Scoping and the Interpretation of Noun Phrases

Scoping and the Interpretation of Noun Phrases

• 12.1 – Scoping Phenomena• 12.2 – Definite Descriptions & Scoping• 12.3 – A Method for Scoping While Parsing• 12.4 – Co-Reference & Binding Constraints• 12.5 – Adjective Phrases• 12.6 – Relational Nouns & Nominalizations• 12.7 – Other Problems in Semantics

12.1 – Scoping Phenomena

• Scope ambiguity– Quantifiers, logical operators, modal operators,

tense operators, or adverbials that allow for multiple semantic interpretations

– Resolution of ambiguity includes lexical, syntactic, semantic, and contextual analysis

• Operator – Any construct that exhibits scoping behavior

Quantifier Scoping

• A dog entered with every man.– One dog repeatedly entered with each man.– One dog entered at the same time as all the men.– Each man entered with some dog.

• Three types of quantifiers (definite, existential, universal)

• Type I – Definite quantifiers (Section 12.2)– Specified individual or group– the, these, John’s, their

Quantifier Scoping

• Type II – Existential (Indefinite) Quantifiers– Indefinite individuals (a) or sets (some)– a, some, many, a few, six, no, several, a bunch of– Test:

• There are Q men who like golf.

• Type III – Universal Quantifiers– All (or nearly all) members of a group– all, each, every, most

Classifying Quantifiers

• Collective/Distributive readings– Collective interpretation regards the NP as a

group collectively being discussed– Distributive interpretation regards the NP as

individual objects each referenced uniquely• Each man lifted the piano. D• Every man lifted the piano.• All the men lifted the piano.• The men lifted the piano. C

Scope & Collective/Distributive

• Scoping ambiguity may be resolved by appropriate collective/distributive reading.

• Each man lifted a piano.– Infer from distributive reading that “a piano”

represents many different pianos• Together, the men lifted a piano.

– Infer from collective reading that “a piano” represents one individual piano

• A piano was lifted by each man.– Still ambiguous

Local Domain

• Local Domain: Set of constituents within the closest NP or S of a parse tree

• Figure 12.1 on p. 354– Jill read Mary’s book about the depression.– Local domain of Jill: Jill, read, Mary’s, book,

about, the, depression– Local domain of Mary’s: Mary’s, book, about,

the, depression– Local domain of the: the, depression

Local Domain Concepts

• Dominating Constituent: S or NP containing the specified local domain

• Horizontal Relationship: Two constituents that belong to the same local domain (e.g., “the” to “depression”)

• Vertical Relationship: One constituent is dominating constituent of another (e.g., PP to “about”)

• Relationships extend to quantifiers

Horizontal Scoping

• Qualifier strength– each > wh- > every > all, some, several, a– Who saw every dog?– Who saw each dog?

• Structural relationships also cause order– Every man saw a dog.– A man saw every dog.

• Positional preferences– preposed constituents > surface subjects >

postposed adverbials > direct/indirect objects

Resolving Horizontal Scoping Ambiguity

• Pulling/Lifting out: Removing an ambiguous term from inside a logical form and placing it as wrapped around that logical form to disambiguate.

• Order of pull-outs determines scope resolution

• (<PRES LOVES1><EVERY m1 MAN><A d1 DOG>)• (A d1:(DOG d1)(<PRES LOVES1><EVERY m1 MAN>d1))• (EVERY m1:(MAN1 m1)(A d1:(DOG d1)<PRES LOVES> l1

m1 d1))• (PRES (EVERY m1:(MAN1 m1)(A d1:(DOG1 d1)(LOVES1 l1

m1 d1))))

Vertical Scoping

• Ambiguous quantifier lifted over dominating constituent

• Scope Islands: relative clauses that prohibit quantifiers from lifting out– Some man rewarded a boy who gave each dog a bone.

• The dogs that ran in each race are hungry.– No vertical lifting: Only the dogs that ran all the races

are hungry.– Vertical lifting: Any dog running in any race is hungry.

The dogs that ran in each race are hungry.

• Unscoped logical form:(HUNGRY1 h1 <THE d1 (& ((PLUR DOG1) d1)(RUNS-

IN1 r1 d1 <EACH r2 RACE1>))>)• No vertical lifting:(THE d1:(& ((PLUR DOG1) d1)(EACH r2:(RACE1 r2)

(RUNS-IN1 r1 d1 r2))(HUNGRY h1 d1)))• Vertical lifting:(EACH r2:(RACE1 r2)(THE d1:(& ((PLUR DOG1) d1)

(RUNS-IN1 r1 d1 r2))(HUNGRY1 h1 d1)))

Vertical Lifting

• Semantic interpretation may suggest the appropriate lifting procedure– The man in every boat rows.

