A semantic intro

1. A semantic intro

2. Intuition I

3. John is playing guitar. predicate individual proposition

4. The guy is playing guitar. predicate individual proposition

5. A guy is playing guitar. predicate individual proposition

6. The intuition that proper names, definite and indefinite DPs refer to individuals is very strong in semantic theories like DRT where we have a level of representation in which we keep track of the individuals that have been introduced.

7. The semantics of Ds and DPs in GQT

8. x y z v John came in. He saw a guy. x = John come in(x) The guy was happy. x = y guy(z) see(x,z) v = z guy(z) happy(z)

9. Intuition II

10. A boywas unhappy boy unhappy A creates a relation between two sets. It signals that there’s at least one element in the intersection.

11. Every light (in the christmas tree) was burning. light burn Every creates a relation between two sets. It signals that all elements of the first set are also part of the second set.

12. The intuition that determiners create relations between sets is the basis for Generalized Quantifier Theory. Unlike DRT, Generalized Quantifier Theory has no level of representation that keeps track of the individuals that have been introduced. We call DRT a dynamic theory of meaning whereas Generalized Quantifier Theory is taken to be a static theory of meaning.

13. The semantics of Ds and DPs in GQT

14. A boy was unhappy. x (boy(x) & unhappy(x)) There’s at least one individual x who is a boy and who is unhappy. There’s at least one individual x who is in the intersection of the set of boys and unhappy individuals.

15. A boy was unhappy. x (boy(x) & unhappy(x)) I II This is what lambda’s do for us!

16. A boy was unhappy. PQx (P(x) & Q(x)) I PQx (P(x) & Q(x)) (boy) II Qx (boy(x) & Q(x)) (unhappy) x (boy(x) & unhappy(x))

17. Every light was burning. PQx (P(x) → Q(x)) I PQx (P(x) → Q(x)) (light) II Qx (light(x) →Q(x)) (burn) x (light(x) → burn(x))

18. Comparing the two intuitions

19. Individual x Predicate = Proposition entity ??? truth value Predicate = Proposition / Individual “almost a proposition but it still needs an individual” “a function that takes an individual and returns a proposition” <e,t>

20. Individual x Predicate = Proposition e t <e,t> output input In our GQT overview we didn’t look at predicates as functions but rather as sets. This is however a simple matter of perspective and we will assume that sets are of type <e,t>.

21. A boy was unhappy x (boy(x) & unhappy(x)) t A boy Qx (boy(x) & Q(x)) < <e,t> , t > A PQx (P(x) & Q(x)) <e,t> , <e,t> > < < , t >

22. Discussion Whereas a DRT analysis takes a boy to be an expression of type e, a GQT analysis takes a boy to be an expression of type <<e,t>,t>. In both analyses a boy will be able to combine with predicates (of type <e,t>) and give rise to a proposition: e x <e,t> = t <<e,t>,t> x <e,t> = t How to decide which intuition is correct?

23. Discussion Do we have to decide? We can assume that DPs like a boy have a basic type but can shift from one type to another on the basis of well defined type-shift rules. This is the basis for the theory of type-shifting to which we return after we discuss Longobardi.

24. Recap Carlson > BP is not the plural counterpart of a > BPis not even a normal indefinite > BPs refer to kinds and the context decides whether you get the kind or an existential reading. > existential readings are obtained through a realization operation baked into predicates > the whole story hinges on scope facts

25. Narrow and wide scope of a boy Assumption Negation can apply at the predicate level or at the sentence level. This allows us to derive a narrow and a wide scope reading for a boy in combination with the predicate to play and negation. N.B. The preferred realizations of the corresponding sentences differ: with narrow scope we would normally say No boy was playing whereas with wide scope we would probably say There was a boy who wasn’t playing. For the sake of illustration I will however present the analysis as if we were analyzing a boy wasn’t playing.

26. Indefinites (predicate level negation) not to play x (-play (x)) <e,t> a boy Qy(boy(y)&Q(y)) <<e,t>,t> Qy(boy(y)&Q(y)) x (–play(x)) Qy(boy(y)&Q (y)) x (–play(x)) x (–play(x)) y(boy(y)&x(-play(x )) (y)) y y(boy(y)&-play(y))

27. Indefinites (sentence level negation) to play x(play(x)) <e,t> a boy Qy(boy(y)&Q(y)) <<e,t>,t> Qy(boy(y)&Q(y)) x (play(x)) Qy(boy(y)&Q (y)) x (play(x)) x (play(x)) y(boy(y)&x(play(x )) (y)) y y(boy(y)&play(y)) - y(boy(y)&play(y))

28. Bare plurals (predicate level negation) not to play xk(-y(R(y,xk)&play(y)) <e,t> boys boyk e xk(-y(R(y,xk)&play(y)) boyk xk(-y(R(y,xk )&play(y)) boyk boyk

29. Longobardi(as treated in Dayal)

30. Some background >syntactician >Italian (works at Trieste) >interested in the structure of DPs (cf. Abney 1987) DP NP D’ DP N’ D NP D’ N N’ D N

31. Expletive articles > In certain contexts, the definite article doesn’t seem to add anything to the semantics. > The reason it appears in these contexts seems to be tied only to syntax. Longobardi assumes this to be the case with: > proper names The John, The Mary, ... (Greek champions these uses) > kind referring nouns

