lect14-semantics.ppt

600.465 - Intro to NLP - J. Eisner 1
Semantics
From Syntax to Meaning!

Programming Language
Interpreter
 What is meaning of 3+5*6?
 First parse it into 3+(5*6)
+
3 *
5 6
E E
F
E
E E
3
F
N
5
N
6
N
*
+

Programming Language
Interpreter
 What is meaning of 3+5*6?
 First parse it into 3+(5*6)
 Now give a meaning to
each node in the tree
(bottom-up)
+
3 *
5 6
E E
F
E
E E
3
F
N
5
N
6
N
*
+
3
5 6
30
33
3
5 6
30
33
add
mult

Interpreting in an Environment
 How about 3+5*x?
 Same thing: the meaning
of x is found from the
environment (it’s 6)
 Analogies in language?
+
3 *
5 x
3
5 6
30
33
E E
F
E
E E
3
F
N
5
N
6
N
*
+
3
5 6
30
33
add
mult

Compiling
 How about 3+5*x?
 Don’t know x at compile time
 “Meaning” at a node
is a piece of code, not a
number
E E
F
E
E E
3
F
N
5
N
x
N
*
+
3
5 x
mult(5,x)
add(3,mult(5,x))
add
mult
5*(x+1)-2 is a different expression
that produces equivalent code
(can be converted to the
previous code by optimization)
Analogies in language?

What Counts as Understanding?
some notions
 Be able to translate (a compiler is a translator …)
 Good definition? Depends on target language.
 English to English? bah humbug!
 English to French? reasonable
 English to Chinese? requires deeper understanding
 English to logic? deepest - the definition we’ll use!
 all humans are mortal = x [human(x)  mortal(x)]
 Assume we have logic-manipulating rules that then tell us
how to act, draw conclusions, answer questions …

some notions
 We understand if we can respond appropriately
 ok for commands, questions (these demand response)
 “Computer, warp speed 5”
 “throw axe at dwarf”
 “put all of my blocks in the red box”
 imperative programming languages
 database queries and other questions
 We understand a statement if we can determine
its truth
 If you can easily determine whether it’s true, why did
anyone bother telling it to you?
 Comparable notion for understanding NP is to identify
what it refers to. Useful, but what if it’s out of sight?

some notions
 We understand statement if we know how to
determine its truth (in principle!)
 Compile it into a procedure for checking truth against the world
 “All owls in outer space are bachelors”
for every object x
if x is a owl
if location(x)  outerspace
if x is not a bachelor
return false
return true
 What if you don’t have an flying robot? (Write the code anyway)
 How do you identify owls and bachelors? (Assume library calls)
 What if space is infinite, so the procedure doesn’t halt?
Same problem for “All prime integers …” (You won’t actually run it)
meaning

some notions
 We understand statement if we know how one
could (in principle) determine its truth
 Compile it into a procedure that checks truth against the world
 Better: Compile it into a mathematical formula
 x owl(x) ^ outerspace(x)  bachelor(x)
 Now you don’t have to worry about running it
 Either true or false in the world: a mathematical question!
 Statement claims that the world is such that this statement is true.
 Auden (1956): “A sentence uttered makes a world appear
Where all things happen as it says they do.”
 But does this help? Can you check math against the real world?
 What are the x’s that x ranges over? Which ones make owl(x) true?
 Model the world by an infinite collection of facts and entities
 Wittgenstein (1921): “The world is all that is the case. The world is
the totality of facts, not of things.”

some notions
 We understand statement if we know how one
could (in principle) determine its truth
 Compile it into a procedure that checks truth against the world
 Better: Compile it into a mathematical formula
 x owl(x) ^ outerspace(x)  bachelor(x)
 Equivalently, be able to derive all logical consequences
 What else is true in every world where this statement is true?
 Necessary conditions – let us draw other conclusions from sentence
 And what is false in every world where this sentence is false
 Sufficient conditions – let us conclude the sentence from other facts
 “Recognizing textual entailment” is an NLP task ( competitions!)
 John ate pizza. Can you conclude that John opened his mouth?
 Knowing consequences lets you answer questions (in principle):
 Easy: John ate pizza. What was eaten by John?
 Hard: White’s first move is P-Q4. Can Black checkmate?

