Scope parallelism in coordination in Dependent Type Semantics

Transcription

1 Scope parallelism in coordination in Dependent Type Semantics Yusuke Kubota 1 Robert Levine 2 1 University of Tsukuba, Ohio State University 2 Ohio State University LENLS 12 Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 1 / 27

2 Outline The Geach RNR problem: overview Problems with prior accounts of Geach quick review of Hybrid TLCG The Geach problem in Hybrid TLCG [Steedman, 2012] s (non-)solution in CCG nalysis in Hybrid TLCG + Dependent Type Semantics Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 2 / 27

3 The Geach data [Geach, 1972] (1) Every boy admires, and every girl detests, some saxophonist ( > > ; > > ) NB: (1) lacks readings in which the RNR ed existential scopes above the universal in one conjunct but below it in the other conjunct Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 3 / 27

4 The Geach data [Geach, 1972] (1) Every boy admires, and every girl detests, some saxophonist ( > > ; > > ) NB: (1) lacks readings in which the RNR ed existential scopes above the universal in one conjunct but below it in the other conjunct The scope parallelism problem in Geach sentences is not restricted to RNR, since cases such as (2), first noted in [Hirshbühler, 1982], show that it holds in VP ellipsis as well (2) Canadian flag was hanging in front of every window and an merican flag was too Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 3 / 27

5 Rules in Hybrid TLCG Connective Introduction Elimination / [ϕ; x; ] n b ϕ; F ; B /I n b; λxf ; B/ a; F ; /B b; G; B /E a b; F (G); \ [ϕ; x; ] n ϕ b; F ; B \I n b; λxf ; \B [ϕ; x; ] n b; F ; B λϕb; λxf ; B I n b; G; B a; F ; B\ \E b a; F (G); a; F ; B b; G; B E a(b); F (G); Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 4 / 27

6 Quantifiers and Slanting We follow [Oehrle, 1994] and much subsequent work in his framework (see also [Muskens, 2003], [de Groote, 2001]) in taking generalized quantifiers to have the form in (3): (3) λϕλσσ(some ϕ); λq (where E E Q; S (S NP) Q = def λp xq(x) P (x)) But it follows as an Hybrid TLCG theorem that from this form, by hypothetical reasoning, we can infer a variety of directional versions, eg (S/NP)\S: (4) λσ 1 σ 1 (some saxophonist); E sax; S (S NP) ϕ 1 ; P ; S/NP ϕ 2 ; x; NP ϕ 1 ϕ 2 ; P (x); S λϕ 2 ϕ 1 ϕ 2 ; λxp (x); S NP ϕ 1 some saxophonist; sax(λxp (x)); S some saxophonist; λp sax(λxp (x)); (S/NP)\S E E Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 5 / 27

7 Getting the Geach readings in Hybrid TLCG > > (5) ϕ 2 admires; λwadmire(w)(v); S/NP [ϕ 1 ; V ; (S/NP)\S] 1 ϕ 2 admires ϕ 1 ; V (λwadmire(w)(v)); S λϕ 2 ϕ 2 admires ϕ 1 ; λvv (λwadmire(w)(v)); S NP every boy admires ϕ 1 ; λσ 1 σ 1 (every boy); boy; S (S NP) boy(λvv (λwadmire(w)(v))); S every boy admires; λv boy(λvv (λwadmire(w)(v))); S/((S/NP)\S) In parallel fashion we obtain (6) every girl detests; λu S/((S/NP)\S) girl(λzu (λudetest(u)(z))); s usual, we take coordination to correspond in general to Partee and Rooth s generalized conjunction and disjunction operators, Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 6 / 27

8 which yields (7) every boy admires and every girl detests; λw boy(λzw (λxadmire(x)(z))) girl(λzw (λxdetest(x)(z))); S/((S/NP)\S) When (7) combines as argument with the slanted version of some saxophonist derived in (4), we get the reading in which the latter s denotation is distributed over the conjunction (4) some saxophonist; λp E sax(λxp (x)); (S/NP)\S Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 7 / 27

9 > We derive the alternative scoping more simply, as follows every boy admires ϕ 1; every boy admires; λx boy(λyadmire(y)(x)); S boy(λyadmire(y)(x)); S/NP and the same for every girl detests; λx girl(λydetest(y)(x)); S/NP which, under generalized conjunction, together yield every boy admires and every girl detests; λw boy(λyadmire(y)(w)) girl(λzdetest(z)(w)); S/NP every boy admires and every girl detests ϕ 2; boy(λyadmire(y)(v)) girl(λzdetest(z)(v)); S λϕ 2every boy admires and every girl detests ϕ 2; λv boy(λyadmire(y)(v)) girl(λzdetest(z)(v)); S NP ϕ 2; v; NP λσ 1σ 1(some saxophonist); E sax; S (S NP) every boy admires and every girl detests some saxophonist; sax(λv boy(λyadmire(y)(v)) girl(λzdetest(z)(v))); S E Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 8 / 27

