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Intersective and Subsective Adjectives Ling 5205: Semantics

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Intersective and Subsective Adjectives Ling 5205: Semantics Outline Attributive uses of adjectives Practice Summary References Intersective and subsective adjectives Ling 5205: Semantics Brian Reese Institute of Linguistics University of Minnesota [email protected] 1 / 32 Outline Attributive uses of adjectives Practice Summary References 1 Attributive uses of adjectives 2 Practice 3 Summary 2 / 32 Outline Attributive uses of adjectives Practice Summary References 1 Attributive uses of adjectives 2 Practice 3 Summary 3 / 32 Outline Attributive uses of adjectives Practice Summary References Modificational adjectives So far we have considered only predicative occurrences of adjectives; but adjectives also occur before nouns in attributive, or modificational, uses. Examples (1) a. Tina is tall. (Predicative) b. Thin is thin. (2) a. Tina is a tall woman. (Modificational) b. The tall engineer visited us. c. I met five tall astronomers. 4 / 32 Outline Attributive uses of adjectives Practice Summary References Modificational adjectives In many cases there are strong semantic relations between modificational and predicative uses of adjectives. (We will focus on the equivalence in 3a.) Examples (3) a. Tina is a Chinese pianist , Tina is Chinese and Tina is a pianist. b. My doctor wears no white shirts , No shirts that my doctor wears are white. c. Dan saw six carnivorous animals , Six animals that Dan saw are carnivorous. 5 / 32 Outline Attributive uses of adjectives Practice Summary References New semantic assumptions Common nouns denote et functions; indefinite article a when used in predicative NPs denotes the identity function on et functions. Examples (4) Tina [ is [ a pianist]] (5) a. pianist = pianistet J K b. a = a(et)(et) = is = λget:g J K (6) (is(a(pianist)))(tina) = pianist(tina) = 1 if tina 2 pianist∗ and 0 otherwise 6 / 32 Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (7) Tina [ is [ a [ Chinese pianist ]]] a *type-mismatch* a(et)(et) Chinese pianist chineseet pianistet Problem: We have no way to compose two et functions into an et function using function application. 7 / 32 Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Two ways to resolve the type mismatch: Introduce a new compositional rule that lets us combine two et functions (cf. Heim & Kratzer's Predicate Modification); Assume an additional (et)(et) denotation for Chinese. Examples (8) a. chinese : et (Predicative) b. chinesemod :(et)(et) (Modificational) 8 / 32 Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Entailments in (3a) suggest defining modificational uses of Chinese in terms of its predicative denotation and propositional conjunction. Intuitively (9) is the function mapping any set X to the intersection of X with the set of Chinese entities. Examples (3a) Tina is a Chinese pianist , Tina is Chinese and Tina is a pianist. , Tina is Chinese and a pianist. mod (9) chinese(et)(et) = λfet.λxe:chinese(x) ^ f(x) 9 / 32 = (chinesemod(pianist))(tina) . applying is and a (identity functions) = ((λfet.λxe:chinese(x) ^ f(x))(pianist))(tina) . definition of chinesemod = (λxe:chinese(x) ^ pianist(x))(tina) . application to pianist = chinese(tina) ^ pianist(tina) . application to tina We immediately account of the equivalence in (3a)! Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (10) (is(a(chinesemod(pianist))))(tina) . compositional analysis 10 / 32 = ((λfet.λxe:chinese(x) ^ f(x))(pianist))(tina) . definition of chinesemod = (λxe:chinese(x) ^ pianist(x))(tina) . application to pianist = chinese(tina) ^ pianist(tina) . application to tina We immediately account of the equivalence in (3a)! Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (10) (is(a(chinesemod(pianist))))(tina) . compositional analysis = (chinesemod(pianist))(tina) . applying is and a (identity functions) 10 / 32 = (λxe:chinese(x) ^ pianist(x))(tina) . application to pianist = chinese(tina) ^ pianist(tina) . application to tina We immediately account of the equivalence in (3a)! Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (10) (is(a(chinesemod(pianist))))(tina) . compositional analysis = (chinesemod(pianist))(tina) . applying is and a (identity functions) = ((λfet.λxe:chinese(x) ^ f(x))(pianist))(tina) . definition of chinesemod 10 / 32 = chinese(tina) ^ pianist(tina) . application to tina We immediately account of the equivalence in (3a)! Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (10) (is(a(chinesemod(pianist))))(tina) . compositional analysis = (chinesemod(pianist))(tina) . applying is and a (identity functions) = ((λfet.