Computational Semantics GSLT Johan Bos University of Edinburgh

1
Computational SemanticsGSLTJohan
BosUniversity of Edinburgh
2
This course

• This course is based on material fromWorking
  with Discourse Representation Theory An
  Advanced Course in Computational Semantics(by
  Patrick Blackburn Johan Bos)
• It is a continuation of the introductory course
  Representation and Inference
• More information www.comsem.org

3
Overview

• Discourse Representation Theory
• Building Discourse Representations
• Pronoun Resolution
• Presupposition Projection
• Implementation various versions of CURT

4
Part I

• Discourse Representation Theory

5
Overview of DRT

• DRT employs a language based on box-like
  structures called DRSs
• We will be making heavy use of DRSs in this
  course, for different purposes
• DRSs are Pictures (something like mental
  models)
• DRSs are Programs (the dynamic perspective)

6
Interpreting Discourse

• Discourse a sequence of several natural language
  sentences
• How can we represent the meaning of discourse?
• It is clearly not just the conjunction of the
  first-order representations of its individual
  sentences
• We will explain why with a few simple examples

7
Some examples showing that this is not
straightforward

• Example 1Mia is a woman. She loves Vincent.
• FOL representationA woman(mia)love(x,vincent)
  B woman(mia)love(mia,vincent)

8
Some examples showing that this is not
straightforward

• Example 2A woman snorts. She collapses.
• FOL RepresentationA ?y(woman(y)snort(y))collap
  se(x)B ?y(woman(y)snort(y))collapse(y)C
  ?y(woman(y)snort(y)collapse(y))

9
Some examples showing that this is not
straightforward

• Example 3If a woman snorts, she collapses.
• FOL RepresentationA ?y(woman(y)snort(y))?colla
  pse(x)B ?y(woman(y)snort(y))?collapse(y)C
  ?y(woman(y)snort(y)?collapse(y)) D
  ?y(woman(y)snort(y)?collapse(y))

10
Context Change Potential

• We need to start with the right representation
• Basic FOL does not seem to give us the right
  means
• Manipulation with quantifier scope and free
  variables
• Not the right intuitions about how discourse
  works
• We need a representation that naturally mirrors
  the context change potential of an utterance

11
Discourse Representation Structures

• A new discourse starts a new DRS
• This DRS is meant to represent the meaning of an
  entire discourse
• When a new sentence is parsed, the DRS is
  expanded
• The x in the top of the box is adiscourse
  referent
• The expressions woman(x) and snort(x) are
  DRS-conditions

12
Processing subsequent sentences

• Lets now interpretShe collapses
• We will do three things
• Add a new discourse referent
• Add condition collapse(y)
• Add a further condition xy
• Why did we do this?
• She is a pronoun
• Pronouns introduce a discourse referent which get
  identified with an accessible discourse referent

13
Further examples of DRSs

• Proper namesMia snorts
• Quantified NPsEvery man smokes.

?
14
Further examples of DRSs

• NegationMia does not have a car
• DisjunctionMia smokes or snorts

?
?
15
Syntax of DRSs

• If x1xn are discourse referents, and C1Cn are
  conditions, then is a DRS

16
Terms

• A term ? is either a constant or a discourse
  referent

17
Syntax of DRS-conditions

• If R is a relation symbol of arity n, and tau
  ?1?n are terms, then R(?1?n) is a DRS-condition
• If ?1 and ?2 are terms then ?1?2 is a
  DRS-condition
• If B is a DRS, then ?B is a DRS-condition
• If B1 and B2 are DRSs, then B1?B2 and B1?B2 are
  DRS-conditions

18
Semantics of DRSs

• Given that a DRS is supposed to be a picture, it
  seems natural to say that a DRS is satisfied in a
  model iff it is an accurate image of the
  information recorded inside the model
• For instance

Satisfied in a model iff It is possible to
associate X and y with entities of the model such
that x is a woman, y is a boxer, and x and y
stand in the admire relation
19
Semantics of complex DRS-conditions

• A negated DRS will be satisfied if it is not
  possible to embed it in the model
• A disjunctive DRS-condition will be satisfied if
  at least one of the disjuncts can be embedded in
  the model
• An implicative DRS-condition will be satisfied if
  every way of embedding the antecedent DRS, gives
  rise to an embedding of the consequent DRS

