Formal and Computational Semantics
Lecture 2
Ambiguity and underspecification
Robin Cooper
University of Gothenburg
14th Dec, 2010
Outline
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Outline
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Lexical ambiguity
I
Kim ran to the bank
4 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Lexical ambiguity
I
Kim ran to the bank
I
Kim ran to the riverbank
4 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Lexical ambiguity
I
Kim ran to the bank
I
Kim ran to the riverbank
I
Kim ran to the bank to get her money
4 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Lexical ambiguity
I
Kim ran to the bank
I
Kim ran to the riverbank
I
Kim ran to the bank to get her money
I
Kim ran to the bank before it closed
4 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Syntactic ambiguity without semantic ambiguity
I
NP → NP and NP
I
Kim and Lee and Chris arrived early
5 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
S
VP
NP
arrived early
NP
NP
Kim
and
and
NP
NP
Chris
Lee
6 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
S
NP
VP
arrived early
NP
Kim
and
NP
NP
Lee
and
NP
Chris
7 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Syntactic ambiguity with semantic ambiguity
I
NP → NP or NP
I
Kim and Lee or Chris arrived early
8 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
S
VP
NP
arrived early
NP
NP
Kim
and
or
NP
NP
Chris
Lee
True if only Chris arrived early
9 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
S
VP
NP
arrived early
NP
Kim
and
NP
NP
or
Lee
NP
Chris
False if only Chris arrived early
10 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Anaphora
I
Kim saw Lee and she smiled at him
11 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Anaphora
I
Kim saw Lee and she smiled at him
I
Kimi saw Leej and shei smiled at himj
11 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Anaphora
I
Kim saw Lee and she smiled at him
I
Kimi saw Leej and shei smiled at himj
I
Kimi saw Leej and shej smiled at himi
11 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quantifier scope ambiguity
I
a company representative interviews every new employee
12 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quantifier scope ambiguity
I
a company representative interviews every new employee
I
∃x[company representative(x) ∧ ∀y [new employee(y ) →
interview(x, y )]]
12 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quantifier scope ambiguity
I
a company representative interviews every new employee
I
∃x[company representative(x) ∧ ∀y [new employee(y ) →
interview(x, y )]]
I
∀y [new employee(y ) →
∃x[company representative(x) ∧ interview(x, y )]]
12 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quantifier scope ambiguity
I
a company representative interviews every new employee
I
∃x[company representative(x) ∧ ∀y [new employee(y ) →
interview(x, y )]]
I
∀y [new employee(y ) →
∃x[company representative(x) ∧ interview(x, y )]]
I
some suprising examples:
12 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quantifier scope ambiguity
I
a company representative interviews every new employee
I
∃x[company representative(x) ∧ ∀y [new employee(y ) →
interview(x, y )]]
I
∀y [new employee(y ) →
∃x[company representative(x) ∧ interview(x, y )]]
I
some suprising examples:
I
two boys ate two pizzas
12 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quantifier scope ambiguity
I
a company representative interviews every new employee
I
∃x[company representative(x) ∧ ∀y [new employee(y ) →
interview(x, y )]]
I
∀y [new employee(y ) →
∃x[company representative(x) ∧ interview(x, y )]]
I
some suprising examples:
I
I
two boys ate two pizzas
most students read most books
12 / 32
Outline
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
How many readings?
I
In most democratic countries most politicians can fool most
of the people on almost every issue most of the time. (Hobbs,
1983)
I
120 readings
I
. . . but no politician can fool all of the people all of the time
14 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
How do you disambiguate?
I
not practical to ask users to disambiguate
15 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
How do you disambiguate?
I
not practical to ask users to disambiguate
I
first you have to explain to the user what the ambiguity is. . .
15 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
How do you disambiguate?
I
not practical to ask users to disambiguate
I
first you have to explain to the user what the ambiguity is. . .
I
. . . and then it is not clear that you can find enough
unambiguous natural language sentences to express the
different readings
15 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
How do you disambiguate?
I
not practical to ask users to disambiguate
I
first you have to explain to the user what the ambiguity is. . .
