pointing to, so we need to be able to change who we point to need to be able to change who we point to (accomplished by modifying the assignment (accomplished by modifying the assignment function).function).


[1][1]M,gM,g = =S [S [xx [ [S] [ [S]MM,,gg[1/[1/xx] ] ] ]] ]

[S[S]]M,gM,g = =S [S [xx [ [S] [ [S]MM,,gg[1/[1/xx] ] ] ]([S]] ]([S]M,gM,g) =) =xx [ [S] [ [S]MM,,gg[1/[1/xx] ] ] =] =xx [BOND likes [BOND likes gg[1/[1/xx](1) ] =](1) ] =xx [BOND likes x] [BOND likes x]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


Great, we have Great, we have [S[S]]M,gM,g as a as a predicate that predicate that means means things Bond things Bond likeslikes..

Now to Now to every fishevery fish..

FishFish is a property, is a property, true of fish; that true of fish; that is:is:xx [ [x x is a fish in is a fish in M]M]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


What we’re looking for What we’re looking for is a way to verify is a way to verify that every individual that every individual that is a fish is also that is a fish is also an individual that an individual that Bond likes.Bond likes.

That is:That is:xx [ [xx is a fish is a fish xx is a thing Bond is a thing Bond likes]likes]

[S[S]]M,gM,g is the predicate is the predicate things Bond likesthings Bond likes. . [N][N]M,gM,g is the predicate is the predicate fishfish..

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


Informally, Informally, everyevery takes takes twotwopredicates, and yields predicates, and yields truetrueif everything that if everything that satisfiessatisfiesthe first predicate alsothe first predicate alsosatisfies the second.satisfies the second.

<<e,t>,<<e,t>,t>><<e,t>,<<e,t>,t>>

[[everyevery]]M,gM,g = = PP [ [ QQ [ [xx [ [PP((xx) ) QQ((xx)] ] ])] ] ]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


[every][every]M,gM,g = =PP [ [ QQ [ [xx [ [PP((xx) ) QQ((xx)] ] ])] ] ]

[N][N]M,gM,g = [fish] = [fish]M,gM,g = =yy [ [y y is a fish in M]is a fish in M]

[DP][DP]M,gM,g = =[every][every]M,gM,g ( [fish] ( [fish]M,gM,g ) = ) =PP[[QQ [[xx [ [PP((xx) ) QQ((xx)] ] ] ()] ] ] (yy[[y y is is a fish] )=a fish] )=QQ [ [xx [ [yy [ [y y is a fish](x) is a fish](x) QQ((xx)] ] =)] ] =QQ [ [xx [ [x x is a fish is a fish QQ((xx)] ])] ]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S


[DP][DP]M,gM,g = =QQ [ [xx [ [x x is a fish is a fish QQ((xx)] ])] ]

[S[S]]M,gM,g = =yy [BOND likes y] [BOND likes y]

[S][S]M,gM,g = = QQ[[xx [x is a fish [x is a fish QQ((xx)] ])] ]

((yy [BOND likes y]) = [BOND likes y]) =xx [x is a fish [x is a fish yy [BOND likes [BOND likes y](y](xx)] =)] =xx [x is a fish [x is a fish BOND likes BOND likes xx] ]

S

DP VP

Vt

likes

Bond

DP

Det

every

N

fish

t1

S

1

S

PhewPhew

And, we’ve done it. We’ve derived And, we’ve done it. We’ve derived the truth conditions for the truth conditions for Bond Bond likes every fishlikes every fish::

xx [ [xx is a fish in M is a fish in M BOND likes BOND likes xx ] ]

For every individual For every individual xx, if , if xx is a is a fish, then Bond likes fish, then Bond likes xx..

New semantic rulesNew semantic rules

The new semantic rules we needed The new semantic rules we needed (lexical entries, we’re still using (lexical entries, we’re still using the same Functional Application and the same Functional Application and Pass-up rules) were:Pass-up rules) were:

[every][every]M,gM,g = = PP [ [ QQ [ [ xx [ [PP((xx) ) QQ((xx)] ] ])] ] ]

[[ii]]M,gM,g = = S [S [xx [ [S] [ [S]MM,,gg[[ii//xx] ] ] ]] ]

Loren hates a bookLoren hates a book We’ve worked out an interpretation for We’ve worked out an interpretation for a single quantificational determiner, a single quantificational determiner, everyevery, but we can in a parallel way , but we can in a parallel way give a meaning to give a meaning to aa (as in (as in a booka book).).

