semantic analysis read j & m chapter 15.. the principle of compositionality there’s an...
TRANSCRIPT
Semantic Analysis
Read J & M Chapter 15.
The Principle of Compositionality•There’s an infinite number of possible sentences and an infinite number of possible meanings.
•But we need to specify the relationship between the two with a finite number of rules.
•What finite classes can we work with:
•Words
•Grammar rules
•So we need to find a way to define the meaning of an entire sentence as a function of the meaning of the words it contains and the rules that are used to put those words together.
Deriving the Meaning of Sentences
John saw Bill.
e Isa(e, Seeing) Agent(e, John) AE(e, Bill)
S
NP VP
PN V NP
John saw PN
Bill
Attaching Semantic Rules to Grammar Rules
John saw Bill. e Isa(e, Seeing) Agent(e, John) AE(e, Bill)
S
NP VP
PN V NP
John saw PN
Bill
A … {f(.sem, .sem …)
PN John {John}
{e Isa(o,Person) Name(o, John)}
NP PN {PN.sem}
Handling the VerbS
NP VP
PN V NP
John saw PN
Bill
S NP VP {VP.sem(NP.sem)}
NP PN {PN.sem}
PN John {John}
PN Bill {Bill}
VP V NP {V.sem(NP.sem)}
V saw {x y e Isa(e, Seeing) Agent(e,y) AE(e,x) }
Common NPs
John has a cat.
S
NP VP
PN V NP
John has DET Nom
a N
cat
e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat)
When Arguments Are Quantified
e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat)
S NP VP {VP.sem(NP.sem)}
NP PN {PN.sem}
NP DET Nom {DET.sem x Nom.sem}
PN John {John}
DET a {}
Nom N {Isa(x N.sem)}
N cat {cat}
VP V NP {V.sem(NP.sem)}
V has {x y e Isa(e, Owning) Agent(e,y) AE(e,x) }
We Get the Wrong Answer
The answer we want:
e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat)
The answer we’re going to get as things stand now:
e Isa(e, Owning) Agent(e, John) AE(e, x Isa(x, Cat))
This isn’t even a valid formula.
Complex TermsA complex term has the following structure:
<Quantifier variable body>
Using one in our example, we get:
e Isa(e, Owning) Agent(e, John) AE(e, < x Isa(x, Cat)>)
Now we add the following rewrite rule for converting complex terms to ordinary FOPC expressions:
P(<Quantifier variable body>) Quantifer variable body Connective P(variable)
In this case:
AE(e, < x Isa(x, Cat)>) x Isa(x, Cat) AE(e, x)
Note: If Quantifier is then Connective is . If , then it’s .
The Revised Grammar
S NP VP {VP.sem(NP.sem)}
NP PN {PN.sem}
NP DET Nom {<DET.sem x Nom.sem(x)>}
PN John {John}
DET a {}
Nom N {z Isa(z, N.sem)}
N cat {cat}
VP V NP {V.sem(NP.sem)}
V has {x y e Isa(e, Owning) Agent(e,y) AE(e,x) }
Do We Yet Have the Right Answer?
The answer we’ve got now:
e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat)
But suppose we want something like:
x Isa (x, Cat) Owner-of(x, John)
In this case, we can view our initial answer as an intermediate representation and use it to form whatever other answer we like by applying inference rules.
Or Suppose We Want a Completely Different Kind of Representation
More on QuantifiersEveryone ate a cookie.
S NP VP {VP.sem(NP.sem)}
NP Pro {Pro.sem}
NP DET Nom {<DET.sem x Nom.sem(x)>}
DET a {}
Nom N {z Isa(z, N.sem)}
Pro everyone {< x person(x)>}
N cookie {cookie}
VP V NP {V.sem(NP.sem)}
V ate {x y e Isa(e, Eating) Agent(e,y) AE(e,x) }
e x x' Isa(e, Eating) (person(x') Agent(e, x')) Isa(x, cookie) AE(e,x)
Different Argument StructuresJohn served Bill.
John served steak.S NP VP {VP.sem(NP.sem)}
NP PN {PN.sem}
NP MassN {MassN.sem}
MassN steak {steak}
PN John {John}
PN Bill {Bill}
VP V NP {V.sem(NP.sem)}
VP V NP1 NP2 {V.sem(NP1.sem)(NP2.sem)
V served {x y e Isa(e, Serving) Agent(e,y) AE(e,x) }
V served {x y e Isa(e, Serving) Agent(e,y) Ben(e,x) }
V served {x y z e Isa(e, Serving) Agent(e,z) AE(e,y)
Ben(e, x)}
Sentences that Aren’t DeclarativeClose the window.
S VP {IMP(VP.sem(DummyYou))}
Do you sell pretzels?
S Aux NP VP {YNQ(VP.sem(NP.sem))}
Who sells pretzels?
S WhPro VP {WHQ(x, VP.sem(x)}}
WHQ(x, e Isa(e, Selling) Agent(e,x) AE(e, pretzels)
Compound Noun Phrases
leather jacket {x Isa(x, jacket) NN(x, leather)}
riding jacket
winter jacket
letter jacket
Nom N {x Isa(x, N.sem)}
Nom N Nom {x Nom.sem(x) NN(x, N.sem)}
N jacket {jacket}
N leather {leather}
Compound NPs, an Alternative
leather jacket {x Isa(x, jacket) madeof(x, leather)}
riding jacket {x Isa(x, jacket) usedfor(x,riding)}
winter jacket
letter jacket
Nom N {x Isa(x, N.sem)}
Nom N Nom {x Nom.sem(x) madeof(x, N.sem)}
Nom N Nom {x Nom.sem(x) usedfor(x, N.sem)}
N jacket {jacket}
N leather {leather}
N winter {winter}
Infinitive Verb Phrases
I told Mary to eat.
S
NP VP
Pro V NP VPto
I told PN infTo VP
Mary to V
eat
e, f Isa(e, telling) Isa(f, eating) Agent(e, Speaker) Ben(e, Mary) AE(e, f) Agent(f, Mary)
Noncompositional Semantics
Coupons are just the tip of the iceberg.
That’s just the tip of Mrs. Ford’s iceberg.
John kicked the bucket.
John would have kicked the bucket.
# The bucket was kicked by John.
She turned up her toes.
# She turned up his toes.
Mary threw in the towel.
Mary thought about throwing in the towel.
# Mary threw in the white towel.
willy nilly pell mell helter skelter
Semantic Grammars
If we know we have a limited semantic representation, then build a grammar that is less general and that maps more directly to the semantic interpretation we want.
Example – Eating Italian Food
An Alternative
InfoRequest I want to go (to) eat (some) FoodType Time
{Retrieve (x, isa(x, Restaurant)
nationality(x, FoodType.sem))}
FoodType Nationality (food) {Nationality.sem}
Retrieve(x, isa(x, Restaurant) nationality(x, Italian))