semantic analysis read j & m chapter 15.. the principle of compositionality there’s an...

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))