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]

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1 Attributive uses of adjectives

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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 ∈ 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 {tina}

biologistet : characterizes the set {tina, mary}

skillful (et)(et) (pianist): characterizes the singleton set {tina} J K skillful (et)(et) (biologist): characterizes the singleton set {mary} 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 by f.

Outline Attributive uses of adjectives Practice Summary References Non-intersective adjectives

Must still account for the entailment in (21); adjectives exhibiting this entailment are called subsective (or restrictive). What (21) tells us is that skillful (pianist) cannot be any set of entities; it must be some subsetJ ofK the set of pianists.

Example

(21) Tina is a skillful pianist ⇒ Tina is a pianist.

17 / 32 Outline Attributive uses of adjectives Practice Summary References Non-intersective adjectives

Must still account for the entailment in (21); adjectives exhibiting this entailment are called subsective (or restrictive). What (21) tells us is that skillful (pianist) cannot be any set of entities; it must be some subsetJ ofK the set of pianists.

Example

(21) Tina is a skillful pianist ⇒ Tina is a pianist.

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 by f.

17 / 32 Outline Attributive uses of adjectives Practice Summary References Subsective modification

Winter analyzes subsective entailments by combining an analysis in terms of arbitrary (et)(et) functions with an intersective analysis. skillfularb is not the denotation of the word skillful; it’s an arbitrary function we make use of in our analysis.

Examples

(22) Let skillfularb be an arbitrary (et)(et) function.

mod arb (23) skillful = λfet.λxe.(skillful (f))(x) ∧ f(x)

18 / 32 Outline Attributive uses of adjectives Practice Summary References Subsective modification

Example

(24) (is(a(skillfulmod(pianist))))(tina) . compositional analysis

= (skillfulmod(pianist))(tina) . applying is and a

arb = ((λfet.λxe.(skillful (f))(x) ∧ f(x))(pianist))(tina) . definition (23)

arb = (λxe.(skillful (pianist))(x) ∧ pianist(x))(tina) . application to pianist

= skillfularb(pianist)(tina) ∧ pianist(tina) . application to tina

19 / 32 Outline Attributive uses of adjectives Practice Summary References Subsective modification

The analysis accounts for the subsective entailment in (21) and the lack of entailment between (20a) and (20d).

Examples

(25) a. Tina is a skillful pianist. b. skillfularb(pianist)(tina) ∧ pianist(tina)

(26) a. Tina is a skillful pianist and a biologist. b. skillfularb(pianist)(tina) ∧ pianist(tina) ∧ biologist(tina)

(27) a. Tina is a skillful biologist and a pianist. b. skillfularb(biologist)(tina) ∧ biologist(tina) ∧ pianist(tina)

20 / 32 Outline Attributive uses of adjectives Practice Summary References Intersective and subsective modification

Categorize an adjective A as intersective or subsective based on the entailments A supports; let X be a proper name and N a common noun.

A is intersective – X is a AN ⇔ X is A and X is a N e.g. Dan is a Dutch man ⇔ Dan is Dutch and Dan is a man A is subsective – X is a AN ⇒ X is N e.g. Dan is a skillful pianist ⇒ Dan is a pianist

For a function F from ℘(E) to ℘(E) we define: F is intersective – There is a set A, s.t. for every set B: F (B) = A ∩ B. F is subsective – For every set B: F (B) ⊆ B.

21 / 32 Outline Attributive uses of adjectives Practice Summary References Intersective and subsective adjectives

Classifying adjectives as intersective or subsective is a complex problem both empirically and theoretically. Denotation of many adjectives is highly context-dependent.

Examples

(28) a. Tina is a tall child ⇒? Tina is tall.

b. Tina is a thin hippo ⇒? Tina is thin.

(29) Tina is a child and she is tall.

(30) a. The children in the kindergarten built a tall snowman. b. The children in the senior high school built a tall snowman. (Krifka 1999)

22 / 32 Outline Attributive uses of adjectives Practice Summary References Intersective and subsective modification

As semantic concepts, subsective and intersective functions apply to other lexical categories and syntactic constructions.

