The Mechanics of Selection and Coercion in Grammar James Pustejovsky
GL2007 Paris Ecole´ Normale Sup´erieure May 10, 2007 Outline
• Motivation: Why make the lexicon generative? • Methodology: How do we discover generative mechanisms? • Theory of Selection: Types, Qualia, and Coercion • Challenges: - Integrating Discourse Structure and GL - Adding Dynamic Types to GL
1 Questions Addressed by GL
• Encoding Context through Lexical Typing • Architecture: How does the grammar encode or license selection in language? • Expressiveness: How much argument information can and should be selected/selectable? • Descriptiveness: How does selection contribute to coverage of the data?
2 Assumptions
• Language meaning is compositional. • Compositionality is a desirable property of a semantic model. • Many linguistic phenomena appear non-compositional. • Generative Lexicon exploits richer representations and rules to fix holes in the compositionality model. • Richer representations involve Lexical Decomposition. • Richer rules involve Coercion, Subselection, Co-composition.
3 The Principle of Compositionality
The meaning of a complex expression is determined by its structure and the meanings of its constituents.
4 The Principle of Compositionality
The meaning of a complex expression is determined by its structure and the meanings of its constituents.
Questions . . .
5 The Principle of Compositionality
The meaning of a complex expression is determined by its structure and the meanings of its constituents.
Questions . . .
What is the nature of the structure? What is the meaning of a constituent? What counts as a constituent?
6 Challenges to Simple Compositionality
(1) a. Mary began [to eat her breakfast]. b. Mary began [eating her breakfast]. c. Mary began [her breakfast].
(2) a. Mary enjoyed her beer. b. John enjoys his coffee in the morning. c. Bill enjoyed the movie.
7 Verbal Polysemy
(3) a. The woman baked a potato in the oven. b. The woman baked a cake in the oven.
(4) a. John swept. b. John swept the floor. c. John swept the dirt into the corner. d. John swept the dirt off the sidewalk. e. John swept the floor clean. f. John swept the dirt into a pile. shovel, rake, shave, weed.
8 (5) a. John whistled. b. John whistled at the dog. c. John whistled a tune. d. John whistled a warning. e. John whistled her appreciation. f. John whistled to the dog to come. yell, snap, whisper.
9 Manner/Result Complementarity
(6) Manner and result meaning patterns are in complementary distribution: a verb lexicalizes only one. Levin & Rappaport, 1991 (7) a. manner: hit, pound, smear, sweep b. result: clean, cover, empty, put What about... (8) a. climb: John climbed the wall. (manner of motion + result of motion) b. drown: Mary drowned in the river. (manner of dying + resulting in death)
10 Unaccusatives and Selectional Specificity
(9) Externally Caused Events: break, etc. a. The vase broke. b. Mary broke the vase. c. The storm broke the window. (10) Internally Caused Events: decay, bloom, etc. a. The flowers bloomed early. b. *The gardener bloomed the flowers.
11 Adjectival Selection
Adjectives modify specific aspect of the Noun: (11) a. a former professor b. my former car c. the retired admiral (12) a. the escaped prisoner b. an unbaked cake (13) a. the vacation/well-built house b. a fast/young typist c. some bright/expensive bulbs d. a long/scratched record/CD.
12 Most Composition is Considered Function Application
1. What is the nature of the function? 2. What does it apply to; i.e., what can be an argument? 1. John loves Mary. 2. love(Arg1,Arg2) 3. Apply love(Arg1,Arg2) to Mary 4. =⇒ love(Arg1,Mary) 5. Apply love(Arg1,Mary) to John 6. =⇒ love(John,Mary)
13 Type Structure and Logical Form
• Compositional operations proceed according to the type theory • Logical Form is computed from richer qualia structures associated with each type
14 Entity Types and Predicate Types
The Simply Typed λ-Calculus (a) e is a type. (b) t is a type. (c) If a and b are types, then a → b is a type. A simple type tree: t @ @ @ e e @→ t Function Application: If α is of type a, and β is of type a → b, then β(α) is of type b.
15 Compositionality in Practice
(a) John loves Mary.