20
Accessibility

• Resolving anaphoric pronouns is subject to
  accessibility constraints
• Accessibility is a geometric concept, defined in
  terms of the ways DRSs are nested into each other
• A DRS B1 is accessible from DRS B2 when B1 equals
  B2, or when B1 subordinates B2

21
Subordination

• A DRS B1 subordinates B2 iff
• B1 immediately subordinates B2
• There is a DRS B such that B1 subordinates B and
  B subordinates B2
• B1 immediately subordinates B2 iff
• B1 contains a condition ?B2
• B1 contains a condition B2?B or B?B2
• B1 contains a condition B2 ? B
• B1 ? B2 is a condition in some DRS B

22
The accessibility constraint

• Suppose a pronoun has introduced a new discourse
  referent y into the universe of some DRS B.
• Then we are only free to add the condition yx
  to the conditions of B if x is declared in an
  accessible DRS from B

23
Accessibility examples

• A woman walks.She collapses.
• Every woman walks.?She collapses.

?
24
Donkey Sentences

• If a farmer owns a donkey, he beats it.
• Every farmer who owns a donkey beats it.

?
25
Interpreting DRSs

• There are two popular ways of doing this
• Embedding Semantics (Kamp Reyle)
• Dynamic Semantics(Groenendijk Stokhof)
• We will use the translation fromDRSs to
  First-Order Logic

26
From DRT to First-Order Logic

• DRT and First-Order Logic are obviously related
• Given a vocabulary, we can use it to build either
  DRSs or first-order languages
• They are interpreted in the same models
• Translating DRSs into FOL (and back) is
  straightforward and efficient
• We will use the function (.)fo to translate DRSs
  into first-order formulas

27
Translating DRT to FOLDRSs
(
)fo ?x1 ?xn((C1)fo(Cn)fo)
28
Translating DRT to FOLDRS-Conditions
(R(x1xn))fo R(x1xn) (x1x2)fo
x1x2 (?B)fo ?(B)fo (B1?B2)fo (B1)fo ?
(B2)fo
29
Translating DRT to FOLImplicative DRS-conditions
?B)fo ?x1?xn(((C1)fo(Cn)fo)?(B)fo)
(
30
Implementation

• DRT in Prologdrs(D,C) (D and C Prolog
  lists)imp(B1,B2)or(B1,B2)not(B)
• Prolog Variables as discourse referents
• Compiling DRSs into First-Order logic drs2fol.pl
• Show examples of the translation

31
Part II

• Building Discourse Representations

32
Building DRSs

• We know now what DRT is, and developed some
  Prolog tools to work with DRSs
• But how can we construct DRSs for English
  discourses in a systematic and automatic way?
• There are various ways to do this we will
  explore the lambda-based method

33
Building DRSs with lambdas

• We will use the lambda-calculus as a tool to
  build DRSs for sentences
• We will use ? to mark missing information in the
  DRS
• We call this combination ?-DRT
• It will allow us to use a number of off-the-shelf
  tools, such as ?-conversion.

34
The Merge

• We will introduce a new operator
• The indicates a merge between two DRSs
• The merge is used to combine two DRSs into one
  larger DRS

)
(

35
Merge Reduction

• Replacing a merged DRS for a new DRS by taking
  the union of the two universes and conditions
• The merge is precisely the operation on DRSs we
  need to state in the lexical semantics

(
)
36
Merge-reduction can only be applied after
?-conversion

• Consider the exampleA woman walks and a woman
  talks
• This is of course not the result we want!

(
)
37
Lexical SemanticsNouns and proper names

• boxer
• Vincent

?x.
?u.(
u_at_x)
38
Lexical SemanticsDeterminers

• a
• every

?p.?q.((
p_at_x)q_at_x)
?p.?q.
p_at_x) ?q_at_x
(
39
Lexical SemanticsVerbs

• dances
• admires

?x.
?u.?x.u_at_?y.
40
Lexical SemanticsAdjectives

• big

?u.?x.(
u_at_x)
41
Example derivation
S
VP
NP
IV
N
DET
man
Every
dances
42
Example derivation
S
VP
NP
N
IV
?y.
DET
p_at_x) ?q_at_x
?p.?q. (
?z.
man
dances
Every
43
Example derivation
S
_at_?y.
p_at_x) ?q_at_x
?p.?q. (
VP
NP
Application NP?DET N
N
IV
DET
?z.
man
dances
Every
44
Example derivation
S
?y.
_at_x) ?q_at_x
?q. (
VP
NP
?-conversion
N
IV
DET
?z.
man
dances
Every
45
Example derivation
S
) ?q_at_x

