Response to Problem Set 5 Semantics Linguist Problem Set read the ppt carefully, understanding what the professor teach. then finish the problem set Introd
Response to Problem Set 5 Semantics Linguist Problem Set read the ppt carefully, understanding what the professor teach. then finish the problem set Introduction to Linguistics
Semantics I
Semantics:
How form relates
to meaning.
Syntax:
Structure of
sentences.
Morphology:
Structure of words.
Phonology:
Structure of sounds.
Phonetics:
How sounds are
articulated.
Basics
Form and Meaning
form
/ð?
thekæt
cat sæt
sat
on
?n ð?
themæt/
mat
meaning
Compositionality
Sentences follow the principle of compositionality: the
meaning of the whole is the meaning of the parts plus
how they are combined.
form
the cat sat
on the mat
meaning
What is Meaning?
We distinguish two aspects of linguistic meaning:
sense and reference.
Sense is the mental representation of a meaning.
The concept in your mind when you hear table.
Reference is the actual entities in the world that an
utterance refers to.
If I say that table and point at a particular table, the
referent is that actual physical thing.
Sense and Reference
Sense
Reference
that cup
Sense and Reference
Sense: A mental representation of the meaning of a
linguistic expression.
Reference: The set of real objects in the world that a
linguistic expression in a particular utterance refers to.
Some expressions have sense but have no reference!
Example:
A unicorn
Sense: A horse-like four-legged creature with one
horn on its forehead head.
Reference: Ø, empty set
(in our world).
Sense without Reference
Examples of expressions with sense but no reference:
Could a linguistic expression have reference without
having sense?
The queen of the United States
The tie that I am wearing
The first person on Mars
Zeus
Multiple Senses, Same Reference
The most populous country in the world
Reference
Reference
The country that hosted the 2008 Olympics
The most populous country in the world and The country
that hosted the 2008 Olympics have di?erent senses.
But they have the same reference (the country of China).
Multiple Senses, Same Reference
The most populous country in the world
Reference
Reference
The country that hosted the 2008 Olympics
You can tell the senses are di?erent because:
1. In the future or the past, the references for these expressions might
change to two di?erent things.
2. You can know that China is the most populous country in the world and
not know that it is the country that hosted the 2008 Olympics.
Sense vs. Reference
An expression can have sense without having reference.
Sense is like the definition of a word.
Two expressions can have di?erent senses but the same
reference.
Reference is the actual objects in the world picked out by
a word in context.
The set of objects in the world that match the
definition given by the sense.
Compositional and
Lexical Semantics
Semantics
Semantics is the study of how the form of a linguistic
expression relates to its meaning (sense and reference).
There are two kinds of semantics:
Lexical semantics: Study of the sense and reference
of words.
Compositional semantics: Study of how the meanings
of words combine to form the meanings of sentences.
Sense of a Word
How does the mind represent the
sense of a word?
The sense of a word is a mental representation of its
meaning.
How are word meanings stored in the mind?
?
How does the mind represent the
sense of a word?
How are word senses stored in the mind?
Option 1: Dictionary-style definitions?
?
Dictionary Definitions?
A dictionary definition defines the sense of a word in
terms of other words.
For example,
Problem: Dictionary definitions are circular!
proud: Feeling or showing pride.
divine: Being or having the nature of a deity.
pride: The quality or state of being proud.
deity: A divine entity
?
How does the mind represent the
sense of a word?
How are word senses stored in the mind?
Option 1: Dictionary-style definitions?
Option 2: Mental images?
?
Mona Lisa
Mental Image Definitions?
Words often seem to conjure up mental images. Could
those be the word senses?
For instance, when I say bird, you may think of
something like:
Problem: But these are also birds!
?
Mental Image Definitions?
Words often seem to conjure up mental images. Could
those images be the word senses?
Di?erent people may get di?erent images for the same
word:
food
?
How does the mind represent the
sense of a word?
How are word senses stored in the mind?
Option 1: Dictionary-style definitions?
Option 2: Mental images?
Option 3: Usage-based definitions?
?
Usage-Based Definitions?
?
Usage-based definitions define the sense of a word in
terms of the contexts where it can be used.
For a word like ongchoi, list the sentences it could be
used in:
If you know what ongchoi means, then you know you
can use it with these other words.