S:t. love(j, m) ¨H ¨¨ HH ¨ H John:e. j VP: e → t. λx[love(x, m)] ¨H ¨¨ HH ¨ H John V:e → (e → t) NP:e. m
love. λxλy[love(y, x)] Mary
16 Type Checking vs. Model Checking
(14) Arguments can be viewed as pretests for performing the action in the predicate.
(15) If the argument conditions are not satisfied, the predicate throws an error.
17 Type Checking vs. Model Checking
(16) Arguments can be viewed as pretests for performing the action in the predicate.
(17) If the argument conditions are not satisfied, the predicate throws an error. Then What?
18 Argument Typing as Abstracting from the Predicate
(18) Richer typing for arguments: i. Identifies specific predicates in the body of the expression that are characteristic functions of an argument; ii. pulls this subset of predicates out of the body, and creates a pretest to the expression as a restricted quantification over a domain of sorts, denoted by that set of predicates.
19 Argument Typing as Abstracting from the Predicate
(19) τ σ z}|{ z}|{ λx2λx1[Φ1,... Φx1 ,... Φx2 ,..., Φk] σ and τ are sets of predicates describing properties of arguments to the predicate complex.
20 Predicate Abstractions Become Argument Types
(20)
λx2 : σ λx1 : τ[Φ1,..., Φk − {Φx1, Φx2}] (21) σ and τ have now become reified as types on the arguments.
21 Generative Lexicon
• Two classes of sortal constraints on a concept: – Argument structure – Event structure • These bind into the Qualia Structure • Compositional Rules invoke – Type Selection: Exact match of the type – Type Accommodation:The type is inherited – Type Coercion: Type selected must be satisfied
22 Argument and Body in Generative Lexicon
(22) Environ z AS }| ES { Body z }| { z }| { z }| { λxn . . . λx1 λem . . . λe1 [Q1 ∧ Q2 ∧ Q3 ∧ Q4; C]
AS: Argument Structure ES: Event Structure Qi: Qualia Structure C: Constraints
23 Qualia Structure
Formal: the basic category which distinguishes it within a larger domain; Constitutive: the relation between an object and its constituent parts; Telic: its purpose and function; Agentive: factors involved in its origin or “bringing it about”.
24 Compositionality
• Local context modeled as Strong Selection. • Compositional rules refer to these types: • Types can be selected; • Types can be accommodated. • Types can be exploited (coercion). • Types can be introduced (coercion). • Composition can license new interpretations (cocompose).
25 Mechanisms of Selection refer to Type Level
Types of Expressions in Language (Level) • Natural Types: atomic concepts of formal, const, and agentive; • Artifactual Types: Adds concepts of telic; • Complex Types: Cartesian types formed from both Natural and Artifactual types.
26 Level of Types in the Major Categories
1. Noun N: rock, water, woman, tiger, tree F: knife, beer, husband, dancer C: book, lunch, university, temperature 2. Verb N: fall, walk, rain, put, have F: donate, spoil, quench C: read, perform
27 3. Adjective N: red, large, flat F: useful, good, effective C: rising
28 Mechanisms of Selection
• Pure Selection: The type a function requires is directly satisfied by the argument. • Accommodation: The type a function requires is inherited by the argument. • Coercion: The type a function requires is wrapped around the argument, embedding it within the required type.
29 GL Lexical Structure
α arg1 = x argstr = ... event1 = e1 eventstr = (23) event2 = e2 const = what x is made of formal = what x is qualia = telic = e : function of x 2 agentive = e1: how x came into being
30 Motivating the Notion of Natural Kind
(24) a. Nominal Predication: How the common noun behaves predicatively; b. Adjectival Predication: How adjectives modifying the the common noun can be interpreted; c. Interpretation in Coercive Contexts: How NPs with the common noun are interpreted in coercive environments.
31 Types in Generative Lexicon: Pustejovsky (2001,2007), Asher and Pustejovsky (2005)
The Type Language (25)a.e the type of entities; t, truth values. (σ, τ range over simple types, and subtypes of e.) b. If σ and τ are types, then so is σ → τ; c. If σ and τ are types, then so is σ • τ; d. If σ and τ are types, then so is σ ⊗Q τ, for Q = const(c), telic(t), or agentive(a).