Lecture Plan
 Today:
 First, intro to -calculus and logical notation
 Let’s look at some sentences and phrases
 What logical representations would be reasonable?
 Tomorrow:
 How can we build those representations?
 Another course (AI):
 How can we reason with those representations?

Logic: Some Preliminaries
Three major kinds of objects
1. Booleans
 Roughly, the semantic values of sentences
2. Entities
 Values of NPs, e.g., objects like this slide
 Maybe also other types of entities, like times
3. Functions of various types
 A function returning a boolean is called a
“predicate” – e.g., frog(x), green(x)
 Functions might return other functions!
 Function might take other functions as
arguments!

Logic: Lambda Terms
 Lambda terms:
 A way of writing “anonymous functions”
 No function header or function name
 But defines the key thing: behavior of the function
 Just as we can talk about 3 without naming it “x”
 Let square = p p*p
 Equivalent to int square(p) { return p*p; }
 But we can talk about p p*p without naming it
 Format of a lambda term:  variable expression

Logic: Lambda Terms
 Lambda terms:
 Let square = p p*p
 Then square(3) = (p p*p)(3) = 3*3
 Note: square(x) isn’t a function! It’s just the value x*x.
 But x square(x) = x x*x = p p*p = square
(proving that these functions are equal – and indeed they are,
as they act the same on all arguments: what is (x square(x))(y)? )
 Let even = p (p mod 2 == 0) a predicate: returns true/false
 even(x) is true if x is even
 How about even(square(x))?
 x even(square(x)) is true of numbers with even squares
 Just apply rules to get x (even(x*x)) = x (x*x mod 2 == 0)
 This happens to denote the same predicate as even does

Lambda calculus vs. AP calculus
Blondie, Oct. 3, 2013

Logic: Multiple Arguments
 Lambda terms denote functions of 1 argument
 But how about functions like multiplication?
 We can fake multiple arguments [“currying”]
 Define times as x y (x*y)
 Claim that times(5)(6) is 30
 times(5) = (x y x*y) (5) = y 5*y
 If this function weren’t anonymous, what would we call
it?
 times(5)(6) = (y 5*y)(6) = 5*6 = 30

Logic: Multiple Arguments
 All lambda terms have one argument
 But we can fake multiple arguments ...
 We’ll write “times(5,6)” as syntactic sugar for
times(5)(6) or perhaps times(6)(5)
 times(5,6) = times(5)(6)
= (x y x*y) (5)(6) = (y 5*y)(6) = 5*6 = 30
 So we can always get away with 1-arg functions ...
 ... which might return a function to take the next
argument. Whoa.
 Remember: square can be written as x square(x)
 And now times can be written as x y times(x,y)
Notation varies; doesn’t
matter as long as you’re
consistent

Grounding out
 So what does times actually mean???
 times was defined in terms of * .
 But does * mean multiplication?
 If * was defined as another lambda term, then
times(5,6) = *(5,6) = (blah blah blah)(5)(6)
but where do we stop?
 Similarly, what does bachelor mean?
 Maybe we defined
bachelor = x (male(x) and not married(x))
but how is male defined?
 Same problem as in programming languages
and dictionaries.

Grounding out
 As in programming languages: something has
to be built in.
 Don’t keep doing substitutions forever!
 Eventually we have to “ground out”
in a primitive term
 Primitive terms are bound to object code
 Maybe *(5,6) is handled by the hardware
 Maybe male(John) is too [visual cortex]
 What code is executed by loves(John, Mary)?

Logic: Interesting Constants
 Thus, have “constants” that name some of the
entities and functions (e.g., *):
 JoeBiden - an entity
 red – a predicate on entities
 holds of just the red entities: red(x) is true if x is red!
 loves – a predicate on 2 entities
 loves(JoeBiden, JillBiden)
 Question: What does loves(JillBiden) denote?
 Can define other named objects from the constants
 Can define a meaning for each English word from
the named objects
 Meaning of each English word is defined in terms of
the constants [maybe indirectly]

Logic:
Connectives & Quantifiers
 p OR q (= p  q) “p or q”
 p AND q (= p  q = p,q) “p and q”
 NOT p (= p = ~p) “not p”
 p  q “if p then q”
 x “for all x”
 x “there exists x”
 “all pigs are big”
 x pig(x)  big(x) “for all x, if pig(x), then big(x)”
 “some pig is big”
 x pig(x) AND big(x)
there exists some x such that pig(x) AND big(x)
 “most pigs are big”
??
 “all big things are pigs” (asymmetric!)
= “some big things are pigs” (symmetric!)