Examples

(31) a. Tina [smiled [charmingly]] ⇒ Tina smiled. b. Tina [ran [with John]] ⇒ Tina ran.

(32) a. Tina [is [a [pianist [from Rome]]]] ⇔ Tina is a pianist and Tina is from Rome. b. Tina [is [a [pianist [who [praised herself]]]]] ⇔ Tina is a pianist and Tina praised herself.

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24 / 32 Outline Attributive uses of adjectives Practice Summary References Practice

Account for the entailment between (33a) with the adverb charmingly and (33b):

(i) Describe the restriction on the adverb’s denotation by completing the following: the function charmingly of type maps any set A characterized by to .

(ii) Account for the same entailment by postulating a λ-term for charmingly in terms of an arbitrary function charminglyarb.

(iii) Simplify the λ-terms for the two sentences and explain why the ≤ relation must hold between them in every model.

Example

(33) a. Tina smiled charmingly. b. Tina smiled.

25 / 32 Outline Attributive uses of adjectives Practice Summary References Practice

Repeat the analysis for the sentences below.

(i) The function with of type maps any entity to a function mapping any characteristic function χA to . (ii) Postulate a λ-term for with in terms of an arbitrary function witharb.

(iii) Simplify the terms you get for the sentences.

Examples

(34) a. Tina ran with John. b. Tina ran.

26 / 32 Outline Attributive uses of adjectives Practice Summary References Practice

Account for the equivalence between the sentences below by defining the denotation from. Note that given the entailment patterns below from Rome is an intersective modifier. We therefore define its modificational use in terms of a basic predicative use. What is the type of from, what lambda expression do we assoicate with it? Give derivations establishing the equivalence below.

Examples

(35) a. Tina is a pianist from Rome. b. Tina is a pianist and Tina is from Rome.

27 / 32 Outline Attributive uses of adjectives Practice Summary References Practice

Account for the entailments below by postulating proper restrictions on the denotation of the word very. We need to assume versions of very with two different types. What are these types? Give the restriction for both types.

Examples

(36) a. Tina is very tall ⇒ Tina is tall. b. Tina is a very tall student ⇒ Tina is a tall student.

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29 / 32 Outline Attributive uses of adjectives Practice Summary References Lexical denotations

Constant denotations: given by definition and do not vary between models; function words Combinators; defined via their workings on other functions with no further definitions; is, herself Logical; defined by means of additional concepts, e.g. propositional negation and conjunction; not, andt, andet.

Arbitrary denotations: denotations vary between models; content words Arbitrary denotations: no restrictions hold within models other than those imposed by their types; tina, pianist, smile, etc. Denotations defined on the basis of other arbitrary denotations; modificational adjectives like skillfulmod

30 / 32 Outline Attributive uses of adjectives Practice Summary References Lexical denotations and their restrictions

Denotation Type Restrictions Category tina e – proper name smile et – intransitive verb praise e(et) – transitive verb pianist et – common noun chinese et – predicative adjective mod chinese (et)(et) intersective: λfet.λxe. modificational adjective chinese(x) ∧ f(x) mod skillful (et)(et) subsective: λfet.λxe. modificational adjective (skillfularb(f))(x) ∧ f(x) is (et)(et) combinator: λget.g copula (auxiliary verb) a (et)(et) combinator: λget.g indefinite article herself (e(et))(et) combinator: reflexive pronoun λRe(et).λxe.R(x)(x) not (et)(et) logical: λget.λxe. ∼(g(x)) prediate negation t and t(tt) logical: λxy.λyt.y ∧ x sentential conjunction andet (et)((et)(et)) logical: predicate conjunction λfet.λget.λxe.g(x) ∧ f(x)

31 / 32 Outline Attributive uses of adjectives Practice Summary References ReferencesI

Heim, Irene & Angelika Kratzer. 1998. Semantics in generative grammar. Blackwell. Krifka, Manfred. 1999. Introduction to semantics. Lecture notes, LIN-380M, University of Texas at Austin. Winter, Yoad. 2016. Elements of formal semantics: An introduction to the mathematical theory of meaning in natural language. Edinburgh University Press.

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