?q. (
VP
NP
?-conversion
N
IV
DET
?z.
man
dances
Every
46
Example derivation
S
?q.
?q_at_x
VP
NP
-reduction
N
IV
DET
?z.
man
dances
Every
47
Example derivation
S
?q.
?q_at_x
VP
?z.
NP
No operation required VP?IV
N
IV
DET
man
dances
Every
48
Example derivation
_at_?z.
?q.
?q_at_x
S
Application S?NP VP
VP
NP
N
IV
DET
man
dances
Every
49
Example derivation
? ?z. _at_x
S
?-conversion
VP
NP
N
IV
DET
man
dances
Every
50
Example derivation
?
S
?-conversion
VP
NP
N
IV
DET
man
dances
Every
51
Implementation

• Grammar, Lexicon
• Semantic rules, lexical semantics
• Merge reduction
• Alpha-conversion for DRSs
• Prolog lambdaDRT.pl
• alphaConversionDRT.pl, mergeDRT.pl

52
Adding Inference

• Use theorem prover and model builder for
  performing inferences on DRSs
• We will use the translation from DRT to
  First-Order Logic
• We will apply this method to consistency and
  informativeness checking

53
Consistency Checking

• Assume B is the DRS of a discourse
• And ? the translation of B (B)fo?
• Now we give ? to a model builder, and ?? to a
  theorem prover
• If the theorem prover finds a proof, B is
  inconsistent
• If the model builder finds a model, B is
  consistent

54
Informativeness Checking

• Assume B is the DRS of a discourse
• And ? the translation of B (B)fo?
• Now we give ? to a theorem prover, and ?? to a
  model builder
• If the theorem prover finds a proof, B is not
  informative
• If the model builder finds a model, B is
  informative

55
Demo of CURT (curtDRT.pl)

• Examples
• Showing readings and models
• Inference consistency, informativeness
• What we really want
• Pronouns!

56
Part III

• Pronoun Resolution

57
Pronoun Resolution

• We will concentrate on 3rd person singular
  personal pronouns in English
• he/him/himself
• she/her/herself
• it/itself
• We will focus on anaphoric pronouns
• In this course we wont consider
• Deictic pronouns
• Cataphoric useAfter he lost the match, Butch
  left town.
• Pleonastic use of pronounsIts about nine
  oclock in the morning.

58
Recall DRS structure constrains antecedents

• DRS implication
• A woman snorts. She collapses
• Every woman snorts. She collapses
• DRS negation
• Mia ordered a five dollar shake. Vincent tasted
  it.
• Mia didnt order a five dollar shake. Vincent
  tasted it.

59
Grammatical agreement

• In English, pronouns come with a gender and
  number feature
• Only refer to antecedents carrying the same
  feature values
• he (singular, male)
• men/boys, male animals
• she (singular, female)
• women/girls, female animals, things
  regarded as female, e.g. vehicles or ships
• it (singular, neuter) things, animals, children

60
Ambiguity

• Butch1 threw a TV2 at the window3.It2,3 broke.
• Butch1 threw a vase2 at the wall3.It2 broke.
• Butch1 walks into his1 modest kitchen2. He1 opens
  the refrigerator3. He1 takes out a milk4 and
  drinks it4.

61
Reflexive Pronouns and Binding Theory

• Examples
• Vincent1 goes to the toilet, and Jules2 enjoys
  himself2.
• Vincent1 enters the restaurant, and Jules2
  watches him1.
• Pronouns obey rules of binding!