And if you see other words in the same contexts, you
know their sense is similar.
How does the mind represent the
sense of a word?
How are word senses stored in the mind?
Option 1: Dictionary-style definitions?
Option 2: Mental images?
Option 3: Usage-based definitions?
We dont know exactly how the human brain represents
word meanings.
But if you know the sense of a word, then you
definitely know when it can be used.
So we use usage-based definitions for now.
?
Reference of a Word
Reference of a Word
Words have di?erent kinds of reference.
A proper name refers to a single particular entity in the
world:
China
Nicolas Cage
Reference of a Word
Words have di?erent kinds of reference.
What does a common noun refers to?
Does Sally have a cat?
?
Could it be a particular cat in the world?
The answer could be: No, Sally has never had a cat.
The common noun cat refers to the set of all cats in the
world.
cat
Reference of a Word
Words have di?erent kinds of reference.
What is the reference of an adjective?
green
Set of all green things in the world
Reference of a Word
Words have di?erent kinds of reference.
What is the reference of an intransitive verb?
walks
All the things in the world that are walking
Reference of a Word
Words have di?erent kinds of reference.
A common noun refers to the set of entities in the world
that are described by that noun.
An adjective refers to the set of entities in the world that
are described by that adjective.
An intransitive verb refers to the set of entities in the
world that are described by that intransitive verb.
A proper name refers to a single particular entity in the
world.
Relationships
Between Words
Relationships Between Words
All words in a languageare linked in a web of semantic
relationships.
We define relationships between words in terms of their
reference.
poodle
dog
cat
animal
cow
Relationships Between Words
dog
?
poodle
Relationships Between Words
hypernym
dog
?
hyponym
poodle
The reference of poodle is
a subset of the reference
of dog.
All poodles are dogs.
But not all dogs are
poodles.
So we say poodle is a
hyponym of dog.
And dog is a hypernym of
poodle.
Hypernymy
hypernym
hyponym
dog
poodle
X is a hypernym of Y
i? the reference of Y is
a subset of the
reference of X.
X is a hyponym of Y i?
the reference of Y is a
superset of the
reference of X.
Relationships Between Words
Relationships Between Words
groundhog
?
woodchuck
Synonymy
groundhog
synonyms
woodchuck
Groundhog and
woodchuck refer to
the same set of
entities.
So they are synonyms.
X and Y are synonyms
i? they have the same
reference.
Relationships Between Words
good
alive
old
?
?
?
bad
dead
young
Antonymy
antonyms
good
alive
old
bad
antonyms
antonyms
dead
young
X and Y are antonyms
i? their references
contrast in some way.
Kinds of Antonyms
Two words X and Y are complementary antonyms i?
there is no entity in the reference of both X and Y.
complementary
antonyms
alive
dead
Set of everything
that is alive
Set of everything
that is dead
Complementary Antonyms
Test: Does not X imply Y and vice versa?
If yes, then X and Y are complementary antonyms.
complementary
antonyms
alive
dead
Set of everything
that is alive
Set of everything
that is dead
Kinds of Antonyms
gradable
antonyms
hot
cold
If something is not cold, does
that imply that it is hot?
No, it could be lukewarm.
So hot and cold are not
complementary antonyms.
We call them gradable
antonyms: they identify
di?erent directions on a scale.
Hot
Lukewarm
Cold
Relationships Between Words
All words in a languageare linked in a web of semantic
relationships.
Some of the relationships are:
Two words are hypernyms if one names a superset of the
other.
Two words are hyponyms if one names a subset of the
other.
Two words are synonyms if they have the same reference.
Two words are antonyms if they have contrasting
references.
Complementary antonyms if they are mutually
exclusive.
Gradable antonyms if they name di?erent ends of a
scale.
Linguis 3: Introduction to Linguistics
Winter 2019
Problem Set 5: Semantics
Due 3/1/2019. 100 points possible
1. Do the following expressions refer to a single entity in the world, or a set of
multiple entities in the world? (2 points each)
a. student
b. Massachusetts
c. car
d. man
e. movie
f. Statue of Liberty
2. In what way is each of the following pairs of words related? In cases of hypernymy,
indicate which word is the hyponym and which oen is the hypernym. In cases of
antonymy, tell what kind of antonym it is. (2 points each)
a. shallow
deep
b. suite
sweet
c. table
furniture
d. unmarried
married
e. sofa
couch
f. win
lose
3. i. Propose a hypernym for each of the following words. (2 points each)
a. hammer
b. T-shirt
c. pink
d. fish
ii. Propose a hyponym for each of the following expressions. (2 points each)
a. appliance
b. musical instrument
c. furniture
d. fish
4. For each of the following expressions, determine whether it expresses a proposition
or not. Remember, if you are dealing with a proposition, you can question its truth value.
