LX502 Semantics 1. Non-verbal predicates (nouns, adjectives, prepositions) Many nouns and adjectives can be treated in the same way as intransitive verbs. [[ dog ]] = [l x : x Î De . x is a dog] = [l x . x is a dog] “the function that maps every x Î De to 1 if x is a dog and to 0 otherwise” [[ blue ]] = [l x : x Î De . x is blue] = [l x . x is blue] S [[ Bruce ]] = Bruce – TN NP1 VP [[ boy ]] = [l x . x is a boy] – by TN [[ VP ]] = [[ DP ]] = [[ NP ]] = [[ N ]] = [[ boy ]] – by NN N V DP 2 [[ NP1 ]] = [[ N ]] = [[ Bruce ]] – by NN D NP Bruce is 2 [[ S ]] = [[ VP ]] ( [[ NP1 ]] ) – by FA = [l x . x is a boy] ( Bruce ) a N = 1 iff Bruce is a boy boy Transitive nouns, adjectives, and prepositions are analogous to transitive verbs [[ fond ]] = [l x . [l y . y is fond of x]] [[ part ]] = [l x . [l y . y is part of x]] [[ in ]] = [l x . [l y . 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 ]] Ç [[ in Texas ]] intersective modifier
DP [[ city ]] = l x . x is a city – by TN D NP [[ Texas ]] = Texas – by TN [[in]] = l x . [l y . y is in x] – by TN N PP a [[PP]] = [[P]] ( [[NP2]] ) – by FA P NP = l x . [l . y is in x] (Texas) city = l y . y is in Texas [[N]] = [[ city ]] = l x . x is a city – by NN in N [[NP]] = ?? Texas Predicate Modification (PM) If a is a branching node with daughters { b, g }, and [[ b ]] and [[ g ]] are both in D
3. Non-intersective modifiers D NP D NP (4) Felix is a gray cat N N’ = Felix is gray and Felix is a cat a AP a AP (5) Felix is a gray cat entails Felix is a gray animal N A cat A AP (6) Fievel is a big mouse =? Fievel is big and Fievel is a mouse gray smart A cat (7) Fievel is a big mouse entails? Fievel is a big animal gray 1 LX502 Semantics
[[ big ]] = [l f : f Î D
[[ gray ]] = [l f : f Î D
[[the]] is a function applied to a predicate (a function) to yield an individual: f: D
(8) [[the]] = [l f : f Î D
(8)'[[the]] = [l f : f Î D
(11)The domain of [[the]] contains just those functions f Î D
Homework: Exercise p. 66: Kaline is a [ [ [ gray cat ] in Texas ] fond of Joe ] Exercise 1, p. 79 Exercise 2, p. 80
Readings of interest: Hintikka, J. and Kulas, J. (1985). Anaphora and definite descriptions: Two applications of game-theoretical semantics. Dordrecht: Reidel. Maratsos, M. P. (1976). The use of definite and indefinite reference in young children: An experimental study 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.
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