62
Implementation

• Decide how to represent (unresolved) pronouns in
  DRSs
• Add pronouns to lexicon and grammar
• Design semantic templates for pronouns
• Extend ontology with semantic features of
  pronouns
• Add rules for the binding constraints
• Prolog curtPDRT.pl

63
Representing pronouns

• We wont resolve pronouns rightaway, but instead
  represent them with Alfa-DRSs first
• Example he walks

?
(
)
64
Extend Grammar and Lexicon

• New grammar rules
• T ? S TT ? S NP ? ProPro ? shePro ? herPro
  ? herself

65
Lexical Semantics Pronouns

• He/him/himself
• She/her/herself
• It/itself

?u.(
u_at_x)
?u.(
u_at_x)
?u.(
u_at_x)
66
Extend the ontology

• New axioms
• ?x(plant(x)?neuter(x))?x(object(x)?neuter(x))?x
  (event(x)?neuter(x))?x(man(x)?male(x))?x(woman(x
  )?female(x))
• Axioms for disjointness?x(neuter(x)??male(x))?x
  (neuter(x)??female(x))?x(female(x)??male(x))

67
Rules for Binding Theory (1)

• Feature for reflexive noun phrasesVP ?
  TVrefX NPrefXNPrefX ?
  ProrefXProrefyes?himselfProrefno?him
• Lexical semantics for TVs

TVrefX,sem?u.?x.u_at_?y.
?love
68
Rules for Binding Theory (2)

• This will give us
• Vincent1 loves him1
• Vincent1 loves himself1
• Exclude DRSs if
• The feature refyes is attached to conditions
  with different variables
• The feature refno is attached to conditions with
  identical variables

69
Demo of CURT (curtPDRT.pl)

• Examples
• Vincent likes Mia. She smokes.
• Vincent likes himself/him/her/herself
• No man loves himself/herself
• If a man walks, he smokes.
• What do we learn from this
• Use of expensive theorem proving for rather
  obvious cases
• Sometimes rather funny judgements (negation,
  implication)

70
Add sortal check

• Some readings obtained are obviously wrong
  (inconsistent)
• Use information from ontology to weed out such
  cases
• This handles some cases, but not all
• Cases with equality
• Conflicts that cover more than one DRS
• It is a sound but incomplete inference technique,
  but it is efficient it to use complementary to
  our theorem prover

71
Part IV

• Presupposition Projection

72
Presupposition Projection- Overview -

• We will learn what the typical problems
  associated with presuppositions are
• Concentrate on a DRT based approach of Rob van
  der Sandt
• Extend our earlier implementation of pronoun
  resolution
• Access to further inference methods

73
Presuppositions (1)

• Examples
• The couple that won the dance contest was pleased
• Jody loves her husband
• Vincent regrets that Mia is married
• These examples force us to take something for
  granted
• There is a couple that won the dance contest
• Jody is married
• Mia is married

74
Presuppositions (2)

• Given contexts with contrary information, these
  sentences do not make sense at all
• Jody is not married. ?? She loves her husband.
• Mia is not married.Vincent regrets that Mia is
  married.

75
Presuppositions (3)

• Whatever were dealing with here, it is not
  ordinary entailment
• Both
• Jody loves her husband.
• Jody does not love her husband.
• imply that Jody is married

76
Presuppositions (4)

• We are dealing with presuppositions!
• The sentences Jody loves her husband and Jody
  doesnt love her husband both imply that Jody
  has a husband
• We say that Jody has a husband is presupposed
  by these sentences
• This presuppositions is triggered by the
  possessive pronoun her

77
Presupposition Triggers

• Definite NPs (the man, Mias husband)
• Factive verbs (to regret, to know)
• Implicative verbs (to manage)
• Certain adjectives (other, new)
• Clefts (it was Butch who killed Vincent)
• Iterative adverbs (too, again)

78
Dealing with Presupposition

• Fine why not go through our lexicon, mark all
  presupposition triggers, and when analysing a
  sentence, check if the context agrees with the
  presuppositions of that sentence.
• Issues we need to deal with
• The Binding Problem
• The Projection Problem
• Presuppositional Accommodation

79
The Binding Problem

• ExampleA boxer nearly escaped from his
  apartment.
• Trigger his apartment presupposes that someone
  has an apartment.
• But who? A boxer? Any boxer?