For example, we know that ?Fido is a dog? expresses a proposition because we can ask
Is it true that Fido is a dog?? Conversely, a dog all by itself does not express a
proposition because we cannot ask ?Is it true that a dog? ?(2 point each)
a. a.woman
b. like Bob
c. the smallest country in the world
d. Sally wondered who would be at the party
e. Bob hates Polly
f. accidentally
g. Polly liked
h. under the bed
i.
Sally likes to sleep
j.
bring some beer
5. For each pair of the following sentences, determine whether ?one entails the other?,
whether they are ?mutually entailing?, whether they are ?incompatible?, or ?none of the
above?. Explain your answers. (2 points each)
a. Fifi is a poodle.
Fifi is a dog.
b. My last name is Jones.
My fathers last name was Jones.
c. Bob inherited a car from his grandma.
Bob owns a car.
d. Sally lives in Ohio.
Sally lives in Europe.
e. Sally lives in Ohio.
Sally lives in the United States.
f. Polly speaks Russian.
Polly is from Russia.
g. Polly doesnt speak Russian.
Polly is from Russia.
h. Bob lives in the capital of Ohio.
Bob lives in Columbus.
i. Not all dogs bark.
Some dogs dont bark.
j. Sally said she liked Polly.
Sally said she didnt like Polly.
k. Polly thinks that Fido is a dog.
Fido is a dog.
6. Which of the following are examples of ?relative intersection?, and which are
examples of ?pure intersection?? (2 points each)
a. lavender crayons
b. huge TVs
c. old temples
d. square rugs
e. fast trains
f. empty bottles
g. long streets
h. sliding doors
i. beautiful cars
Introduction to Linguistics
Semantics II
Form and Meaning
form
the cat sat
on the mat
meaning
Semantics So Far
We distinguish two aspects of linguistic meaning:
sense and reference.
Sense is the mental representation of a meaning.
Reference is the actual entities in the world that a
linguistic expression refers to.
Sense
that cup
Reference
Lexical Semantics Review
Lexical semantics studies the meaning (sense and
reference) of words.
Words have di?erent kinds of reference:
Proper names refer to one specific entity.
Common nouns, adjectives, and intransitive verbs
refer to sets of entities.
Words are related to each other:
Hyponyms identify a subset of the referents of
hypernyms.
Synonyms have the same reference.
Antonyms have contrasting reference.
Semantic Ambiguity
Words can have multiple meanings.
Homonyms are words that sound the same, but have
totally unrelated meanings.
bat
bat
Semantic Ambiguity
Words can have multiple meanings.
Homonyms are words that sound the same, but have
totally unrelated meanings.
form
meaning
bat
bat
Semantic Ambiguity
Words can have multiple meanings.
When a word has multiple, related meanings then the
word is polysemous.
paper
paper
Semantic Ambiguity
Words can have multiple meanings.
When a word has multiple, related meanings then the
word is polysemous.
form
paper
meaning
Compositional
Semantics
Semantics
Compositional semantics is the study of how the
meanings of words combine to form the meanings of
sentences.
form
the cat sat
on the mat
meaning
Are All Meanings Compositional?
The meaning of It is raining today is
compositional.
You could figure out the meaning of the
sentence by looking up the meanings of the
words.
The meaning of It is raining cats and dogs is not
compositional.
It is an idiom: a sentence whose meaning is not
a function of the meanings of its parts.
Compositional vs. Noncompositional
Bob pulled strings to get the job.
Bob pulled strings to unravel the cloth.
Bob kicked the bucket.
Bob kicked the door.
Composition of Adjective and Noun
green
Set of all green things in the world
sweater
Set of all sweaters in the world
Composition of Adjective and Noun
N
Adj
N
green sweater
Set of all green things in the world
Set of all sweaters in the world
Composition of Adjective and Noun
N
Adj
N
green sweater
Set of all things in the world that are both green and a sweater
Intersective Adjectives
The meaning of some adjective + noun combinations is
the intersection of the references of the adjective and
noun.
