LX502 Semantics

1

NP

N

NP

N

city

Texas

PP

P

in

DP

D

a

NP2

N

boy

DP

D

a

NP1

S

VP

VN

Bruce is

AP

A

NP

N

cat

gray

DP

D

aAP

A

NP

smart

DP

D

a

AP

A

N’

N

cat

gray

1. Non-verbal predicates (nouns, adjectives, prepositions)Many nouns and adjectives can be treated in the same way as intransitive verbs.

[[ dog ]] = [λx : x ∈ De . x is a dog] = [λx . x is a dog]“the function that maps every x ∈ De to 1 if x is a dog and to 0 otherwise”

[[ blue ]] = [λx : x ∈ De . x is blue] = [λx . x is blue]

[[ Bruce ]] = Bruce – TN[[ boy ]] = [λx . x is a boy] – by TN[[ VP ]] = [[ DP ]] = [[ NP2 ]] = [[ N ]] = [[ boy ]] – by NN[[ NP1 ]] = [[ N ]] = [[ Bruce ]] – by NN[[ S ]] = [[ VP ]] ( [[ NP1 ]] ) – by FA = [λx . x is a boy] ( Bruce ) = 1 iff Bruce is a boy

Transitive nouns, adjectives, and prepositions are analogous to transitive verbs[[ fond ]] = [λx . [λy . y is fond of x]][[ part ]] = [λx . [λy . y is part of x]][[ in ]] = [λx . [λy . y is in x]]

2. Predicates as restrictive modifiers in NP(1) a part [PP of Asia] (argument)(2) a city [PP in Texas] (restrictive modifier/adjunct)(3) Bruce, [PP from New Jersey] (nonrestrictive modifier)

[[ city in Texas ]] = [[ city ]] ∩ [[ in Texas ]] intersective modifier

[[ city ]] = λx . x is a city – by TN[[ Texas ]] = Texas – by TN[[in]] = λx . [λy . y is in x] – by TN

[[PP]] = [[P]] ( [[NP2]] ) – by FA= λx . [λ. y is in x] (Texas)= λy . y is in Texas

[[N]] = [[ city ]] = λx . x is a city – by NN

[[NP]] = ??

Predicate Modification (PM)If α is a branching node with daughters { β, γ }, and [[ β ]] and [[ γ ]] are both in D<e,t>(both are functions of type <e,t>), then [[ α ]] = λx ∈ De . [ [[ β ]](x) = [[ γ ]](x) = 1].

[[NP]] = λx . [ [[N]](x) = [[PP]](x) = 1 ]= λx . [ λx . x is a city](x) = [λy . y is in Texas](x) = 1= λx . [ x is a city = x is in Texas = 1 ]

3. Non-intersective modifiers(4) Felix is a gray cat

= Felix is gray and Felix is a cat(5) Felix is a gray cat entails Felix is a gray animal(6) Fievel is a big mouse

=? Fievel is big and Fievel is a mouse(7) Fievel is a big mouse entails? Fievel is a big animal

LX502 Semantics

2

[[ big ]] = [λf : f ∈ D<e,t> . [λx : x ∈ De . f(x) = 1 and the size of x is big]]

[[ big ]] = [λf : f ∈ D<e,t> . [λx : x ∈ De . f(x) = 1 and the size of x is above theaverage size of the elements of {y : f(y) = 1} ]]

[[ gray ]] = [λf : f ∈ D<e,t> . [λx : x ∈ De . f(x) = 1 and x is gray]]

[[ small ]] = [λx : x ∈ De . the size of x is below that of the contextually salient standard ]

4. Definite determiners

[[the]] is a function applied to a predicate (a function) to yield an individual: f: D<e,t> à De[[the]] applied to [[dog]] yields “the dog Rover”[[the]] applied to [[president of the USA]] yields “Clinton”

Uniqueness presupposition: a definite DP presupposes that there exists a single unique individual(in the utterance context) denoted by the DP.

(8) [[the]] = [λf : f ∈ D<e,t> & there is exactly one x s.t. f(x) = 1 . the unique y s.t. f(y) = 1 ]

(8)'[[the]] = [λf : f ∈ D<e,t> & there is exactly one x ∈ Ce s.t. f(x) = 1 .the unique y ∈ C s.t. f(y) = 1, where Ce is a contextually salient subset of De

(9) I will meet you at the elevator in CAS.(10)I will meet you at the escalator in CAS.

(11)The domain of [[the]] contains just those functions f ∈ D<e, t> which satisfy the condition thatthere is exactly one x for which f(x) = 1 (in the utterance context).

(12)A partial function from A to B is a function from a subset of A to B.

(13)John is on the escalator in CAS.

(14) α is uninterpretable if it can be proved from the semantics alonethat α is outside the domain of [[ ]].

(15) α is a presupposition failure if it is a contingent matter of factthat α is outside the domain of [[ ]].

Homework:Exercise p. 66: Kaline is a [ [ [ gray cat ] in Texas ] fond of Joe ]Exercise 1, p. 79Exercise 2, p. 80

Readings of interest:

Hintikka, J. and Kulas, J. (1985). Anaphora and definite descriptions: Two applications of game-theoreticalsemantics. Dordrecht: Reidel.

Maratsos, M. P. (1976). The use of definite and indefinite reference in young children: An experimentalstudy of semantic acquisition. Cambridge: Cambridge University Press.

Partee, B. H. (1995). Lexical semantics and compositionality. In L.R. Gleitman and M. Liberman(Eds.), Language. An invitation to cognitive science. 2nd edition (Vol. 1, pp. 311-360). Cambridge,MA: MIT Press.

Partee, B. H., ter Meulen, A., & Wall, R.E. (1990). Mathematical methods in linguistics.Dordrecht/Boston: Kluwer.