Semantics

Question 1

Predicates

Answer 1

semantic category, distinct from syntactic categories like adjective etc.
picks out a set of objects with the property in question: a chair denotes the property of being a chair, happy denotes the property of being happy etc.

Question 2

Referring Expressions

Answer 2

picks out a specific, salient individual (eg, proper names)

argument of the predicate

Question 3

Individual

Answer 3

relates to any object you wish to refer to (yourself, your feet, the chair you’re sitting on)

Question 4

Proposition

Answer 4

combine a subject (referring expression) with a predicate to yield a proposition
roughly, a sentence meaning
can be true or false

Question 5

is/was

Answer 5

syntactic glue

Question 6

Truth Conditions

Answer 6

a proposition can be true or false in a given situation.
recipe for finding out the truth conditions -
‘Barack Obama is very happy’ is true iff the individual denoted by ‘Barack Obama’ is in the set of very happy things at the time in question.

Question 7

iff

Answer 7

if and only if

Question 8

1-Place Predicate

Answer 8

verb takes just one argument (subject)

Question 9

2-Place Predicate

3-Place Predicate

Answer 9

involves 2 individuals

involves 3 individuals

Question 10

4-Place Predicate

Answer 10

syntactically a ditransitive verb but there is a difference between this and a 3-place predicate in semantics
involves 4 individuals:
[SHE] bet [ME] [THIS AMOUNT] [THAT…]

Question 11

Propositional Attitudes

Answer 11

predicates that describe the way that individuals relate to propositions (believe, doubt, hope, consider)
“They believe that the Earth is flat”
- believe takes 2 arguments: an individual (they) and a proposition (the Earth is flat)

Question 12

Recursion

Answer 12

can have attitudes about people’s attitudes

= recursion of propositional attitudes

Question 13

Using Logic to Refer to Individuals

Answer 13

constants: using a single lower-case letter
London is denoted by ‘l’
Obama is denoted by ‘o’

variables: using x, y, z

Question 14

Variable Individuals

Answer 14

meaning changes - denote different variables at different times

Question 15

Using Logic to Refer to Predicates

Answer 15

Dog denotes a set of individuals that the have the property of being dogs.
{x : x is a dog}
property of individuals, denoted by x
{} - refers to set

Question 16

Using Logic to Refer to Propositions

Answer 16

• propositions either denote true or false.
• if a proposition is formed from an individual and a set, the proposition denotes T or F iff the individual is in the set.
• ‘Dog’ could denote a function mapping individuals in the set of dogs to T, and others to F (function dog’)

Fido denotes f
cat denotes cat’
Fido is a cat denotes cat’(f)
(T iff f is in {x: x is a cat}

Question 17

Using Logic to Refer to N-Place Predicates

Answer 17

a 1-place predicate is true or false of an individual; an n-place predicate is true or false of a list of individuals
- denotes sets of individuals

Love denotes { : x loves y} etc.
<> = list

Fido loves Butch denotes love’(f,b)
T iff ∈ {x,y : x loves y}
Fido gave Butch to Obama denotes give’(f,b,o)
T iff ∈ {x,y,z : x gave y to z}

Question 18

Using Logic to Refer to Propositional Connectives

Answer 18

for propositions P and Q

P & Q is true iff P is true and Q is true
P ∨ Q is true if at least one of P and Q is true (P or Q)
~P is true iff P is false (negation of P)
P -> Q is true unless P is true and Q is false (if P then Q)

Question 19

Using Logic to Refer to Propositions as Arguments

Answer 19

for now:

Believe denotes { : x believes that y}

Question 20

A ⊂ B, B ⊃ A

Answer 20

A is a proper subset of B; B is a proper superset of A (every member of A is also a member of B; at least one member of B is also a member of A)

Question 21

A ⊆ B

Answer 21

A is a subset of B (but also allows the possibility that A = B)

Question 22

|A| = 2

Answer 22

A contains 2 members (cardinality of A)

Question 23

|A| > |B|

Answer 23

A contains more members than B

Question 24

x ∈ A

Answer 24

x is a member of the set of A

Question 25

x ∈/ A

Answer 25

x is not a member of the set of A

Question 26

A ∩ B

Answer 26

the union of A and B (what you get if you join both sets together)

Question 27

A - B

Answer 27

the complement of B with respect to A; the set of things which are members of A but not B (what happens if you take A and remove everything that is also in B)

Question 28

Denotation of Quanitifiers

Answer 28

No dog smokes is true iff {x: x is a dog} ∩ {y: y smokes} = Ø (the union of x and y does not exist) Most dogs smoke is true iff |{x: x is a dog} ∩ {y: y smokes}| > |{x: x is a dog} - {y: y smokes}| (the amount of dogs that smoke is greater than the amount of dogs that don't)

Question 29

Every dog smokes (shorthand for universal)

Answer 29

∀ | ∀x [dog'(x)][smoke'(x)]

Question 30

Some dogs smoke (shorthand for existential)

Answer 30

∃ | ∃x [dog'(x)][smoke'(x)]

Question 31

Restriction

Answer 31

roughly, the rest of the NP except for the determiner; the set of individuals we're talking about

Question 32

Scope

Answer 32

the rest of the sentence except for the NP; what we're saying about the individuals identified by the restriction

Question 33

Negation in Logic

Answer 33

Fido doesn't smoke: ~[smoke'(f)] | T iff f ∈/ {x: x smokes}

Question 34

Scope Ambiguity

Answer 34

Unclear what the exact meaning of a sentence is: "Someone owns every dog" - One individual, many dogs. - Every dog is owned by a (possibly different) person.

Question 35

Intersective Modification

Answer 35

the inclusion of an adnominal modifier restricts the denotation of N to a subset: a red dog is a member of the set of red things and the set of dogs: A red dog: ∃x [dog'(x) & red'(x)]

Question 36

Conjunct Elimination

Answer 36

can infer that a red dog is a dog: | A red dog: [dog'(x) & red'(x)] -> dog'(x)

Question 37

First Pass Analysis

Answer 37

every verbal predicate has an extra hidden argument position to accommodate an event argument - so butter is a 3-place predicate, snore is a 2-place predicate... event argument provides a referent for anaphoric 'it'

Question 38

Adverbial Modifiers

Answer 38

Jones buttered the toast with his knife. | ∃e [butter'(j,t,e) & WITH(his-knife,e)]

Question 39

Individuation

Answer 39

Multiple individuals and events can overlap

Question 40

Incorporating Participant Roles

Answer 40

``` AGENT(x,e) = T iff x intentionally initiates e LOCATION(x,e) = T iff x is the location at which e occurs ``` Jones buttered the toast ∃e [butter'(e) & AGENT(j,e) & PATIENT(t,e)] butter'(e) = T iff e is an event of buttering