Logic: Interesting Constants
 most – a predicate on 2 predicates on
entities
 most(pig, big) = “most pigs are big”
 Equivalently, most(x pig(x), x big(x))
 returns true if most of the things satisfying the
first predicate also satisfy the second predicate
 similarly for other quantifiers
 all(pig,big) (equivalent to x pig(x)  big(x))
 exists(pig,big) (equivalent to x pig(x) AND big(x))
 can even build complex quantifiers from English phrases:
 “between 12 and 75”; “a majority of”; “all but the smallest 2”

Model Theory
 Equivalent notions:
 A “world” (semantics)
 A “outcome” (probability)
 A “model” (math)
 All of these specify “everything”
 A collection of consistent facts
 Maybe infinite
 Maybe derived from a smaller set by reasoning
 Remember: The world is made of facts, not things!
 Or, a collection of consistent values for random vars
 All derived as functions of the same outcome

600.465 – Intro to NLP – J. Eisner 24
Random Variables:
What is “variable” in “p(variable=value)”?
• p(x1=h) * p(x2=o | x1=h) * …
• Outcome is a sequence of letters
• x2 is the second letter in the sequence
• p(number of heads=2) or just p(H=2) or p(2)
• Outcome is a sequence of 3 coin flips
• H is the number of heads
• p(weather’s clear=true) or just p(weather’s clear)
• Outcome is a race
• weather’s clear is true or false
Answer: variable is really a function of Outcome

A reasonable representation?
 Gilly swallowed a goldfish
 First attempt: swallowed(Gilly, goldfish)
 Returns true or false. Analogous to
 prime(17)
 equal(4,2+2)
 loves(JoeBiden, JillBiden)
 swallowed(Gilly, Jilly)
 … or is it analogous?

A reasonable representation?
 But we’re not paying attention to a!
 goldfish isn’t the name of a unique object the
way Gilly is
 In particular, don’t want
Gilly swallowed a goldfish and Milly
swallowed a goldfish
to translate as
swallowed(Gilly, goldfish) AND swallowed(Milly, goldfish)
since probably not the same goldfish …

Use a Quantifier
 Better: g goldfish(g) AND swallowed(Gilly, g)
 Or using one of our quantifier predicates:
 exists(g goldfish(g), g swallowed(Gilly,g))
 Equivalently: exists(goldfish, swallowed(Gilly))
 “In the set of goldfish there exists one swallowed by Gilly”
 Here goldfish is a predicate on entities
 This is the same semantic type as red
 But goldfish is noun and red is adjective .. #@!?

Tense
 Previous attempt: exists(goldfish, g swallowed(Gilly,g))
 Improve to use tense:
 Instead of the 2-arg predicate swallowed(Gilly,g)
try a 3-arg version swallow(t,Gilly,g) where t is a time
 Now we can write:
t past(t) AND exists(goldfish, g swallow(t,Gilly,g))
 “There was some time in the past such that a goldfish was among
the objects swallowed by Gilly at that time”

(Simplify Notation)
 Previous attempt: exists(goldfish, swallowed(Gilly))
 Improve to use tense:
 Instead of the 2-arg predicate swallowed(Gilly,g)
try a 3-arg version swallow(t,Gilly,g)
 Now we can write:
t past(t) AND exists(goldfish, swallow(t,Gilly))
 “There was some time in the past such that a goldfish was among
the objects swallowed by Gilly at that time”