10 Mixed readings But note that the following sign is also derivable: every girl detests; λu U (λw girl(λzdetest(w)(z))); S/((S/NP)\S) which is of the same syntactic type as what we derived earlier for the distributed interpretation of the RNRed indefinite: every boy admires; λv boy(λvv (λwadmire(w)(v))); S/((S/NP)\S) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 9 / 27

11 Mixed readings But note that the following sign is also derivable: every girl detests; λu U (λw girl(λzdetest(w)(z))); S/((S/NP)\S) which is of the same syntactic type as what we derived earlier for the distributed interpretation of the RNRed indefinite: every boy admires; λv Conjoining them yields: boy(λvv (λwadmire(w)(v))); S/((S/NP)\S) (8) every boy admires and every girl detests; λw boy(λvw (λwadmire(w)(v))) W (λu girl(λzdetest(u)(z)); S/((S/NP)\S)) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 9 / 27

12 Mixed readings But note that the following sign is also derivable: every girl detests; λu U (λw girl(λzdetest(w)(z))); S/((S/NP)\S) which is of the same syntactic type as what we derived earlier for the distributed interpretation of the RNRed indefinite: every boy admires; λv Conjoining them yields: boy(λvv (λwadmire(w)(v))); S/((S/NP)\S) (8) every boy admires and every girl detests; λw boy(λvw (λwadmire(w)(v))) W (λu girl(λzdetest(u)(z)); S/((S/NP)\S)) pplied to the slanted form of some saxophonist, we will obtain (9) every boy admires and every girl detests some saxophonist; boy(λv sax(λwadmire(w)(v))) sax(λu girl(λzdetest(u)(z)); S E E which is the unavailable mixed reading Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 9 / 27

13 Steedman s solution: Skolem terms Steedman proposes a CCG solution for the Geach problem reinterpretating existentials not as generalized quantifiers but rather generalized Skolem terms corresponding either to constants (with wide scope) when unbound, or functional terms containing variables which become bound when in the scope of a universal Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 10 / 27

14 RNR revisited Steedman s solution for the Geach sentence facts hinges on the fact that a given Skolem term must correspond either a constant or a function on the value of the variable bound by some universal (10) In (10), the determination of which of these possibilities is realized (Skolem specification) is made only FTER the RNRed element combines with the S/NP conjunction and is distributed under the scope of the universal in conjunct at the point Every boy admires and every girl detests S/NP : λx y[boy (y) admire (x)(y)] z[girl (z) detest (x)(z)] some saxophonist (S/NP )\S : λqq(skolem (sax )) S : y[boy (y) admire (skolem (sax ))(y)] z[girl (z) detest (skolem (sax ))(z)] S : y[boy (y) admire (sk (y) sax )(y)] Hence both Skolem terms are interpreted as varying functions, corresponding to narrow scope under each universal But if the original Skolem term s status is specified BEFORE λ-conversion distributes it among the conjuncts, it will not be under any quantifier s scope, and hence will be a constant, scoping wide Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 11 / 27

15 Empirical problems with Steedman s account While Steedman s analysis blocks the mixed reading the means by which it does so rule out in advance any possibility of an existential scoping narrowly with respect to the RNR coordination but widely with respect to a universal in either or both conjuncts because if it s a constant, it outscopes everything, and if it s not, it must be under the scope of some universal But examples of just this sort, ruled by the Skolem term analysis, are readily available Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 12 / 27

16 (11) Every merican respects, and every Japanese admires, some novelist namely, their respective most recent Nobel Prize winner The crucial part of the interpretation can be paraphrased as There is some merican novelist such that very merican respects that novelist and there is some Japanese novelist such that every Japanese person respects that novelist so that the existential interpretation distributes over the conjunction (like a Skolem function), but within each conjunct takes widest scope (like a constant) Hybrid TLCG however can license (11) unproblematically, so that Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 13 / 27

17 we are left in the unsatisfactory situation of either blocking mixed readings for Geach sentences but undergenerating (11) (via the CCG analysis), or licensing (11) and while overgenerating the mixed Geach reading (via Hybrid TLCG) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 14 / 27

18 Solution for the Geach puzzle in words (12) Every boy admires, and every girl detests, some saxophonist ( > > ; > > ) (13) Every boy i is such that there is a saxophonist j such that he i admires him j, and every girl k is such that there is a saxophonist l such that she k admires him l Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 15 / 27

