Propositions and rigidity in Layered DRT

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1 Propositions and rigidity in Layered DRT Emar Maier and Bart Geurts University of Nijmegen ESSLLI 2003 Workshop Direct Reference and Specificity 19th August 2003

2 1 Kripke/Kaplan on rigid terms names and indexicals are directly referential/rigid designators wide-scope behavior w.r.t. operators

3 1 Kripke/Kaplan on rigid terms names and indexicals are directly referential/rigid designators wide-scope behavior w.r.t. operators not synonymous with the description giving their descriptive meaning, as shown by Kripke-Kaplan examples (1) and (2): Sam the person called Sam (1) a. Sam is called Sam b. The person called Sam is called Sam

4 2 I the speaker (2) a. I am the speaker b. The speaker is the speaker

5 3 Discourse Representation Theory meaning encoded in descriptive representational conditions in a DRS

6 3 Discourse Representation Theory meaning encoded in descriptive representational conditions in a DRS definite NPs treated as presuppositions 2-stage interpretation (van der Sandt 1992; Geurts 1999): syntactic module Prel builds preliminary DRS from sentence pragmasemantic resolution algorithm

7 3 Discourse Representation Theory meaning encoded in descriptive representational conditions in a DRS definite NPs treated as presuppositions 2-stage interpretation (van der Sandt 1992; Geurts 1999): syntactic module Prel builds preliminary DRS from sentence pragmasemantic resolution algorithm merges Prel(σ) with previous discourse-/background-drs performs anaphora and presupposition Resolution (binding new presuppositions to old representations or accommodating them)

8 4 Resolution 1. presuppositions are to be bound (e.g. anaphors) 2. otherwise, accommodate as high as possible (e.g. some definite descriptions, factive complements)

9 4 Resolution 1. presuppositions are to be bound (e.g. anaphors) 2. otherwise, accommodate as high as possible (e.g. some definite descriptions, factive complements) presupposition resolution accounts for definite NP s wide-scope behavior how about the alleged special behavior of proper names/indexicals?

10 5 Descriptivism Geurts (1997) suggests that names are like other definite NP s

11 5 Descriptivism Geurts (1997) suggests that names are like other definite NP s both definite, thus presupposition triggers

12 5 Descriptivism Geurts (1997) suggests that names are like other definite NP s both definite, thus presupposition triggers reduction: John = the person called John accounts for proper name s normal wide scope behavior,

13 5 Descriptivism Geurts (1997) suggests that names are like other definite NP s both definite, thus presupposition triggers reduction: John = the person called John accounts for proper name s normal wide scope behavior, but also the (rare) other behaviors that proper names appear to share with definite descriptions...

14 6 no familiarity required (global accommodation): (3) My best friend is John

15 6 no familiarity required (global accommodation): (3) My best friend is John narrow scope (local and intermediate accommodation): (4) If alphabetical order had been the method of electing the American president, Aaron Aardvark might have been president

16 6 no familiarity required (global accommodation): (3) My best friend is John narrow scope (local and intermediate accommodation): (4) If alphabetical order had been the method of electing the American president, Aaron Aardvark might have been president bound variable (presupposition binding/cancellation): (5) If a child is christened Bambi, then Disney will sue Bambi s parents

17 6 no familiarity required (global accommodation): (3) My best friend is John narrow scope (local and intermediate accommodation): (4) If alphabetical order had been the method of electing the American president, Aaron Aardvark might have been president bound variable (presupposition binding/cancellation): (5) If a child is christened Bambi, then Disney will sue Bambi s parents but no account for Kaplan-Kripke examples!

18 7 Layered DRT (conservative) extension of standard DRT

19 7 Layered DRT (conservative) extension of standard DRT abstract interface for representing the interaction of different types of information layers for e.g. presuppositions, implicatures, asserted (Fregean) content, syntactic features,...

20 7 Layered DRT (conservative) extension of standard DRT abstract interface for representing the interaction of different types of information layers for e.g. presuppositions, implicatures, asserted (Fregean) content, syntactic features,... all layers get truthconditional evaluation

21 8 Applications binding problems (reference marker can be employed at several layers at once Geurts & Maier (ms)) denial (denial can be directed at one specific layer Maier & van der Sandt (to appear)) rigidity

22 9 Rigid designation in LDRT represent proper names and indexicals as descriptive conditions,

23 9 Rigid designation in LDRT represent proper names and indexicals as descriptive conditions, but at separate layer k add 2-dimensional semantics to rigidify only that layer

24 9 Rigid designation in LDRT represent proper names and indexicals as descriptive conditions, but at separate layer k add 2-dimensional semantics to rigidify only that layer extension: at representational level, treat k like presupposition layer (to account for bound variable uses of names)

25 10 Syntax primitive symbols: a set X of reference markers some sets Pred n of n-place predicates a set Λ of layer labels