Event Properties
 Previous: t past(t) AND exists(goldfish, swallow(t,Gilly))
 Why stop at time? An event has other properties:
 [Gilly] swallowed [a goldfish] [on a dare]
[in a telephone booth] [with 30 other
freshmen] [after many bottles of vodka had
been consumed].
 Specifies who what why when …
 Replace time variable t with an event variable e
 e past(e), act(e,swallowing), swallower(e,Gilly),
exists(goldfish, swallowee(e)), exists(booth, location(e)), …
 As with probability notation, a comma represents AND
 Could define past as e t before(t,now), ended-at(e,t)
“Davidsonian event variable”
(after Donald Davidson, 1980)

Quantifier Order
 Gilly swallowed a goldfish in a booth
 Gilly swallowed a goldfish in every booth
exists(goldfish, swallowee(e)), all(booth, location(e)), …
 Does this mean what we’d expect??
g goldfish(g), swallowee(e,g) b booth(b)location(e,b)
says that there’s only one event
with a single goldfish getting swallowed
that took place in a lot of booths ...

Quantifier Order
 Groucho Marx celebrates quantifier order ambiguity:
 In this country a woman gives birth every 15 min.
Our job is to find that woman and stop her.
 woman (15min gives-birth-during(15min, woman))
 15min (woman gives-birth-during(15min, woman))
 Surprisingly, both are possible in natural language!
 Which is the joke meaning (where it’s always the same woman)
and why?

Quantifier Order
exists(goldfish, swallowee(e)), all(booth, location(e)), …
g goldfish(g), swallowee(e,g) b booth(b)location(e,b)
 Does this mean what we’d expect??
 It’s e b which means same event for every booth
 Probably false unless Gilly can be in every booth
during her swallowing of a single goldfish

exists(goldfish, swallowee(e)), all(booth, b location(e,b))
Quantifier Order
 Other reading (b e) involves quantifier raising:
 all(booth, b [e past(e), act(e,swallowing), swallower
(e,Gilly), exists(goldfish, swallowee(e)), location(e,b)])
 “for all booths b, there was such an event in b”

Intensional Arguments
 Willy wants a unicorn
 e act(e,wanting), wanter(e,Willy), exists(unicorn, u wantee(e,u))
 “there is a particular unicorn u that Willy wants”
 In this reading, the wantee is an individual entity
 e act(e,wanting), wanter(e,Willy), wantee(e, u unicorn(u))
 “Willy wants any entity u that satisfies the unicorn predicate”
 In this reading, the wantee is a type of entity
 Sentence doesn’t claim that such an entity exists
 Willy wants Lilly to get married
 e present(e), act(e,wanting), wanter(e,Willy),
wantee(e, e’ [act(e’,marriage), marrier(e’,Lilly)])
 “Willy wants any event e’ in which Lilly gets married”
 Here the wantee is a type of event
 Sentence doesn’t claim that such an event exists
 Intensional verbs besides want: hope, doubt, believe,…

Intensional Arguments
 Willy wants a unicorn
 e act(e,wanting), wanter(e,Willy), wantee(e, u unicorn(u))
 “Willy wants anything that satisfies the unicorn predicate”
 here the wantee is a type of entity
 Problem:
 g unicorn(g) is defined by the actual set of unicorns (“extension”)
 But this set is empty: g unicorn(g) = g FALSE = g pegasus(g)
 Then wants a unicorn = wants a pegasus. Oops!
 So really the wantee should be criteria for unicornness (“intension”)
 Traditional solution involves “possible-world semantics”
 Can imagine other worlds where set of unicorns  set of pegasi

Possible Worlds
 Traditional solution involves “possible-world semantics”
 Wittgenstein (1921): “The world is all that is the case. The
world is the totality of facts, not of things.”
 Can imagine other worlds where set of unicorns  set of pegasi
 Most facts can vary according to which world w you’re in:
 loves(Joe, Jill)
 most(x pig(x), x big(x))
most( pig , big )
 wants(Willy, unicorn)
wants(Willy, u unicorn(u))
loves(w, Joe, Jill)
most(w, x pig(w, x), x big(w, x))
most(w, pig(w) , big(w) )
wants(w, Willy, unicorn)
wants(w, Willy, w’ u unicorn(w’,u))
“intension” of unicorn, not tied to current world w
Function checks in any world w’ whether something is a unicorn
These criteria are the same in every world:
unicorn  w’ u (has_horn(w’,u), horselike(w’,u), magical(w’,u), …)