32 Qualia Structure as Types
(26) type feature structure: x: α const : β formal : α qualia = telic : τ agentive : σ
33 Qualia as Types
x: α ⊗c β (27) ⊗t τ ⊗a σ
34 Qualia as Types
x: α ⊗c β (28) ⊗t τ ⊗a σ with an unlabeled qualia value x: α (29) ⊗ τ
35 Natural Entities
Entities formed from the application of the formal and/or const qualia roles:
For the predicates below, eN is structured as a join semi-lattice, heN, vi; (30)a.physical, human, stick, lion, pebble b. water, sky, rock
36 Natural Entity Types as a Lattice
(31) Entity ¨¨HH ¨¨ HH ¨ H Physical Abstract ¨ H ¨¨ HH ¨¨ HH Stuff Individuated Mental Ideal @ @@ inanimate animate
37 Natural Predicate Types
Predicates formed with Natural Entities as arguments:
(32)a.fall: eN → t b. touch: eN → (eN → t) c. be under: eN → (eN → t) Expressed as typed arguments in a λ-expression:
(33)a.λx: eN[fall(x)] b. λy : eNλx: eN[touch(x,y)] c. λy : eNλx: eN[be-under(x,y)]
38 Artifactual Entity Types: eA
Entities formed from the Naturals by adding the agentive or telic qualia roles: (34) Expressed as types:
a. Artifact Entity: x : eN ⊗a σ x exists because of event σ
b. Functional Entity: x : eN ⊗t τ the purpose of x is τ
c. Default Artifactual Entity: x :(eN ⊗a σ) ⊗t τ x exists because of event σ for the purpose τ
39 Artifactual Entity Types
Examples of types in eA.
(35)a.beer: liquid ⊗t drink (liquid ⊗a brew) ⊗t drink (expressing Agentive) b. knife: phys ⊗t cut (phys ⊗a make) ⊗t cut (expressing Agentive) c. house: phys ⊗t live in (phys ⊗a build) ⊗t live in (expressing Agentive)
40 Human Functional Entity Types
(36) telic and agentive constraints on the Natural Type human: a. boss, friend; b. dancer: human ⊗ dance c. wife, husband: human ⊗a marry
41 Artifactual Predicate Types
Predicates formed with Artifactual Entities as arguments:
(37)a.spoil: eN ⊗t τ → t b. fix: eN ⊗t τ → (eN → t)
Expressed as typed arguments in a λ-expression:
(38)a.λx: eA[spoil(x)] b. λy : eAλx: eN[fix(x,y)] (39)a.The beer spoiled. b. Mary fixed the watch.
42 Complex Entity Types
Entities formed from the Naturals and Artifactuals by a product type between the entities, i.e., the dot, •.
(40)a.Mary doesn’t believe the book. b. John sold his book to Mary.
(41)a.John wrote the exam last night in under 10 minutes. b. The exam lasted more than three hours this morning.
43 Dot Objects: eC
(42) Expressed as types:
a. Complex Entity: x : ei • ej, for i, j of any level b. Complex Predicate: P : x : ei • ej → t
44 Complex Predicate Types
Predicates formed with Complex Entity Types as arguments:
(43) read: phys • info → (eN → t)
Expressed as typed arguments in a λ-expression:
(44) λy : phys • info λx: eN[read(x,y)] (45) Mary read the book.
45 Enriching Compositionality
If all you have for composition is function application, then you need to create as many lexical entries for an expression as there are environments it appears in. (Weak Compositionality) Two ways to overcome this: (1) Type Shifting Rules: Partee-Rooth MG, CG, HPSG. (2) Type Coercion Operations: GL, Hendriks, Moens and Steedman
46 Maintaining Compositionality
– Generative Mechanisms of Argument Selection: ∗ Selection ∗ Accommodation ∗ Coercion: (i) Introduction (ii) Exploitation – Qualia-based Type Structure: ∗ Natural, ∗ Artifactual, ∗ Complex.