When the meanings combine in this way, it is called
pure intersection.
An adjective that combines with the meaning of a noun
in this way is called an intersective adjective.
Examples:
Healthy cow
Blue suit
Subsective Adjectives
What about big whale?
Problem: the meaning of big is relative!
whale
Set of all whales in the world
big
Set of all big things in the world
Subsective Adjectives
Big and small are subsective adjectives: their reference
depends on the noun they are modifying.
whale
Set of things
that are small,
for a whale
Set of all whales in the world
small whale
Subsective Adjectives
Big is a subsective adjective: its reference depends on
the noun it is modifying.
The meaning of big whale is not just the intersection of the
reference of big and the reference of whale.
Because the reference of big is relative to the noun.
This is a case of relative intersection.
Other examples:
Tall person
Loud music
Good food
Nonintersective Adjectives
How about alleged criminal?
An alleged criminal might not be in the set of criminals.
So alleged is a nonintersective adjective.
How about fake gun?
A fake gun is not a gun that is fakeits not a gun!
So fake is an anti-intersective adjective.
Composition of Adjectives and Nouns
N
Adj
N
Adjectives and nouns compose in a number of ways:
Pure intersection: The reference of the Adj+N is the intersection
of the reference of the Adj and the reference of the N.
Adjectives that participate in pure intersection are called
intersective adjectives.
Relative intersection: The reference of the Adj+N is a subset of
the reference of the N, defined by the Adj.
Adjectives that participate in relative intersection are called
subsective adjectives.
Nonintersection: The reference of the Adj+N combination is not
necessarily a subset of the reference of the N.
Anti-intersection: The reference of the Adj+N combination is
definitely not a subset of the reference of the N.
Reference of a
Sentence
Reference of a Sentence
The reference of a noun, adjective, or intransitive verb is a set of
entities in the world.
What is the reference of a sentence?
China is the most populous country in the world.
?
Propositions
A sentence conveys an assertion that something about the
world is true.
The sense of a sentence is a proposition: something that can
be true or false in the world.
Sentences have truth values: they are either true or false.
The reference of a sentence is its truth value.
Sentence
China is the most
populous country in the
world.
I am wearing a tie.
Truth Value
true
false
Propositions
A proposition is anything that can have any truth value.
Whether true or false doesnt matter.
What matters is it could be true or could be false.
Truth Value
Expresses
a Proposition?
true
Yes
false
Yes
Green sweater
N/A
No
The cat
N/A
No
Expression
China is the most
populous country in the
world.
I am wearing a tie.
Proposition Test
An expression X expresses a proposition if it makes sense in
any possible world to say: It is true that X.
It is true that
China is the most populous country in the world.
It is true that I am wearing a tie.
It is true that green sweater.
It is true that the cat.
?
?
?
?
Truth Conditions
A proposition has truth conditions: conditions that would
make it true or false in the world.
Expression
Truth Value
The queen of England is sleeping.
?
We dont know whether this proposition is true or false.
But we know its truth conditions: what would the world have to
be like to make this true?
It would have to be the case that: On [insert current date] at
exactly [insert current time] the individual that the Queen of
England refers to is asleep.
How to build a
proposition
Composition of Verb Phrase and Noun Phrase
S
The proposition expressed
by this NP + VP is:
It is true that Bob is a subset
of
the
people
who
are
walking.
NP
VP
Bob walks.
The person Bob himself
Set of all things that are walking in the world
Composition of Verb Phrase and Noun Phrase
Sense
Bob walks.
Reference
A
The person Bob himself
A is a subset of B.
true
B
Set of all things that are walking in the world
Composition of NP and VP
S
NP
VP
Bob walks.
The sense of an NP + VP combination is the
proposition:
The reference of the NP is a subset of the
reference of the VP.
The reference of an NP + VP combination in the
world is:
True or false.
Relationships
Between Propositions
Relationships Between Propositions
There are relationships between propositions.
All dogs bark.
Entails
Sallys dog barks.
One proposition entails another i? in all possible worlds where
the first proposition is true, the second proposition is also true.
Relationships Between Propositions
Does not entail
China is the
most populous
country in the …
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