Scoping and the Interpretation of Noun Phrases

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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> l1m1 d1)) • (PRES (EVERY m1:(MAN1 m1)(A d1:(DOG1 d1)(LOVES1 l1m1d1))))

11. 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.

12. The dogs that ran in each race are hungry. • Unscoped logical form: (HUNGRY1 h1 <THE d1 (& ((PLUR DOG1) d1)(RUNS-IN1 r1d1 <EACH r2 RACE1>))>) • No vertical lifting: (THE d1:(& ((PLUR DOG1) d1)(EACH r2:(RACE1 r2)(RUNS-IN1 r1d1r2))(HUNGRY h1d1))) • Vertical lifting: (EACH r2:(RACE1 r2)(THE d1:(& ((PLUR DOG1) d1)(RUNS-IN1 r1d1r2))(HUNGRY1 h1d1)))

13. 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

14. 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

15. 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

16. 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

17. 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)

18. Example • When does each plane fly? (S SCOPEPOS + QS (<WH t1 (TIME t1)><EACH p1 (PLANE1 p1)>) SEM (& (FLIES1 f1p1)(AT-TIME f1t1))) • After scope sorting: (S SCOPEPOS – QS nil SEM (EACH f1:(PLANE1 p1) (WH t1:(TIME t1) (& (FLIES1 f1p1)(AT-TIME f1t1)))))

19. Example • The flights that each man took… (S SCOPEPOS + QS (<EACH m1 MAN1>) SEM (TAKES1 t1m1 x)) • After scope sorting: (S SCOPEPOS – QS nil SEM (EACH m1:(MAN1 m1)(TAKES1 t1m1 x))) (S SCOPEPOS – QS (<EACH m1 MAN1>) SEM (TAKES1 t1m1 x))

20. More Scoping Ambiguities • PP modifiers (use QSPP feature) (NP SCOPEPOS + QS <THE f1 (& (FLIGHT1 f1)(DEST f1c1))> QSPP <EACH c1 CITY1> SEMf1) • Relative clauses (use QSREL feature) • Unary operators (tense, negation) (S SCOPEPOS + QS (<THE m1 MAN1><PAST><A d1 DOG1>) SEM (SEES1 s1m1d1))

21. 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)

22. 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

23. 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

24. C-command • A constituent C is said to C-command constituent X if and only if: • C does not dominate X. • 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”

25. Reflexive Use • Reflexivity constraint: • A reflexive pronoun must refer to an NP that C-commands it and is in the same local domain. • 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

26. 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: • A nonpronominal NP cannot co-refer with an NP that C-commands it.

27. 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: • A nonreflexive pronoun may be bound to the variable of a universally quantified NP only if the NP C-commands the pronoun.

28. Computing Co-References • Constraints: • 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)

29. 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))))

30. 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)

31. 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

32. 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)

33. 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))

34. 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))>

35. 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

36. 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

37. 12.7 – Other Problems in Semantics • Further problems not studied in detail in the text • Mass Terms • Generics • Intensional Operators & Scoping • Noun-Noun Modifiers

38. 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.

39. 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

40. 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

41. 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

42. 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?