19 Solution for the Geach puzzle in words (12) Every boy admires, and every girl detests, some saxophonist ( > > ; > > ) (13) Every boy i is such that there is a saxophonist j such that he i admires him j, and every girl k is such that there is a saxophonist l such that she k admires him l Note that the same interpretive parallelism holds in binding: (14) Every Englishman respects, and every merican loves, his mother (14) doesn t mean: Every Englishman respects his own mother and every merican respects x, where x is some contextually salient person s mother Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 15 / 27

20 naphora in DTS (15) man entered He sat down (16) [ ] x : Ent λc v : u : Man(x) Enter(π 1 u) SitDown(@ 1 (c, v)) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 16 / 27

21 naphora in DTS (15) man entered He sat down (16) [ ] x : Ent λc v : u : Man(x) Enter(π 1 u) SitDown(@ 1 (c, 1 = λcπ 1 π 1 π 2 1 (c, v) = π 1 π 1 v Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 16 / 27

22 naphora in DTS (15) man entered He sat down (16) [ ] x : Ent λc v : u : Man(x) Enter(π 1 u) SitDown(@ 1 (c, 1 = λcπ 1 π 1 π 2 1 (c, v) = π 1 π 1 v Note: The analysis of anaphora resolution is from [Bekki, 2014] [ ] x : Ent We sometimes write [(x : Ent) Man(x)] for Man(x) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 16 / 27

23 Mixed binding problem isn t a problem [Bekki, 2014] (17) Each of John and Bill loves his father Reading 1: John loves his own father and Bill loves his own father Reading 2: Both John and Bill love the same person s father Unavailable reading: John loves his own father and Bill loves somebody else s father Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 17 / 27

24 Mixed binding problem isn t a problem [Bekki, 2014] (17) Each of John and Bill loves his father Reading 1: John loves his own father and Bill loves his own father Reading 2: Both John and Bill love the same person s father Unavailable reading: John loves his own father and Bill loves somebody else s father (18) [ x : Ent λcl(j, π 1 ((@ 1 : γ 1 FatherOf(x, (@ 0 : γ 0 e)(c, j)) [ x : Ent L(b, π 1 ((@ 1 : γ 1 FatherOf(x, (@ 0 : γ 0 e)(c, b)) ] )(c, j))) ] )(c, b))) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 17 / 27

25 Hybrid TLCG + DTS (19) a λϕλσσ(every ϕ); λp λqλc(u : [(x : Ent) P xc]) Q(π 1 u)(c, u); S (S NP) N [ b λϕλσσ(some ϕ); λp λqλc S (S NP) N u : [(x : Ent) P xc] Q(π 1u)(c, u) c λσσ(it); λp λcp (@ 1 1 c); S (S NP) ] ; Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 18 / 27

26 Donkey anaphora (20) λϕλσ σ(every ϕ); λp λqλc (v : h x : Ent P xc i ) Q(π 1 v)(c, v); S (S NP) N farmer; λxλc Fx; N λσwho σ(ε); λp λqλxλc Qxc P xc; (N\N) (S NP) λσσ(a donkey); λqλc "» # y : Ent u : Dy ; Q(π 1 u)(c, u) S (S NP) who owns a donkey; λqλxλcqxc " ϕ1; # 1 x; NP ϕ 1 h owns a donkey; u : [(y : Ent) Dy] λc O(x, π 1 u) " ϕ2; # 2 y; NP λϕ 2ϕ 1 owns ϕ 2; λyλco(x, y); S NP i ; S λϕ 1ϕ h 1 owns a donkey; i u : [(y : Ent) Dy] λxλc O(x, π 1 u) ; S NP h u : [(y : Ent) Dy] O(x, π 1 u) farmer who owns a donkey; λxλcfx h u : [(y : Ent) Dy] O(x, π 1 u) i ; N λσσ(every " farmer who owns a donkey); # x : Ent» λqλc(v : u : [(y : Ent) Dy] Fx ) Q(π 1 v)(c, v); S (S NP) O(x, π 1 u) i ; N\N Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 19 / 27

27 Donkey anaphora (cont) (21) λσσ(every farmer who owns a donkey); λqλc(v :» x : Ent Fx» u : [(y : Ent) Dy] O(x, π 1 u) Q(π 1v)(c, v); S (S NP) ) λσσ(it); λp λcp (@ 1c) 1c); S (S NP) h ϕ3; i 3 z; NP h ϕ4; i 4 w; NP λϕ 4ϕ 3 beats ϕ 4; λwλcb(z, w); S NP ϕ 3 beats it; 1c); S λϕ 3ϕ 3 beats it; 1c); S NP every farmer who owns a donkey beats it; λc(v :» x : Ent» u : [(y : Ent) Dy] Fx O(x, π 1 u) ) B(π 1(c, v)); S Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 20 / 27