26 10 Syntax primitive symbols: a set X of reference markers some sets Pred n of n-place predicates a set Λ of layer labels if x X, L Λ, then x L is a labeled reference marker if x 1,..., x n X, L Λ, then P L (x 1,..., x n ) is a labeled condition

27 11 if ϕ and ψ are labeled conditions, L Λ, then L ϕ, ϕ L ψ, and ϕ L ψ are also labeled conditions if U is a set of labeled reference markers and Con a set of labeled conditions, then U, Con is an LDRS

28 12 Application Λ = {fr, k, imp, pr}

29 12 Application Λ = {fr, k, imp, pr} fr = the Frege layer, what is said k = Kaplan-Kripke layer for rigid stuff imp = implicature layer pr = (unresolved) presupposition layer

30 13 Examples (6) a. The soup is warm x pr b. soup pr (x) warm fr (x) imp hot imp (x)

31 14 Binding problems e.g. with presuppositions (Karttunen & Peters 1979) (7) a.?someone managed to succeed George V on the throne of England.

32 14 Binding problems e.g. with presuppositions (Karttunen & Peters 1979) (7) a.?someone managed to succeed George V on the throne of England. b. x[succeed george v(x)] { x[had diff succ george v(x)]}

33 14 Binding problems e.g. with presuppositions (Karttunen & Peters 1979) (7) a.?someone managed to succeed George V on the throne of England. b. x[succeed george v(x)] { x[had diff succ george v(x)]} c.? x fr y k george v k (y) succeeded fr (x,y) had difficulty succeeding pr (x,y)

34 15 Semantics M = D, W, I

35 15 Semantics M = D, W, I D is a domain of individuals W is a set of possible worlds I interpretation function (from basic predicates to their intensions in D W )

36 ϕ f L,w = { g f g Dom(g) = = Dom(f) U L (ϕ) ψ Con(ϕ) [ ψ g L,w = 1]} undefined if g [ f g Dom(g) = Dom(f) U L (ϕ) ψ Con(ϕ) [ ψ g L,w {0, 1}]] otherwise 16

37 P K (x 1,..., x n ) f L,w = 1 if K L = or ( x1,..., x n Dom(f) and f(x 1 ),..., f(x n ) I(P )(w) ) = 0 if K L and undefined x 1,..., x n Dom(f) and f(x 1 ),..., f(x n ) / I(P )(w) otherwise 17

38 K ψ f L,w = 1 if K L = or ψ f K L,w = = 0 if K L and ψ f K L,w defined and ψ f K L,w undefined otherwise 18

39 = 1 if K L = or ψ f K L,w = K ψ f = 0 if K L and ψ f K L,w defined and L,w ψ f K L,w undefined otherwise = 1 if both ψ f K L,w and χ f K L,w defined, ψ K χ f and ψ f K L,w χ f K L,w L,w = 0 if ψ f K L,w = χ f K L,w = undefined otherwise 18

40 19 Layered content {{ w W g ϕ f } C f L (ϕ) = L,w if w[ ϕ f L,w defined] undefined otherwise C L (ϕ) = C L (ϕ)

41 20 Problems often undefined (because of layer interdependencies): (8) a. The King of France is bald b. x pr king of france pr (x) bald fr (x)

42 20 Problems often undefined (because of layer interdependencies): (8) a. The King of France is bald x pr b. king of france pr (x) bald fr (x) c. C pr,fr ((8b)) = { w W } there is a bald king of France in w d. C fr (ϕ) undefined

43 21 (9) a. I am speaking b. x k speaker k (x) speaking fr (x)

44 21 (9) a. I am speaking x k b. speaker k (x) speaking fr (x) c. The speaker is speaking d. x fr speaker fr (x) speaking fr (x)

45 21 (9) a. I am speaking x k b. speaker k (x) speaking fr (x) c. The speaker is speaking d. x fr speaker fr (x) speaking fr (x) e. C k,fr ((9b)) = C k,fr ((9d)) = C fr ((9d)) = W f. C fr ((9b)) undefined

46 21 (9) a. I am speaking x k b. speaker k (x) speaking fr (x) c. The speaker is speaking d. x fr speaker fr (x) speaking fr (x) e. C k,fr ((9b)) = C k,fr ((9d)) = C fr ((9d)) = W f. C fr ((9b)) undefined to insure definedness, add extra layers as background for interpretation...