λxe:chinese(x) ^ f(x))(pianist))(tina) . definition of chinesemod = (λxe:chinese(x) ^ pianist(x))(tina) . application to pianist 10 / 32 We immediately account of the equivalence in (3a)! Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (10) (is(a(chinesemod(pianist))))(tina) . compositional analysis = (chinesemod(pianist))(tina) . applying is and a (identity functions) = ((λfet.λxe:chinese(x) ^ f(x))(pianist))(tina) . definition of chinesemod = (λxe:chinese(x) ^ pianist(x))(tina) . application to pianist = chinese(tina) ^ pianist(tina) . application to tina 10 / 32 Outline Attributive uses of adjectives Practice Summary References Modificational adjectives Example (10) (is(a(chinesemod(pianist))))(tina) . compositional analysis = (chinesemod(pianist))(tina) . applying is and a (identity functions) = ((λfet.λxe:chinese(x) ^ f(x))(pianist))(tina) . definition of chinesemod = (λxe:chinese(x) ^ pianist(x))(tina) . application to pianist = chinese(tina) ^ pianist(tina) . application to tina We immediately account of the equivalence in (3a)! 10 / 32 (12) a. Tina is a Chinese pianist and a biologist. b. Tina is a Chinese biologist and a pianist. (13) (C \ P ) \ B = C \ (P \ B) Associative Law = C \ (B \ P ) Commutative Law = (C \ B) \ P Associative Law Outline Attributive uses of adjectives Practice Summary References Intersective adjectives Because the analysis involves intersecting the noun denotation with the predicative adjective denotation, these adjectives are called intersective. Examples (11) Chinese pianist = λxe:chinese(x) ^ pianist(x) J K = chinese∗ \ pianist∗ 11 / 32 Outline Attributive uses of adjectives Practice Summary References Intersective adjectives Because the analysis involves intersecting the noun denotation with the predicative adjective denotation, these adjectives are called intersective. Examples (11) Chinese pianist = λxe:chinese(x) ^ pianist(x) J K = chinese∗ \ pianist∗ (12) a. Tina is a Chinese pianist and a biologist. b. Tina is a Chinese biologist and a pianist. (13) (C \ P ) \ B = C \ (P \ B) Associative Law = C \ (B \ P ) Commutative Law = (C \ B) \ P Associative Law 11 / 32 Outline Attributive uses of adjectives Practice Summary References Summary: intersection adjectives The entailments below follow from the mathematical connection between set-intersection and propositional conjunction. Examples (14) a. Tina is a Chinese pianist. b. Tina is Chinese and a pianist. c. Tina is Chinese and Tina is a pianist. (15) a. Tina is a Chinese pianist and a biologist. b. Tina is a Chinese biologist and a pianist. 12 / 32 Outline Attributive uses of adjectives Practice Summary References Intersective adjectives So far assumed that predicative denotations are basic and derived modificational denotations from them. In some languages modificational adjectives are more marked than their predicative counterparts (Krifka 1999). Examples (16) a. Der Apfel ist gelb. The apple is yellow. b. Der gelbe Apfel liegt auf dem Tisch. The yellow apple is on the table. 13 / 32 Outline Attributive uses of adjectives Practice Summary References Intersective adjectives We could assume that this extra morphology marks the application of a type shifting rule or assign the morphology a separate denotation. Examples mod (17) For any et adjective denotation f, f = λget.λxe:f(x) ^ g(x) (Type shifting rule) (18) -e = attr(et)((et)(et)) = λfet.λget.λxe:f(x) ^ g(x) J K (19) -e ( gelb ) J K J K = (λfet.λget.λxe:f(x) ^ g(x))(yellowet) = λget.λxe:yellow(x) ^ g(x) = yellowmod 14 / 32 Outline Attributive uses of adjectives Practice Summary References Non-intersective entailments Not all modificational adjectives are intersective; e.g. (20a) can be true while (20d) is false. Do not intersect the set of pianists with the set of skillful entities. Examples (20) a. Tina is a skillful pianist and a biologist. b. ) Tina is a pianist. c. ) Tina is a biologist. d. 6) Tina is a skillful biologist and a pianist. 15 / 32 Outline Attributive uses of adjectives Practice Summary References Non-intersective adjectives To analyze these adjectives, we assume basic (et)(et) denotations. Denote arbitrary functions from sets of entities to sets of entities; the output of such functions need not be formed by intersection. Example pianistet : characterizes the singleton set ftinag biologistet : characterizes the set ftina; maryg skillful (et)(et) (pianist): characterizes the singleton set ftinag J K skillful (et)(et) (biologist): characterizes the singleton set fmaryg J K 16 / 32 Subsective modification For any model M, the denotation of skillful in M is an (et)(et) function skillfulmod such that for every et function f in M, the set characterized by skillfulmod(f) is a subset of the set characterized
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