80
The Projection Problem

• Examples
• (1) Mias husband is out of town
• (2) If Mia has a husband, then Mias husband is
  out of town.
• (3) If Mia dates Vincent, thenMias husband is
  out of town.
• Example (1) presupposes that Mia is married, (2)
  does not, and (3) does!
• Complex sentences sometimes neutralise
  presuppositions

81
Accommodation

• Accommodation can be thought of as a way of
  obtaining a robust and realistic treatment of
  presupposition
• ExampleVincent informed his boss.
• Presupposition Vincent has a boss.
• What if we dont have a clue whether Vincent has
  a boss or not?
• Accommodation incorporating missed information
  as long as this not conflicting with other
  information

82
Van der Sandts Theory

• We will use a method due to Rob van der Sandt
• Presuppositions are essentially extremely rich
  anaphoric pronouns
• Presuppositions introduce new DRSs that need to
  be incorporated in the discourse context
• This is a good way of dealing with the binding,
  projection, and accommodation problems

83
Presuppositions in DRT

• We need to carry out two tasks
• Select presupposition triggers in the lexicon
• Indicate what they presuppose
• We will use the alpha-operator
• Example The woman collapses.
• Preliminary DRS

(
?
)
84
Binding Presuppositions

• ExampleA woman snorts. The woman collapses.
• Step 1 Merge with previous discourse.

?
(
(
))
85
Binding Presuppositions

• ExampleA woman snorts. The woman collapses.
• Step 2 Identify with possible antecedent
  discourse referent

?
(
(
))
86
Binding Presuppositions

• ExampleA woman snorts. The woman collapses.
• Step 3 Move information to antecedent

?
(
(
))
87
Binding Presuppositions

• ExampleA woman snorts. The woman collapses.
• Step 4 replace ? by merge

(
(
))
88
Binding Presuppositions

• ExampleA woman snorts. The woman collapses.
• Step 5 perform merge reduction

89
Binding Presuppositions

• ExampleA woman snorts. The woman collapses.
• Note we will use unification instead of explicit
  equality conditions

90
Accommodating Presuppositions

• ExampleIf Mia dates Vincent, then her husband
  is out of town

?
?(
)
91
Global Accommodation

• ExampleIf Mia dates Vincent, then her husband
  is out of town

?
?(
)
92
Global Accommodation

• ExampleIf Mia dates Vincent, then her husband
  is out of town

?
93
Sometimes global accommodation is not a good
option! (projection problem)

• Slightly different exampleIf Mia is married,
  then her husband is out of town

?
94
Intermediate Accommodation

• ExampleIf Mia is married, then her husband is
  out of town

?
?(
)
95
Intermediate Accommodation

• ExampleIf Mia is married, then her husband is
  out of town

?
96
Local Accommodation

• ExampleIf Mia is married, then her husband is
  out of town

?
97
Van der Sandts Algorithm

• Generate a DRS for the input sentence, with all
  elementary presuppositions marked by ?
• Merge this DRS with the DRS of the discourse so
  far processed
• Traverse the DRS, and on encountering an ?-DRS
  try to
• Bind the presupposed information to an accessible
  antecedent, or
• Accommodate the information to a superordinated
  level of DRS
• Remove those DRSs from the set of potential
  readings that violate the acceptability
  constraints

98
The acceptability constraints

• DRSs should not contain free variables
• DRSs should be consistent and informative
• DRSs should also be locally consistent and
  informative

99
Free Variable Check (1)

• Consider the exampleEvery man likes his car
• DRS obtained with Local Accommodation

?
100
Free Variable Check (2)

• Consider the exampleEvery man likes his car
• DRS obtained with Intermediate Accommodation

?
101
Free Variable Check (3)

• Consider the exampleEvery man likes his car
• DRS obtained with Global Accommodation

?
102
The presupposition projection problem solved

• Recall our exampleIf Mia is married, then her
  husband is out of town
• Local constraints play a crucial role here!

Locally informative
Locally uninformative
?
103
The binding problem solved

• ExampleA boxer nearly escaped from his
  apartment.
• Preliminary DRS

?
(
))
(

• Final DRS

104
Proper Names

• Proper Names can be treated as presupposition
  triggers
• Only global accommodation is permitted for proper
  names
• This assures they will always end up in the
  global (outermost) DRS, accessible for subsequent
  pronouns
• ExampleEvery man knows Mia. She is Marselluss
  wife.

?
105
Implementation

• Work in the lexicon
• Implementing accommodation
• Free variable trapping
• The Local Constraints
• Prolog curtPPDRT.pl

106
Summary

• Weve looked at various semantic phenomena
• Pronouns, presupposition,
• And weve implemented a fragment of English
  incorporating these phenomena
• Weve hooked up first-order tools to do genuine
  inference

107
Whereto from here?

• Work on Representation
• Plurals
• Events
• Tense Aspect
• Work on Inference
• Incremental inference
• Use sorts to reduce search space
• Model size estimation