47 22 The weak proposal weak one-dimensional content substitute: (10) C [K] L (ϕ) = W (C K(ϕ) C K L (ϕ)) = { w W w CK (ϕ) w C K L (ϕ) }

48 22 The weak proposal weak one-dimensional content substitute: (10) C [K] L (ϕ) = W (C K(ϕ) C K L (ϕ)) = { w W w CK (ϕ) w C K L (ϕ) } handy for denial applications, but: (11) C [k] fr ((9b)) = W

49 23 Adding another dimension M = D, W, C, I D is a domain of individuals W is a set of worlds I is interpretation function C is a set of contexts, i.e. for all c C: I(speaker)(c), I(Mary)(c),... are singletons

50 23 Adding another dimension M = D, W, C, I D is a domain of individuals W is a set of worlds I is interpretation function C is a set of contexts, i.e. for all c C: I(speaker)(c), I(Mary)(c),... are singletons { = C f KL c (ϕ) L (ϕ) undefined if ϕ k,c = {f} otherwise

51 24 (12) a. Ashley is called Ashley x k b. ashley k (x) ashley fr (x) c. Ashley is Ashley x k y k d. ashley k (x) ashley k (y) x= fr y C k,fr ((12b)) = C k,fr ((12d)) = W, C fr ((12b)), C fr ((12d)) undefined

52 24 (12) a. Ashley is called Ashley x k b. ashley k (x) ashley fr (x) c. Ashley is Ashley x k y k d. ashley k (x) ashley k (y) x= fr y C k,fr ((12b)) = C k,fr ((12d)) = W, C fr ((12b)), C fr ((12d)) undefined Kfr c ((12b)) = C{ x,ash c } fr ((12b)) = { w ash c is in w called Ashley }

53 24 (12) a. Ashley is called Ashley x k b. ashley k (x) ashley fr (x) c. Ashley is Ashley x k y k d. ashley k (x) ashley k (y) x= fr y C k,fr ((12b)) = C k,fr ((12d)) = W, C fr ((12b)), C fr ((12d)) undefined Kfr c ((12b)) = C{ x,ash c } fr ((12b)) = { w ash c is in w called Ashley } Kfr c ((12d)) = C{ x,ash c, y,ash c } ((12d)) = W fr

54 25 Refinements Geurts (1997) suggests that names are like other definite NP s, with e.g. bound variable uses: (13) a. If a child is christened Bambi, then Disney will sue Bambi s parents

55 25 Refinements Geurts (1997) suggests that names are like other definite NP s, with e.g. bound variable uses: (13) a. If a child is christened Bambi, then Disney will sue Bambi s parents b. Every time we do our Beatles act, Ringo gets drunk afterwards

56 26 Names as presuppositions Λ = {pr d, d, pr k, k, fr, imp} pr d = descriptive presupposition layer d = accommodated (descriptive) presupposition pr k = name/indexical presupposition k = rigidifiable layer

57 26 Names as presuppositions Λ = {pr d, d, pr k, k, fr, imp} pr d = descriptive presupposition layer d = accommodated (descriptive) presupposition pr k = name/indexical presupposition k = rigidifiable layer Prel puts names and indexicals in pr k, definite descriptions in pr d

58 26 Names as presuppositions Λ = {pr d, d, pr k, k, fr, imp} pr d = descriptive presupposition layer d = accommodated (descriptive) presupposition pr k = name/indexical presupposition k = rigidifiable layer Prel puts names and indexicals in pr k, definite descriptions in pr d Res tries to bind pr k and pr d whenever possible, otherwise pr k stuff is dropped as high up as possible in k, pr d gets dropped at d

59 27 (14) a. Maybe Rory liked my talk

60 27 (14) a. Maybe Rory liked my talk x prk y prd z prk b. Prel((14a)) = named rory prk talk of prd (y,z) speaker prk (z) like fr (x,y)

61 28 x k y d z k c. Res((14b)) = named rory k talk of d (y,z) speaker k (z) likefr (x,y)

62 29 (15) a. If a child is christened Bambi, then Disney will sue Bambi s parents

63 29 (15) a. If a child is christened Bambi, then Disney will sue Bambi s parents y prk Z prd w prk b. Prel((15a)) = x fr child fr (x) named bambi fr (x) disney prk (y) parents of prd (Z,w) named bambi prk (w) sue fr (y,z)

64 30 y k disney k (y) c. Res((15b)) = x fr Z d child fr (x) named bambi fr (x) parents of d (Z,x) suefr (y,z)

65 31 Further research The dynamics of the pr k layer: how, why, when does pr k stuff become part of new descriptive content (Geurts s (1997) accommodation examples)?

66 31 Further research The dynamics of the pr k layer: how, why, when does pr k stuff become part of new descriptive content (Geurts s (1997) accommodation examples)? difference between names and indexicals?

67 32 References Geurts, Bart Good news about the description theory of names. Journal of Semantics Presuppositions and Pronouns. Amsterdam: Elsevier., & Emar Maier, ms. Layered DRT. (2003). Karttunen, Lauri, & Stanley Peters Conventional implicature. In Syntax and Semantics II: Presupposition, ed. by ChoonKyo Oh & David A. Dineen, New York: Academic Press.

68 33 Maier, Emar, & Rob A. van der Sandt. to appear. Denial and correction in Layered DRT. In Proc. of DiaBruck http: // van der Sandt, Rob A Presupposition projection as anaphora resolution. Journal of Semantics