The meaning we want for The meaning we want for Loren hates a Loren hates a bookbook is that there is some individual is that there is some individual xx such that such that xx is a book and is a book and Loren Loren hates xhates x::

xx [ [x x is a book is a book LOREN hates LOREN hates xx ] ]

Loren hates a bookLoren hates a book

Without running through all of Without running through all of the steps again, what we want the steps again, what we want here is for [here is for [aa]]M,gM,g to take two to take two predicates (here, predicates (here, bookbook, and , and things Loren hatesthings Loren hates), and be true ), and be true if there is some individual that if there is some individual that satisfies both:satisfies both:

[a][a]M,gM,g = = PP [ [ QQ [ [ xx [ [PP((xx) ) QQ((xx)] ] ])] ] ]

Comments about QRComments about QR Quantifier RaisingQuantifier Raising[[SS XX DP DP YY ] ] [ [SS DP [ DP [SS i [ i [SS XX ttii YY ] ] ] ] ] ]

As it is stated, QR applies to any DP, whether As it is stated, QR applies to any DP, whether it is a quantifier or not. So, when do you use it is a quantifier or not. So, when do you use QR?QR?

There are certain situations (e.g., There are certain situations (e.g., Nemo hates Nemo hates every bookevery book) where the structure ) where the structure cannotcannot be be interpreted without QR. When the quantifier is interpreted without QR. When the quantifier is the object of a transitive verb, for example.the object of a transitive verb, for example. A transitive verb needs something of type A transitive verb needs something of type <e><e>. A . A quantifier needs something of type quantifier needs something of type <e,t><e,t> (and is (and is itself of type itself of type <<e,t>,<<e,t>,t>><<e,t>,<<e,t>,t>>). Neither one can ). Neither one can take the other as an argument.take the other as an argument.

Comments about QRComments about QR Quantifier RaisingQuantifier Raising[[SS XX DP DP YY ] ] [ [SS DP [ DP [SS i [ i [SS XX ttii YY ] ] ] ] ] ]

As it is stated, QR applies to any DP, As it is stated, QR applies to any DP, whether it is a quantifier or not. So, whether it is a quantifier or not. So, when do you use QR?when do you use QR?

On the other hand, if you apply QR to a On the other hand, if you apply QR to a name like name like LorenLoren, the semantic , the semantic interpretation becomes more complicated to interpretation becomes more complicated to work out, but the end result (the truth work out, but the end result (the truth conditions) are the same as if you hadn’t conditions) are the same as if you hadn’t done QR. So, you don’t really need QR to done QR. So, you don’t really need QR to interpret the structure.interpret the structure.

Comments about QRComments about QR


As it is stated, QR applies to any DP, whether As it is stated, QR applies to any DP, whether it is a quantifier or not. So, when do you use it is a quantifier or not. So, when do you use QR?QR?

In fact, it turns out that when you have a In fact, it turns out that when you have a quantificational DP as a subject (as in quantificational DP as a subject (as in Every Every fish hates fish hates The Last JurorThe Last Juror), you don’t actually ), you don’t actually need QR in order to interpret the structure need QR in order to interpret the structure either.either. The VP The VP hates hates The Last JurorThe Last Juror is a predicate. is a predicate. EveryEvery applies to applies to fishfish and then can apply to the VP, and then can apply to the VP, resulting in the same truth conditions you would resulting in the same truth conditions you would have if you applied QR.have if you applied QR.




Moreover, if you apply QR to a DP, you Moreover, if you apply QR to a DP, you still have an NP—you could apply QR again still have an NP—you could apply QR again to that same NP if you wanted. Again, like to that same NP if you wanted. Again, like with names, this won’t affect the ultimate with names, this won’t affect the ultimate interpretation, it will just increase the interpretation, it will just increase the amount of effort necessary to work out the amount of effort necessary to work out the truth conditions.truth conditions.




So, the answer is: So, the answer is: Use QR as necessary, Use QR as necessary, where it will result in a different where it will result in a different interpretation from not using QR (or interpretation from not using QR (or when not using QR prevents the structure when not using QR prevents the structure from being interpreted at all).from being interpreted at all).

Every fish likes a Every fish likes a bookbook

Some sentences have more than one quantifier. We know Some sentences have more than one quantifier. We know that, because that, because a booka book is the object of a transitive is the object of a transitive verb, we need to apply QR to verb, we need to apply QR to a booka book. We could refrain . We could refrain from applying QR to from applying QR to every fishevery fish (the subject) because (the subject) because subjects don’t require QR in order to be subjects don’t require QR in order to be interpretable.interpretable.

The result will be, paraphrasing: The result will be, paraphrasing: There is a book There is a book xx such that for every such that for every yy, if , if yy is a fish, then is a fish, then yy likes likes x.x. This is certainly something the sentence can mean. This is certainly something the sentence can mean.

HoweverHowever, the sentence can also mean: , the sentence can also mean: For every For every yy, if , if yy is a fish, then there is a book is a fish, then there is a book xx such that such that yy likes likes xx.. To get this meaning, you must also apply QR to the To get this meaning, you must also apply QR to the subject (after applying QR to the object).subject (after applying QR to the object).

CAS LX 502 Semantics 5b. Pronouns, assignments, and quantifiers 5.7(.1), 6.1.

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Transcript of CAS LX 502 Semantics 5b. Pronouns, assignments, and quantifiers 5.7(.1), 6.1.