I
. . . and then it is not clear that you can find enough
unambiguous natural language sentences to express the
different readings
I
so the user has to know logic!
15 / 32
Outline
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Packing several meanings in a single representation
I
finding all the readings is computationally inefficient
I
. . . and then you have to figure out which of the meanings was
meant
I
Underspecified meaning representations allow you to compute
one single representation from which you can generate
specified meanings if necessary
17 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Cooper storage
Cooper (1983)
18 / 32
S
NP
a representative
VP
interviews
NP
every employee
S
NP
a representative
VP
interviews
NP
λP[P(x0 )]
hλP[∀x[employee(x) → P(x)]], 0i
every employee
S
NP
a representative
VP
λx[interview (x, x0 )]
hλP[∀x[employee(x) → P(x)]], 0i
interviews
NP
λP[P(x0 )]
hλP[∀x[employee(x) → P(x)]], 0i
every employee
S
VP
NP
λP[P(x1 )]
λx[interview (x, x0 )]
hλP[∃x[rep(x) ∧ P(x)]], 1i hλP[∀x[employee(x) → P(x)]], 0i
a representative
interviews
NP
λP[P(x0 )]
hλP[∀x[employee(x) → P(x)]], 0i
every employee
S
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
NP
VP
λP[P(x1 )]
λx[interview (x, x0 )]
hλP[∃x[rep(x) ∧ P(x)]], 1i hλP[∀x[employee(x) → P(x)]], 0i
a representative
interviews
NP
λP[P(x0 )]
hλP[∀x[employee(x) → P(x)]], 0i
every employee
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
20 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∃x[rep(x) ∧ P(x)]](λx1 [interview(x1 , x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
20 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∃x[rep(x) ∧ P(x)]](λx1 [interview(x1 , x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
I
∃x[rep(x) ∧ interview(x, x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
20 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∃x[rep(x) ∧ P(x)]](λx1 [interview(x1 , x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
I
∃x[rep(x) ∧ interview(x, x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∀x[employee(x) →
P(x)]](λx0 [∃x[rep(x) ∧ interview(x, x0 )]])
20 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∃x[rep(x) ∧ P(x)]](λx1 [interview(x1 , x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
I
∃x[rep(x) ∧ interview(x, x0 )])
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∀x[employee(x) →
P(x)]](λx0 [∃x[rep(x) ∧ interview(x, x0 )]])
I
∀y [employee(y ) → ∃x[rep(x) ∧ interview(x, y )]]
20 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval, contd.
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
21 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval, contd.
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∀x[employee(x) → P(x)]](λx0 [interview(x1 , x0 )])
hλP[∃x[rep(x) ∧ P(x)]], 1i
21 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval, contd.
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∀x[employee(x) → P(x)]](λx0 [interview(x1 , x0 )])
hλP[∃x[rep(x) ∧ P(x)]], 1i
I
∀x[employee(x) → interview(x1 , x)]
hλP[∃x[rep(x) ∧ P(x)]], 1i
21 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval, contd.
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∀x[employee(x) → P(x)]](λx0 [interview(x1 , x0 )])
hλP[∃x[rep(x) ∧ P(x)]], 1i
I
∀x[employee(x) → interview(x1 , x)]
hλP[∃x[rep(x) ∧ P(x)]], 1i
I
λP[∃x[rep(x) ∧ P(x)]](λx1 [∀x[employee(x) →
interview(x1 , x)]])
21 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Retrieval, contd.