32. Italian proper names Il mio Gianni ha finalmente telefonato. the my John has finally called My Johnny finally called. *Mio Gianni ha finalmente telefonato. my John has finally called My Johnny has finally called. Gianni mio ha finalmente telefonato. John my has finally called My Johnny has finally called

33. Italian proper names def + poss + name Il mio Gianniha finalmente telefonato. the my John has finally called My Johnny finally called. *Mio Gianniha finalmente telefonato. my John has finally called My Johnny has finally called. Gianni mio ha finalmente telefonato John my has finally called My Johnny has finally called Proposal: il occupies a position that... ... has to be filled ... cannot be filled by mio ... but can be filled by moving Gianni to it poss + name

34. Italian proper names def + poss + name Il mio Gianniha finalmente telefonato. the my John has finally called My Johnny finally called. *Mio Gianniha finalmente telefonato. my John has finally called My Johnny has finally called. Gianni mioha finalmente telefonato John my has finally called My Johnny has finally called Proposal: il occupies a position that... ... has to be filled ... cannot be filled by mio ... but can be filled by moving Gianni to it poss + name evidence for the DP hypothesis ! name + poss

35. English proper names *The my Johnnyha finalmente telefonato. the my Johnhas finally called My Johnnyfinally called. My Johnnyha finalmente telefonato. my John has finally called My Johnnyhas finally called. *Johnny myha finalmente telefonato John my has finally called My Johnny has finally called Proposal: the occupies a position that... ... hasn’t got to be filled ... and therefore shouldn’t be filled ... consequently the moving of Johnny to it is not allowed

36. Italian vs. English proper names ITALIAN ENGLISH Proposal: il occupies a position that... ... has to be filled ... cannot be filled by mio ... but can be filled by moving Gianni to it Proposal: the occupies a position that... ... hasn’t got to be filled ... and therefore shouldn’t be filled ... consequently the moving of Johnny to it is not allowed parameter distinguishing between Italian and English type languages

37. English kind referring nouns *The big dogs bark. Big dogs bark. *Dogs big bark. Proposal: the occupies a position that... ... hasn’t got to be filled ... and therefore shouldn’t be filled ... consequently the moving of dogs to it is not allowed

38. Italian kind referring nouns I grandi cani abbaiano the big dogs bark Big dogs bark. *Grandi cani abbaiano big dogs bark Big dogs bark. *Cani grandi abbaiano dogs big bark Big dogs bark. Proposal: i occupies a position that... ... has to be filled ... cannot be filled by grandi ... cannot be filled by cani

39. Italian proper names vs. kind referring nouns ITALIAN KIND REFERRING Ns ITALIAN PROPER NAMES Proposal: i occupies a position that... ... has to be filled ... cannot be filled by grandi ... cannot be filled by cani Proposal: il occupies a position that... ... has to be filled ... cannot be filled by mio ... but can be filled by moving Gianni to it Only proper names can raise to D.

40. Longobardi: recap UNIVERSAL In order to refer (in argument position) NPs have to be associated with a D. The association with D can be made in syntax or at LF. PARAMETER This association can be made by adding an (overt or covert) D or by moving the noun to D. The latter option is only available for nouns that intrinsically refer to an individual (i.e. proper names). In Italian the association is made in syntax. SETTING SETTING In English the association is made at LF.

41. Longobardi: a small caveat Ho mangiato biscotti. I_have eaten biscuits I ate biscuits. ! Proposal: In ‘properly governed positions’ a null determiner can be inserted into D. = everywhere except in preverbal subject position

42. Type shifting

43. Type-shifting ? Types ? Types... two basic types: - individuals (type e) - truth values (type t) Hu Jintao is president. e x <e,t> = t TRUE! Hu Jintao president(s) type e type <e,t>

44. Type-shifting ? Types ? Types... two basic types: - individuals (type e) - truth values (type t) Hu Jintao [smile]. e x <e,t> = t TRUE! Hu Jintao smile type e type <e,t>

45. Type-shifting ? Types ? Types... two basic types: - individuals (type e) - truth values (type t) President(s) [smile]. <e,t> x <e,t> = ? OOPS... president(s) smile type <e,t> type <e,t>

46. Type-shifting ? Types ? Type-shifting... xPresident(x)  Qx[President(x)&Q(x)] type <<e,t>,t> xPresident(x)  x[President(x)] type e xPresident(x)  KINDx[President(x)] president(s) type <e,t> type e

47. Type-shifting ? Types ? Type-shifting... Qx[President(x)&Q(x)] type <<e,t>,t> x[President(x)] Presidents [smile]. type e <<e,t>,t> x <e,t> = t KINDx[President(x)] e x <e,t> = t smile type e type <e,t>

48. Type-shifting ? Types ? Type-shifting... Can we do whatever we want? NO! Two constraints: THOU SHALT NOT shift unless needed. THOU SHALT NOT shift covertly if Thou hast a determiner that makes the same shift overtly. = Blocking Principle

49. Type-shifting ? Types ? Type-shifting... Qx[President(x)&Q(x)] type <<e,t>,t> x[President(x)] Presidents [smile]. type e <<e,t>,t> x <e,t> = t KINDx[President(x)] e x <e,t> = t smile type e type <e,t>

50. Type-shifting ? Types ? Type-shifting... Hu Jintao the president Hu Jintao (is) the president type e type e type e type e x =? IDENT xPresident(x)  y[y=xPresident(x)] Hu Jintao (is) the president type e type <e,t> x = t type <e,t>