47 Generative Mechanisms of Argument Selection
– Pure Selection: The type a function requires is directly satisfied by the argument. – Accommodation: The type a function requires is inherited by the argument. – Coercion: The type a function requires is imposed on the argument type. This is accomplished by either: ∗ Exploitation: selecting part of the argument’s type structure to satisfy the function’s typing; ∗ Introduction: wrapping the argument with the type the function requires.
48 Type Coercion
– Exploitation: selecting part of the argument’s type structure to satisfy the function’s typing; – Introduction: wrapping the argument with the type the function requires.
49 Two Kinds of Coercion in Language
– Domain-shifting: The domain of interpretation of the argument is shifted; – Domain-preserving: The argument is coerced but remains within the general domain of interpretation.
50 Domain-Shifting Coercion
– Entity shifts to event: I enjoyed the beer – Entity shifts to proposition: I doubt John.
51 Domain-Preserving Coercion
– Count-mass shifting: There’s chicken in the soup. – NP Raising: Mary and every child came.
52 Domain-Preserving Coercion
– Count-mass shifting: There’s chicken in the soup. – NP Raising: Mary and every child came. Actually, they are all over the place: – Natural-Artifactual shifting: – Natural-Complex shifting: – Complex-Natural shifting: – Artifactual-Natural shifting: – Complex-Artifactual shifting: – Complex-Complex shifting: – Artifactual-Artifactual shifting:
53 Function Application with Natural Types
Function Application: If α is of type eN, and β is of type eN → t, then β(α) is of type t. A natural type tree: t @ @ @@ eN eN → t
54 Pure Selection: Natural Type
The rock fell.
(46) ¨SH ¨¨ HH ¨ H eN NP:eN VP V the rock fell λx: eN [fall(x)]
55 Pure Selection: Natural Type
The rock fell.
(47) ¨SH ¨¨ HH ¨ H eN NP:eN VP V the rock fell λx: eN [fall(x)]
56 Function Application with Artifactual Types
Function Application: If α is of type eA, and β is of type eA → t, then β(α) is of type t. An artifactual type tree: t @ @ @@ eA eA → t
57 Pure Selection: Artifactual Type
The beer spoiled.
(48) ¨SH ¨¨ HH ¨ H NPσ ⊗T τ VP liquid ⊗T drink : eA V the beer spoiled
λx: eA[spoil(x)]
liquid ⊗T drink v σ ⊗T τ
58 Pure Selection: Artifactual Type
The beer spoiled.
(49) ¨SH ¨¨ HH ¨ H NPσ ⊗T τ VP liquid ⊗T drink : eA V the beer spoiled
λx: eA[spoil(x)]
liquid ⊗T drink v σ ⊗T τ
59 Function Application with Complex Types
Function Application: If α is of type eC, and β is of type eC → t, then β(α) is of type t. A complex type tree: t @ @ @@ eC eC → t
60 Pure Selection: Complex Type
John read the book.
(50) ¨VPH ¨¨ HH ¨ H p • i - NP:phys • info V ¨H ¨¨ HH ¨ H read Det N λy : p • i λx: eN [read(x,y)] the book
61 Pure Selection: Complex Type
John read the book.
(51) ¨VPH ¨¨ HH ¨ H p • i - NP:phys • info V ¨H ¨¨ HH ¨ H read Det N λy : p • i λx: eN [read(x,y)] the book
62 Accommodation with Natural Types
Accommodation: If α is of type σ, and β is of type τ → t, then, if σ u τ =6 ⊥, then Acc(β, α) is of type σ u τ → t.
63 Type Accommodation: Natural Types
Mary wiped her hands.
VP (52) ¨H ¨¨ HH ¨ H V [surface]- NP:phys ¨H ¨¨ HH ¨ H wipe Det N body part her hands
64 Type Accommodation: Natural Types
Mary wiped her hands.
VP (53) ¨H ¨¨ HH ¨ H V [surface]- NP:phys ¨H ¨¨ HH ¨ H wipe Det N body part her hands
65 Type Accommodation: Natural Types
Mary wiped her hands.