• Probability of vertical lifting of quantifiers– possessives > PP modifiers > reduced relative

clauses > relative clauses– Good: A man in every boat was singing.– Bad: Every man in a boat was singing.

• Context may also provide suggestions• Backtracking approach may be appropriate

12.2 – Definite Descriptions & Scoping

• Definite quantifiers– May act as name

• The child entered with each dog.• Jill entered with each dog.

– May act as a quantified expression• The owner of every house showed us the plumbing.• Each house’s owner showed us the plumbing.

• World knowledge may force correct interpretation of definite quantifier

Handling Definite Phrase Ambiguity

• Referential – Object is found in context• Existential – Knowledge that object exists• Jack has always been afraid of the boss.

– Referential: Sam is the boss. Jack has always been afraid of Sam.

– Existential: Jack has always been afraid of whoever is the boss.

• Syntax and semantics can sometimes suggest the existential reading

• Context is needed at other times

12.3 – Method for Scoping While Parsing

• Approaches– Leave parser, but create an interpretation

procedure that converts logical form to scoped logical form (no syntax)

– Alter parser to produce likely scoping as sentence is parsed (both syntax and semantics)

• This section works with this second approach

Feature Changes

• SEM holds only discourse variables and unambiguous structures

• QS (quantifiers) holds the actual constituents that make up the ambiguous structure

• SCOPEPOS is a binary feature that is set when the parser is to invoke a procedure to sort out the quantifiers (decide what to lift)

Example

• When does each plane fly?(S SCOPEPOS +

QS (<WH t1 (TIME t1)><EACH p1 (PLANE1 p1)>) SEM (& (FLIES1 f1 p1)(AT-TIME f1 t1)))

• After scope sorting:(S SCOPEPOS –

QS nil SEM (EACH f1:(PLANE1 p1) (WH t1:(TIME t1) (& (FLIES1 f1 p1)(AT-TIME f1 t1)))))

Example

• The flights that each man took…(S SCOPEPOS +

QS (<EACH m1 MAN1>) SEM (TAKES1 t1 m1 x))

• After scope sorting:(S SCOPEPOS –

QS nil SEM (EACH m1:(MAN1 m1)(TAKES1 t1 m1 x)))

(S SCOPEPOS – QS (<EACH m1 MAN1>) SEM (TAKES1 t1 m1 x))

More Scoping Ambiguities

• PP modifiers (use QSPP feature)(NP SCOPEPOS +

QS <THE f1 (& (FLIGHT1 f1)(DEST f1 c1))>QSPP <EACH c1 CITY1> SEM f1)

• Relative clauses (use QSREL feature)• Unary operators (tense, negation)(S SCOPEPOS +

QS (<THE m1 MAN1><PAST><A d1 DOG1>) SEM (SEES1 s1 m1 d1))

Sample Parse

• First, design weights to each of the scope operators– tense > the > each > wh- > others > negation

• Use grammars defined with SEM and QS features (such as figure 12.2 on p. 364)

• Create a parse tree and use weights to disambiguate scope (figure 12.3 on p.365)

12.4 – Co-Reference & Binding Constraints

• Co-Reference: How NPs in a sentence may refer to the same object– Jack said he wants to leave.– Jill saw herself in the mirror.– *Jill thought that Jack saw herself.

• Antecedent: First NP in co-reference• Anaphor: Second NP in a co-reference• Intrasentential Anaphora – within sentence• Intersentential Anaphora – within context

Co-Reference Ambiguity

• Ambiguity may exist when pronouns co-refer to other NPs in a sentence or apply to other NPs in the context (not the sentence)

• To determine when co-reference rules are applied, heuristics do not suggest valid, ordered approaches

• C-command: New relationship between constituents used in removing co-reference ambiguities

C-command

• A constituent C is said to C-command constituent X if and only if:

1. C does not dominate X.2. The first branching node that dominates C

also dominates X.• Examples (fig. 12.5 on p. 368)

– L: “Jill” C-commands “Mary”, “her”– L: “Mary” C-commands “her”– R: “Mary’s” C-commands “her”

Reflexive Use

• Reflexivity constraint:1. A reflexive pronoun must refer to an NP that C-

commands it and is in the same local domain.2. A nonreflexive pronoun cannot refer to a C-

commanding NP within the same local domain.• Examples (fig 12.5 on p. 368)

– L: “her” cannot refer to Jill or Mary– R: “her” can refer to Jill

Nonpronominal Co-References

• Neither the antecedent nor anaphor is a pronoun

– After Jill had been questioned for hours, Sue took the tired witness out to lunch.