I
interview(x1 , x0 )
hλP[∃x[rep(x) ∧ P(x)]], 1i
hλP[∀x[employee(x) → P(x)]], 0i
I
λP[∀x[employee(x) → P(x)]](λx0 [interview(x1 , x0 )])
hλP[∃x[rep(x) ∧ P(x)]], 1i
I
∀x[employee(x) → interview(x1 , x)]
hλP[∃x[rep(x) ∧ P(x)]], 1i
I
λP[∃x[rep(x) ∧ P(x)]](λx1 [∀x[employee(x) →
interview(x1 , x)]])
I
∃y [rep(y ) ∧ ∀x[employee(x) → interview(y , x)]]
21 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quasi Logical Form (QLF) I
I
Core Language Engine (CLE) – Alshawi (1992), Alshawi and
van Eijck (1989)
I
Most doctors and some engineers read every article
I
quant(exists, e, Ev(e),
Read(e,
term_coord(A, x,
qterm(most, plur, y, Doctor(y)),
qterm(some, plur, z, Engineer(z))),
qterm(every, sing, v, Article(v))))
22 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quasi Logical Form (QLF) II
I
resolved QLF
quant(most, y, Doctor(y),
quant(every, v, Article(v),
quant(exists, e, Ev(e),
Read(e,y,v))))
&
quant(some, z, Engineer(z),
quant(every, v, Article(v),
quant(exists, e, Ev(e),
Read(e,z,v))))
23 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quasi Logical Form (QLF) III
I
Mary expected him to introduce himself
I
him
a_term(ref(pro, him, sing, [mary]), x, Male(x))
himself
a_term(ref(refl, him, sing, [z,mary]), y, Male(y))
24 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Quasi Logical Form (QLF) IV
I
Does the unresolved QLF have a semantic interpretation?
I
Can you do inference on unresolved QLFs?
25 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Hole semantics I
Bos (1996), Blackburn and Bos (2005), useful brief discussion in
Jurafsky and Martin (2009)
I
a constraint-based approach
I
a company representative interviews every new employee
l1 : ∃x[company representative(x) ∧ h1 ]
l2 : ∀y [new employee(y ) → h2 ]
l3 : interview(x, y )
l1 ≤ h0 , l2 ≤ h0 , l3 ≤ h1 , l3 ≤ h2
l1
h0 , l2
h1 , l3
h2
∃x[company representative(x) ∧ ∀y [new employee(y ) →
interview(x, y )]]
I
I
26 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Hole semantics II
I
l2
h0 , l1
h2 , l3
h1
∀y [new employee(y ) →
∃x[company representative(x) ∧ interview(x, y )]]
I
interpretation of underspecified representations?
27 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Minimal recursion semantics (MRS) I
Copestake et al. (2005)
I
every dog chases some white cat
I
some(y , white(y )∧ cat(y ), every(x, dog(x), chase(x, y )))
h1: every(x, h3, h4)
h3: dog(x)
h7: white(y )
h7: cat(y )
h5: some(y , h7, h1)
h4: chase(x, y )
I
28 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Minimal recursion semantics (MRS) II
I
I
every(x , dog(x ), some(y , white(y ) ∧ cat(y ), chase(x , y )))
h1: every(x, h3, h5)
h3: dog(x)
h7: white(y )
h7: cat(y )
h5: some(y , h7, h4)
h4: chase(x, y )
29 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Minimal recursion semantics (MRS) III
I
I
underspecified representation
h1: every(x, h3, h8)
h3: dog(x)
h7: white(y )
h7: cat(y )
h5: some(y , h7, h9)
h4: chase(x, y )
can be specified by h8 = h5 and h9 = h4
or h8 = h4 and h9 = h1
30 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Minimal recursion semantics (MRS) IV
I
question of interpretation
31 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
natural languages are ambiguous
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
I
there is a large number of readings
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
I
I
there is a large number of readings
unclear how to disambiguate
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
I
I
I
there is a large number of readings
unclear how to disambiguate
proposals for underspecified representations
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
I
I
I
there is a large number of readings
unclear how to disambiguate
proposals for underspecified representations
I
structural manipulation (storage, QLF)
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
I
I
I
there is a large number of readings
unclear how to disambiguate
proposals for underspecified representations
I
I
structural manipulation (storage, QLF)
constraint based (hole semantics, MRS)
32 / 32
Ambiguity in natural language
The computational problem with ambiguity
Underspecification
Summary
I
I
natural languages are ambiguous
this is a computational problem
I
I
I
proposals for underspecified representations
I
I
I
there is a large number of readings
unclear how to disambiguate
structural manipulation (storage, QLF)
constraint based (hole semantics, MRS)
unclear what the interpretation of underspecified
representations is and whether you can reason with them
appropriately
32 / 32