Possible Worlds: More uses
 Modals (woulda coulda shoulda)
 You must pay the rent
 In all possible worlds that are “like” this world,
and in which you fulfill your obligations: you do pay the rent
 You may pay the rent
 In some possible world that is “like” this world,
and in which you fulfill your obligations: you do pay the rent
 You must have paid the rent
 In all possible worlds that are “like” this world, and which
are consistent with my observations: you paid the rent
 You can pay the rent
 In some possible world that is “like” this world, and
in which you have no additional powers: you do pay the rent
deontic modal
deontic modal
(how would you
express epistemic 
in English?)
bouletic modal
… and more …
(varies by language, but always quantifies over some set of “accessible” worlds)
epistemic modal

and in which you fulfill your obligations: you pay the rent
 Counterfactuals
 If you hadn’t, you’d be homeless
except that you didn’t pay the rent: you are now homeless
 What are the “worlds that are ‘like’ this world”? (“accessible” worlds)
 You don’t pay rent, but otherwise change “as little as possible.” (Same
apartment, same eviction laws, no miracles to save you from the gutter, …)
 But rather slippery how to figure out what those “minimum changes” are!
 Lets’s watch instant replays on the Subjunc-TV (Hofstadter, 1979):
 “Here’s what would’ve happened … if Palindromi hadn’t stepped out of bounds”
 “… if only it hadn’t been raining” “… if only they’d been playing against Chicago”
 “… if only they’d been playing baseball” “… if only 13 weren’t prime”
deontic modal

and in which you fulfill your obligations, you pay the rent
 Counterfactuals
 If you hadn’t, you’d be homeless
except that you didn’t pay the rent, you are now homeless
deontic modal
Traditional view is that some worlds are “accessible” and others aren’t.
But reasoning about what would tend to happen if you didn’t pay the rent
seems to require probabilistic reasoning.
So maybe you have something like a family of conditional probability
distributions… such a model can define p(y | x) even when p(x)=0.
You use it as p(world has property b | world has property a).
You learn it from observing the real world and reading statements in books.
probably
^
most
But is this 0/0?
p(homeless | didn’t pay rent) > 0.5

Control
 Willy wants Lilly to get married
 e present(e), act(e,wanting), wanter(e,Willy),
wantee(e, f [act(f,marriage), marrier(f,Lilly)])
 Willy wants to get married
 Same as Willy wants Willy to get married
 Just as easy to represent as Willy wants Lilly …
 The only trick is to construct the representation from the
syntax. The empty subject position of “to get married”
is said to be controlled by the subject of “wants.”

Nouns and Their Modifiers
 Nouns and adjectives both restrict an entity’s properties:
 expert: g expert(g)
 big fat expert: g big(g), fat(g), expert(g)
 Baltimore expert (i.e., expert from Baltimore):
g Related(Baltimore, g), expert(g)
 But they sometimes first combine into compound concepts:
 Adj+N: bogus expert (i.e., someone who has bogus_expertise):
g (bogus(expert))(g) [not g bogus(g), expert(g) since they’re not an expert!]
 N+N: Baltimore expert (i.e., expert on Baltimore – different stress):
g (Modified-by(Baltimore, expert))(g)
 (N+V)+ending: dog catcher:
g e act(e,catching),catcher(e,g),exists(dog,catchee(e))
 garbage collection:
e (act(e, collecting), exists(garbage,collectee(e)))
 If we didn’t make a compound concept first, things would go awry
law expert and dog catcher
= g Related(law,g), expert(g), Related(dog, g), catcher(g) **wrong**
= dog expert and law catcher

We can argue about the details of the compound
representations, e.g., how much of the semantics is explicit in
the lambda-term, how much is in the semantics of individual
words like bogus, and how much is shoved under the carpet into
primitives like Modified-by, which are assumed to piece together
a reasonable meaning using world knowledge and context.
or g (Modified-by(bogus,expert))(g)?
or g (Baltimore(expert))(g)?
or g (expert(Baltimore))(g)?
 g (bogus(expert))(g) … bogus can construct a new concept
g (Modified-by(Baltimore, expert))(g)

 the goldfish that Gilly swallowed
 every goldfish that Gilly swallowed
 three goldfish that Gilly swallowed
Or for real: g [goldfish(g), e [past(e), act(e,swallowing),
swallower(e,Gilly), swallowee(e,g) ]]
g [goldfish(g), swallowed(Gilly, g)]
 three swallowed-by-Gilly goldfish
like an adjective!