– *Jack thought the tired man was dying.• Constraints:

3. A nonpronominal NP cannot co-refer with an NP that C-commands it.

Bound Variables

• Bound Variable: Pronoun is bound by a universal quantifier and refers to each of the individuals being quantified over

– Every man thought he would win the race.– Every cat ate its dinner.

• Constraints:4. A nonreflexive pronoun may be bound to the

variable of a universally quantified NP only if the NP C-commands the pronoun.

Computing Co-References

• Constraints:5. Two co-referential noun phrases must agree

in number, person, and gender.• Three new predicates

– EQ-SET: Equal set (including reflexives)– NEQ-SET: Non-equal set– BV-SET: C-commanding noun phrases

(including bound variables)

Co-Reference Example

• Every boy thought he saw him.• Every boy:

<EVERY b1 (BOY1 b1)>• he:

(PRO h1 (& (HE1 h1)(BV-SET h1 (b1))))• him:

(PRO h2 (& (HE1 h2)(NEQ-SET h2(h1)) (BV-SET h2(b1))))

12.5 – Adjective Phrases

• Intersective adjectives refer to a set of items that match the adjective that intersect the set of items in the noun– the green ball

• Nonintersective adjectives refer to items that do not necessarily belong to one adjective set– the large dog– In SEM with noun: (SLOW1 DOLPHIN1)

SET Operator

• Some adjectives have a complex relationship to modified sets– average grade– toy gun– alleged murderer

• SET operator used as part of the logical form to signal this complex relationship

Comparatives

• Key words such as “more” or xxx-”er” may suggest a comparison between two noun phrases

• Grammar rules for ADJP contain a feature ATYPE with a value COMPARATIVE that become a quantifier (MORE/LESS) along a scale (HAPPY-SCALE)

12.6 – Relational Nouns & Nominalizations

• Some nouns only work in relation to other objects– sister refers to a person with a special family

relationship– author refers to a person with a special career

• Subcategorizations, qualifying these nouns, are suggested b p (& (PERSON p)(AUTHOR-OF b p))

Relational Approach

• Define each relational noun with a binary relation

• Introduce anaphoric element (REL-N1) when the sentence is missing the real element

• <THE a2 (& (PERSON a2)(AUTHOR-OF (PRO b2 REL-N1) a2))>

Relational Nouns

• Words ending in suffixes –er or –or might signal a relational noun (murderer, actor)

• AGENT roles• THEME roles may be filled by the

completion of the relational rule• the murderer of John

– murderer – AGENT– John – THEME

Nominalizations of Verbs

• Relation on verb– the destruction of the city by the Huns– <THE d1 (DESTROY d1

[AGENT <THE h1 (PLUR HUN)>][THEME <THE c1 CITY>])>

• Similar handling to relational nouns

12.7 – Other Problems in Semantics

• Further problems not studied in detail in the text– Mass Terms– Generics– Intensional Operators & Scoping– Noun-Noun Modifiers

Mass Terms

• Count nouns can be identified by number– three clowns, a dog, some flowers

• Mass nouns refer to substances that occur in quantity– sand, some water, gasoline

• Mass nouns require different parse rules or features to signal their differences

• Mass nouns and count nouns can be interchanged with appropriate modifiers.

Generics

• Generic sentences refer to classifications of objects, not individual objects

• A generic statement may not be true for 100% of those objects– Lions are dangerous.– Sea turtles lay approximately 100 eggs.

• The ontology works with the designation “kind”

• Identifying sentence as generic may be problematic

Intensional Operators & Scoping

• Referentially Opaque: Idea that terms may not be equal in all sentences– Sam believes John kissed Sue.– John is the tallest man.– Incorrect: Sam believes the tallest man kissed

Sue.• De Re Belief: Belief about a particular

object• De Dicto Belief: Belief about some

proposition

Noun-Noun Modifiers

• Problems– Which noun modifies which?– What is the semantic relationship?

• pot handles, car paint, stone wall

• In practice, noun-noun modifications are best recovered from context

• Logical form utilizes predicate N-N-MOD

Summary of Chapter 12

• What is scoping and scoping ambiguity?• What are the definite, indefinite, and universal

quantifiers?• How do we deal with scoping in parsing?• What is co-referencing?• What ambiguity arises in adjective phrases?• How are relational nouns and verbs understood?• What are the other issues in ambiguity

resolution?