VP (54) ¨H ¨¨ HH ¨ H V [surface]- NP:phys ¨H ¨¨ HH ¨ H wipe Det N body part her hands
66 Type Coercion: Natural to Artifactual Introduction
The water spoiled.
(55) ¨SH ¨¨ HH ¨ H NP σ ⊗T τ VP liquid : eN V the water spoiled
λx: eA[spoil(x)]
67 Type Coercion: Natural to Artifactual Introduction
The water spoiled.
(56) ¨SH ¨¨ HH σ ⊗T τ¨ H NP σ ⊗T τ VP liquid : eN V the water spoiled
λx: eA[spoil(x)]
68 Type Coercion: Artifactual Accommodation
The water spoiled.
(57) ¨SH ¨¨ HH liquid ⊗T¨τ H NP σ ⊗T τ VP liquid : eN V the water spoiled
λx: eA[spoil(x)]
69 Type Coercion: Natural to Complex Introduction
John read the rumor.
VP (58) ¨H ¨¨ HH ¨phys • info H V - NP:info ¨H ¨¨ HH ¨ H read Det N λy : p • i λx: eN [read(x,y)] the rumor
70 Type Coercion: Natural to Complex Introduction
John read the rumor.
VP (59) ¨H ¨¨ HH phys • info ¨phys • info H V - NP:info ¨H ¨¨ HH ¨ H read Det N λy : p • i λx: eN [read(x,y)] the rumor
71 Type Coercion: Event Introduction
Mary enjoyed her coffee.
VP (60) ¨H ¨¨ HH ¨ H [event] - V NP:liquid ⊗T drink ¨H ¨¨ HH ¨ H [portion]- enjoy Det N [mass] her coffee
72 Type Coercion: Event Introduction
Mary enjoyed her coffee.
VP (61) ¨H ¨¨ HH ¨ H λx.Event(x, NP ) [event] - V NP:liquid ⊗T drink ¨H ¨¨ HH ¨ H [portion]- enjoy Det N [mass] her coffee
73 Type Coercion: Qualia Exploitation
Mary enjoyed her coffee.
VP (62) ¨H ¨¨ HH ¨ H λx.Event(x, NP ) [event] - V NP:liquid ⊗T drink ¨H ¨¨ HH ¨ H [portion]- enjoy Det N [mass] her coffee
74 Type Coercion: Qualia Exploitation
Mary enjoyed her coffee.
VP (63) ¨H ¨¨ HH ¨ H λx.drink(x, NP ) [event] - V NP:liquid ⊗T drink ¨H ¨¨ HH ¨ H [portion]- enjoy Det N [mass] her coffee
75 Type Coercion: Complex Exploitation
The police burned the book.
VP (64) ¨H ¨¨ HH ¨ phys H V - NP:phys • info ¨H ¨¨ HH ¨ H burn Det N λy : physλx: eN [burn(x,y)] the book
76 Type Coercion: Complex Exploitation
The police burned the book.
VP (65) ¨H ¨¨ HH ¨ phys H V - NP:phys • info ¨H ¨¨ HH ¨ H burn Det N λy : physλx: eN [burn(x,y)] the book
77 Type Coercion: Complex Exploitation
Mary believes the book.
VP (66) ¨H ¨¨ HH ¨ info H V - NP:phys • info ¨H ¨¨ HH ¨ H believe Det N λy : physλx: eN [believe(x,y)] the book
78 Type Coercion: Complex Exploitation
Mary believes the book.
VP (67) ¨H ¨¨ HH ¨ info H V - NP:phys • info ¨H ¨¨ HH ¨ H believe Det N λy : physλx: eN [believe(x,y)] the book
79 Types and Composition of Local Contexts: Types
Compositionality mediated through richer selectional mechanisms:
VERB TYPE COMPOSITION Natural Artifactual Complex Selection die(x) fix(x,y) read(x,y) Accommodation wipe(x,hand) spill(beer) burn(x,book) Coercion enjoy(rock) spoil(water) read(x,joke)
80 Types and Composition of Local Contexts: Features
Compositionality mediated through richer selectional mechanisms:
VERB TYPE COMPOSITION Simple Unified Complex Selection die(x) fix(x,y) read(x,y) Accommodation wipe(x,hand) spill(beer) burn(x,book) Coercion enjoy(rock) spoil(water) read(x,joke)
81 That’s all well and good, but...
82 That’s all well and good, but...
What do we actually see in the corpus?