Adverbs
 Lili passionately wants Billy
 Wrong?: passionately(want(Lili,Billy)) = passionately(true)
 Better: (passionately(want))(Lili,Billy)
 Best: e present(e), act(e,wanting), wanter(e,Lili),
wantee(e, Billy), manner(e, passionate)
 Lili often stalks Billy
 (often(stalk))(Lili,Billy)
 many(day, d e present(e), act(e,stalking), stalker(e,Lili),
stalkee(e, Billy), during(e,d))
 Lili obviously likes Billy
 (obviously(like))(Lili,Billy) – one reading
 obvious(like(Lili, Billy)) – another reading

Speech Acts
 What is the meaning of a full sentence?
 Depends on the punctuation mark at the end. 
 Billy likes Lili.  assert(like(B,L))
 Billy likes Lili?  ask(like(B,L))
 or more formally, “Does Billy like Lili?”
 Billy, like Lili!  command(like(B,L))
 or more accurately, “Let Billy like Lili!”
 Let’s try to do this a little more precisely, using
event variables.
 (We’ll leave out the world variables.)

Speech Acts
 What did Gilly swallow?
 ask(x e past(e), act(e,swallowing),
swallower(e,Gilly), swallowee(e,x))
 Argument is identical to the modifier “that Gilly swallowed”
 Is there any common syntax?
 Eat your fish!
 command(f act(f,eating), eater(f,Hearer), eatee(…))
 I ate my fish.
 assert(e past(e), act(e,eating), eater(f,Speaker),
eatee(…))

 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

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
a a
y x e act(e,loving),
lover(e,x), lovee(e,y)
L
y x e act(e,wanting),
wanter(e,x), wantee(e,y)
v x e present(e),v(x)(e)
every nation
s assert(s)
assert(every(nation, x e present(e),
act(e,wanting), wanter(e,x),
wantee(e, e’ act(e’,loving),
lover(e’,J), lovee(e’,L))))

 Add a “sem” attribute 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
 TAG version:
NP
V
loves
VP
S
NP
x
y
loves(x,y)
NP
the bucket
V
kicked
VP
S
NP
x
died(x)
 Template filling: S[sem=showflights(x,y)] 
I want a flight from NP[sem=x] to NP[sem=y]

 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 Joe loves Jill has sem=loves(Jill)(Joe)
 In this style 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, just apply function to argument!
 (version on homework will be a little less pure)

NP
Jill
VPfin
Sfin
ROOT
Punc
.
NP
Joe
Vpres
loves
s assert(s)
loves =
x y loves(x,y)
L
J
y loves(L,y)
loves(L,J)
assert(loves(L,J))
Question: Really the root meaning should be assert(loves(wcurr,L,J))
Then what is the meaning of loves?
And what is the meaning of period?
x y w loves(w,x,y)
s assert(s(wcurr))

AdjP
tall
VPfin
Sfin
ROOT
Punc
.
NP
John
Vpres
is
s assert(s)
adj subj adj(subj)
J
subj tall(subj)
tall(J)
assert(tall(J))
So what do we want here?
tall
= x tall(x)
(adj subj adj(subj))(x tall(x))
= subj (x tall(x))(subj)
= subj tall(subj)
The identity function!
But let’s write it as …

NP
Jill
VPfin
Sfin
ROOT
Punc
.
NP
Joe
Vpres
loves
loves =
x y loves(x,y)
L
J
y loves(L,y)
loves(L,J)
e present(e), act(e,loving),
lover(e,J), lovee(e,L)
x y e present(e),
act(e,loving),
lover(e,y), lovee(e,x)
y e present(e),
act(e,loving),
lover(e,y), lovee(e,L)

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
Now let’s try a more
complex example, and
really handle tense.
Treat –s like
yet another
auxiliary
verb

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
e act(e,loving), lover(e,J), lovee(e,L)
the meaning that we
want here: how can
we arrange to get it?

