Semantics

Semantics

cCS 224n / Lx 237Tuesday, May 11

2004

With slides borrowed from Jason Eisner

Objects

Three Kinds: Boolean – semantic value of sentences Entities

Objects, NPs Maybe space / time specifications

Functions Predicates – function returning a boolean Functions might return other functions Functions might take other functions as

arguments.

Nouns and their modifiers expert

g expert(g) big fat expert

g big(g) fat(g) expert(g) But: bogus expert

Wrong: g bogus(g) expert(g) Right: g (bogus(expert))(g) … bogus maps to new concept

Baltimore expert (white-collar expert, TV expert …) g Related(Baltimore, g) expert(g) Or with different intonation: g (Modified-by(Baltimore, expert))(g) Can’t use Related for that case: law expert and dog catcher

= g Related(law,g) expert(g) Related(dog, g) catcher(g) = dog expert and law catcher

We’ve discussed what semantic representations should look like.

But how do we get them from sentences???

First - parse to get a syntax tree. Second - look up the semantics for each word. Third - build the semantics for each constituent

Work from the bottom up The syntax tree is a “recipe” for how to do it

Compositional Semantics

Add a “sem” feature to each context-free rule S NP loves NP S[sem=loves(x,y)] NP[sem=x] loves NP[sem=y] Meaning of S depends on meaning of NPs

Compositional Semantics

NPVloves

VP

S

NPx

y

loves(x,y)

NP the bucket

Vkicked

VP

S

NPx

died(x)

Instead of S NP loves NP S[sem=loves(x,y)] NP[sem=x] loves NP[sem=y]

might want general rules like S NP VP: V[sem=loves] loves VP[sem=v(obj)] V[sem=v] NP[sem=obj] S[sem=vp(subj)] NP[sem=subj] VP[sem=vp]

Now George loves Laura has sem=loves(Laura)(George) In this manner we’ll sketch a version where

Still compute semantics bottom-up Grammar is in Chomsky Normal Form So each node has 2 children: 1 function & 1 argument To get its semantics, apply function to argument!

Compositional Semantics

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)the meaning that we want here: how can we arrange to get it?

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)

Gwhat function shouldapply to G to yield the desired blue result? (this is like division!)

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)

x loves(x,L)G

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)

x loves(x,L)G

a ax loves(x,L)

We’ll say that“to” is just a bit of syntax that

changes a VPstem to a VPinf with the same meaning.

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)

x loves(x,L)G

a ax loves(x,L)

y x loves(x,y)

L

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)

x loves(x,L)G

a a

y x loves(x,y)

L

x loves(x,L)

x wants(x, loves(G,L))by analogy

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

loves(G,L)

x loves(x,L)G

a a

yx loves(x,y)

L

x loves(x,L)

x wants(x, loves(G,L))

y x wants(x,y)

by analogy

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

x wants(x, loves(G,L))

x present(wants(x, loves(G,L)))

NPGeorge

v x present(v(x)

)

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

x present(wants(x, loves(G,L)))

NPGeorge

present(wants(every(nation), loves(G,L))))

every(nation)

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

present(x wants(x, loves(G,L)))

NPGeorge

present(wants(every(nation), loves(G,L))))

every(nation)

n every(n) nation

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

NPGeorge

present(wants(every(nation), loves(G,L))))

s assert(s)

In Summary: From the Words

NPLaura

Vstem

love

VPstem

VPinf

Tto

Sinf

NPGeorge

VPstem

Vstem

want

VPfin

T-s

Sfin

NP

Nnation

DetEvery

START

Punc.

G

a a

y x loves(x,y) L

y x wants(x,y)

v x present(v(x))

every nation

s assert(s)

assert(present(wants(every(nation), loves(G,L))))

So now what?

Now that we have the semantic meaning, what do we do with it? Huge literature on logical reasoning, and

knowledge learning. Reasoning versus Inference

“John ate a Pizza” Q:What was eaten by John? A: pizza

“John ordered a pizza, but it came with anchovies. John then yelled at the waiter and stormed out.”

Q: What was eaten by John? A: nothing

Problem 1a

Write grammar rules complete with semantic translations that could be added

to thegrammar fragment, which will parse the

above sentence and generate a semantic representation

using the own predicate.