83 Corpus Data on spoil (Patrick Hanks, p.c.)
In both BNC and Associated Press, over 80% of Direct Objects of spoil are Events. Typically, they are Events that one would expect to enjoy. The implicature is that, by spoiling an Event, one kills the enjoyability of it. One might say that spoil is a causative antonym of enjoy. The lexical set of direct objects of spoil include: fun, enjoyment, magic, pleasure, holiday, party, Christmas, birthday, dinner, evening, morning, day, half-hour, event, occasion, view, performance, opera, game, match, ...
84 Plus ¸caChange
(68)a.Mary built a house. b. Mary ate a cookie. (69)a.John closed the door. b. Mary cleaned the table. c. John painted the house. (70)a.People filled the empty hall. b. Mary cleaned the dirty table. (71) The audience left the theatre.
85 Stateless and Event-based Selection
(72)a.Stateless Selection: Selection is performed independent of the operation performed on the argument. Selection is without state information. b. Event-based Selection: Selection is performed over a trace of the operation performed on the argument. Selection is sensitive to the states the argument participates in.
86 Dynamic Typing
(73) Whenever the program α is performed succesfully, φ holds in the discourse. [α]φ (74) It is possible to run the program α such that φ holds in the discourse. hαiφ (75) Given the precondition of ψ, whenever the program α is performed succesfully, φ holds in the discourse. ψ → [α]φ
87 Lexicalizing the statement of change
(76) a. kill: ¬dead(y) → [kill(x, y)]dead(y) b. break: ¬broken(y) → [break(x, y)]broken(y) c. fill: [fill(x, y)]full(y) (77) Stateless Selection a. kill: anim → (eN → t) b. λy : anim λx: eN[kill(x,y)] (78) Stateless Selection with Dynamic Interpretation a. kill: anim → (eN → t) b. λy : anim λx: eN(¬dead(y)[kill(x, y]dead(y))
88 Dynamic Selection
(79)a.Let α¯ refer to the trace of the type α through the event structure, E, associated with the predicate, α¯ → t.
(80) E ¨¨ α → t α → t λyP (y) λyQ(y) 89 Event-based Selection Now a predicate can be represented as two kinds of functional types: (81) a. Stateless: α → t. Reference only to the argument. b. Stateful: α¯ → t. Reference to the trace of the argument through the event structure. (82)a.The temperature is 25 degrees: e → t b. The temperature is rising: e¯ → t 90 Gates Traces let us refer to change as an aspect of the type of the predicate. Hence, a change predicate has a different functional type from a stateless predicate. (83) Gates: Let us define a pair of type operators, p and q, applied over a trace, that initiate or terminate a process or state. We will call the resulting transformations, gating functions. 91 Dynamic Typing (84) Refer to the trace of the argument: If a → b is a type, then a¯ → b is a type. (85) Initiate or terminate the argument: If a¯ → b is a type, then pa → b and aq → b are types. (86) Initiate or terminate a qualia value: If a ⊗ c → b is a type, then a ⊗ pc → b and a ⊗ cq → b are types. (87) Initiate or terminate a dot element: a. If a • c → b is a type, then pa • c → b and aq • c → b are types. 