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
what function should
apply to J to yield the
desired blue result?
(this is like division!)

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
x e act(e,loving),
lover(e,x), lovee(e,L)
J

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
a a
We’ll say that
“to” is just a bit of syntax that
changes a VPstem to a VPinf
with the same meaning.

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
a a
L

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
a a
L
x e act(e,wanting), wanter(e,x),
lover(e’,J), lovee(e’,L))
by analogy

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
a a
L
by analogy
Note applying “want” automatically
renamed the loving event (from e to e’),
to avoid conflict with the wanting event
(also originally named e).
Variable names are arbitrary anyway.

Want to change
e to e present(e),
But blocked by x which is
waiting for the subject NP.
How would you modify
second object on a
stack (x,e,act…)?
Pop x, re-push x
v(x)(e)
x e
present(e),
NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
act(e,wanting),
wanter(e,x),
NP
Joe
v
Your account v is overdrawn, so your
rental application is rejected..
• Deposit some cash x to get v(x)
• Now show you’ve got the money:
e present(e), v(x)(e)
• Now you can withdraw x again:
x e present(e), v(x)(e)
x e present(e),
“pop pop”
“push push”

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
x e present(e), act(e,wanting),
wanter(e,x), wantee(e, e’
act(e’,loving),
NP
Joe
every(nation, x e present(e),
lover(e’,J), lovee(e’,L)))
p every(nation, p)

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
x e present(e), act(e,wanting),
wanter(e,x), wantee(e, e’
act(e’,loving),
NP
Joe
p every(nation, p)
n p
every(n, p)
nation

NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
NP
Joe
s assert(s)

In Summary: From the Words
NP
Jill
Vstem
love
VPstem
VPinf
T
to
Sinf
NP
Joe
VPstem
Vstem
want
VPfin
T
-s
Sfin
NP
N
nation
Det
Every
ROOT
Punc
.
J
a a
L
v x e present(e),v(x)(e)
every nation
s assert(s)
assert(every(nation, x e present(e),
lover(e’,J), lovee(e’,L))))
The semantics that we
deduced for every, -s,
want, to, etc., will work
fine in other sentences
too! (Is one sentence really
enough to figure out a word’s
meaning? Well, some words
are ambiguous …)

Other Fun Semantic Stuff:
A Few Much-Studied Miscellany
 Temporal logic
 Gilly had swallowed eight goldfish
before Milly reached the bowl
 Billy said Jilly was pregnant
 Billy said, “Jilly is pregnant.”
 Generics
 Typhoons arise in the Pacific
 Children must be carried
 Presuppositions
 The king of France is bald.
 Have you stopped beating your wife?
 Pronoun-Quantifier Interaction (“bound anaphora”)
 Every farmer who owns a donkey beats it.
 If you have a dime, put it in the meter.
 The woman who every Englishman loves is his mother.
 I love my mother and so does Billy.

Pragmatics
 I saw this sign in Seattle.
 I’d been in violation of it for
approximately my entire adult life.
 But only technically.
 Pragmatics is the study how we look past
the literal meaning.
 What conclusions should I actually draw
from the fact that you said something?
 Should I use Bayes’ Theorem?
 What conclusions were you trying to get me
to draw?

Uncertainty about the World
Outcome space
Each outcome = a world
Low-prob set of worlds in which
owl(JoeBiden)=true
All (male)
owls are
bachelors
Oh! we must be in a
world where all
owls are bachelors,
or at least a world
where he’d say such
a thing. In my new probability
distribution over
worlds, is Biden more
likely to be a
bachelor?
Only slightly more likely,
since I didn’t think he
was an owl before … nor
tried to act like one. The
new information doesn’t
seem to change that.

Uncertainty about the World
Outcome space
Each outcome = a world
Low-prob set of worlds in which
owl(JoeBiden)=true
All (male)
owls are
bachelors
Oh! we must be in a
world where all
owls are bachelors
…
By the way, what do you
think of the First Lady’s
college course?
… and where
there’s a First
Lady.
Given everything else
I believe about the
world, this means that
almost certainly it is
a world where Biden
is not a bachelor …
… and
therefore not
an owl.

lect14-semantics.ppt

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