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<e,t> (both are functions of type <e,t>), then [[ a ]] = l x Î De . [ [[ b ]](x) = [[ g ]](x) = 1]. [[NP]] = l x . [ [[N]](x) = [[PP]](x) = 1 ] = l x . [ l x . x is a city](x) = [l y . y is in Texas](x) = 1 = l x . [ x is a city = x is in Texas = 1 ] DP DP 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<e,t> . [l x : x Î De . f(x) = 1 and the size of x is big]] [[ big ]] = [l f : f Î D<e,t> . [l x : x Î De . f(x) = 1 and the size of x is above the average size of the elements of {y : f(y) = 1} ]] [[ gray ]] = [l f : f Î D<e,t> . [l x : x Î De . f(x) = 1 and x is gray]] [[ small ]] = [l x : x Î 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]] = [l f : f Î D<e,t> & there is exactly one x s.t. f(x) = 1 . the unique y s.t. f(y) = 1 ] (8)'[[the]] = [l f : f Î D<e,t> & there is exactly one x Î Ce s.t. f(x) = 1 . the unique y Î 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 Î D<e, t> which satisfy the condition that there 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) a is uninterpretable if it can be proved from the semantics alone that a is outside the domain of [[ ]]. (15) a is a presupposition failure if it is a contingent matter of fact that a is outside the domain of [[ ]]. 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. 2.