92 Typing the Predicate as a Change (88) Given a discourse where φ holds, the successful performance of the predicate α brings about ¬φ in the discourse. φ → [α]¬φ Now assume that a gate can mark which argument undergoes the update: (89) Gating embeds change into predicate’s type: a. kill: animq → (eN → t) b. λy : animq λx: eN[kill(x,y)] c. ¬dead(y)[kill(x, y)]dead(y) 93 Dynamic Typing (90)a.The door opened. b. The window closed. (91) State Transitions: a. open: phys • paperture → t b. close: phys • apertureq → t (92) ¬open(x)[open]open(x) (93) Predicates as terminating and initiating functions: fill, empty 94 Two-Gate Transitions (94) John gave a book to Mary. (95) State Transitions: a. give: phys → (human ⊗ phave → (human ⊗ haveq → t)) (96) a. have(x, y)[give(x, y, z)]¬have((x, y) b. ¬have(z, y)[give(x, y, z)]have((z, y) 95 Gates Operate over Qualia Structure 1. Gates over Natural animal: be born, die apple: grow, eat 2. Gates over Artifactual prisoner: arrest, escape audience: assemble, disperse cake: bake, eat 96 3. Gates over Complex i. door: p • a: build(p), destroy(p), open(a), close(a) ii. talk: ev • i: begin(ev), end(ev), prepare(i) 97 Coercion with Gates (1) Verbs encode specific gating functions: a. thing: phys b. animal: anim c. die: animq → t (2) Selection with a Gate: a. The animal died. b. λx: animq[die(x)](the animal : anim) (3) Introduction with a Gate: a. The thing died. b. λx: animq[die(x)](the thing: phys) 98 (1) a. man: human b. prisoner: human ⊗ captive c. escape: eN ⊗ captiveq → t (2) Selection with a Gate: a. The prisoner/captive escaped. b. λx: eN ⊗ captiveq[escape(x)] (the prisoner : human ⊗ captive) (3) Introduction with a Gate: a. The man escaped. b. λx: eN ⊗ captiveq[escape(x)] (the man: human) 99 Derivation involving Gating: Introduction 1. Mary cleaned the car. 2. John filled the glass. 3. Mary broke vase. 100 Encoding Change on the Argument (97) John cleaned the car. (98) a. λyλx(clean(x, y)), hy : phys, x: physi b. clean: phys → (phys → t) Encoding the change, we would have the introduction of a gated predicate over the internal argument y: (99) clean: phys ⊗ pclean → (phys → t) 101 Derivation involving Gating: Introduction 1. an escaped prisoner. 2. a former mayor. 3. The mayor released the prisoner. 102 Gate-Introduction an escaped prisoner (100) λP λx∃e[escaped(e, x) ∧ P (e, x)] x: p; escaped: (p ⊗ captiveq → t) → (p ⊗ captiveq → t). (101) λvprisoner(v) : (human ⊗ captive) → t (102) [[escaped]] = λP λxλe2∃e1[¬captive(e2, x) ∧ captive(e1, x) ∧ e1 ≤ e2 ∧ P (e2, x)]; (103) [[prisoner]] = λxλe[human(x, ) ∧ captive(e, x)] 103 (104) Apply Gate Introduction, giving: [[escaped prisoner]] = λxλe2∃e1[¬captive(e2, x) ∧ captive(e1, x) ∧ e1 ≤ e2 ∧ human(e2, x)]; 104 Temporal Adjectives as Gate-Introduction a former boxer (105) former: (p ⊗ Eq → t) → (p ⊗ Eq → t). (106) λvboxer(v) : (human ⊗T box) → t (107) [[former]] = λP λxλe2∃e1[¬P (e2, x) ∧ P (e1, x) ∧ e1 ≤ e2]; (108) [[boxer]] = λxλe[human(x, ) ∧ box(e, x)] (109) Apply Gate Introduction, giving: [[former boxer]] = λxλe2∃e1[¬box(e2, x) ∧ box(e1, x) ∧ e1 ≤ e2 ∧ human(e2, x)]; 105 Remaining Problems and Issues 1. Expressiveness of Type Composition for GL 2. Constraining the Application of Coercion Rules 3. Extending Linguistic Coverage of GL Explanation 106 Conclusion – Lexical Typing is Structured Lexical Decomposition – The Predicate has Structure: ∗ Qualia Structure ∗ Argument Structure ∗ Event Structure – Context is encoded by strong typing – Distinction between selection, coercion, and exploitation – Selection can be treated as typing rather than presupposition. 107 The End Thank You! 108