28 Binding parallelism (22) Every Englishman respects, and every merican loves, his mother (23)» x : Ent λc(u : E(x)» x : Ent (u : (x)» y : Ent ) R(π 1u, π 1((@ 1 : γ 1 ) L(π 1u, π 1((@ 1 : γ 1 M(y, (@ 0 : γ 0 e)(c, u))» y : Ent M(y, (@ 0 : γ 0 e)(c, u)) )(c, u))) )(c, u))) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 21 / 27

29 Revised entry for the existential quantifier (24) a it; λc@ i c; NP p b admires; λfλxλc(x, fc); (NP\S)/NP p [ u : [(x : Ent) P xc] (25) λϕλσσ(some ϕ); λp λqλc Q(λd@ π 1u i d)(c, u) S (S NP p ) N ] ; where, for all contexts π 1u i c = c i c = π 1 u undefined otherwise Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 22 / 27

30 Revised entry for the existential quantifier (24) a it; λc@ i c; NP p b admires; λfλxλc(x, fc); (NP\S)/NP p [ u : [(x : Ent) P xc] (25) λϕλσσ(some ϕ); λp λqλc Q(λd@ π 1u i d)(c, u) S (S NP p ) N ] ; where, for all contexts π 1u i c = c i c = π 1 u undefined otherwise Cf older entry: [ u : [(x : Ent) P xc] (26) λϕλσσ(some ϕ); λp λqλc Q(π 1u)(c, u) S (S NP) N ll quantifier entries will be revised accordingly, but for expository ease, below we replace the entries of the relevant quantifiers only Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 22 / 27 ] ;

31 Simple sentence involving a quantifier (27) λϕλσσ(every boy); λqλc(v : [(x : Ent) Bx]) Q(π 1v)(c, v); S (S NP) λσσ(some» saxophonist); u : [(x : Ent) Sx] λqλc Q(λd@ π 1u 1 d)(c, u) S (S NP p) ; h ϕ1; i 1 z; NP h ϕ2; f; NP p i 2 λϕ 2ϕ 1 admires ϕ 2; λfλc(z, fc); S NP p ϕ 1» admires some saxophonist; u : [(x : Ent) Sx] λc π 1u ; S 1 (c, u)) λϕ 1ϕ» 1 admires some saxophonist; u : [(x : Ent) Sx] λzλc π 1u ; S NP 1 (c, u)) every boy admires some» saxophonist; u : [(x : Ent) Sx] λc(v : [(x : Ent) Bx]) (π π 1u 1 ((c, v), u)) ; S Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 23 / 27

32 Simple sentence involving a quantifier (27) λϕλσσ(every boy); λqλc(v : [(x : Ent) Bx]) Q(π 1v)(c, v); S (S NP) λσσ(some» saxophonist); u : [(x : Ent) Sx] λqλc Q(λd@ π 1u 1 d)(c, u) S (S NP p) ; h ϕ1; i 1 z; NP h ϕ2; f; NP p i 2 λϕ 2ϕ 1 admires ϕ 2; λfλc(z, fc); S NP p ϕ 1» admires some saxophonist; u : [(x : Ent) Sx] λc π 1u ; S 1 (c, u)) λϕ 1ϕ» 1 admires some saxophonist; u : [(x : Ent) Sx] λzλc π 1u ; S NP 1 (c, u)) every boy admires some» saxophonist; u : [(x : Ent) Sx] λc(v : [(x : Ent) Bx]) (π π 1u ; S 1 ((c, v), u)) [ ] u : [(x : Ent) Sx] (28) λc(v : [(x : Ent) Bx]) (π 1v, π 1u) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 23 / 27

33 Geach sentences Subject wide scope: (29) every boy admires; λpλc(w : [(x : Ent) Bx]) P(λfλc(π 1 w, fc))(c, w); S/((S/NP p )\S) Object wide scope: (30) every girl detests; λpp(λfλc(w : [(x : Ent) Gx]) D(π 1 w, f(c, w))); S/((S/NP p )\S) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 24 / 27

34 Parallel scope is predicted to be good (31) Every boy admires, and every girl detests, some saxophonist Using the object wide scope version for both conjuncts, we obtain: (32) λc» w : [(x : Ent) Sx] t : (u : [(x : Ent) Bx]) (@ π 1w» 1 ((c, w), u)) s : [(x : Ent) Sx] (v : [(x : Ent) Gx]) D(@ π 1s 1 (((c, t), s), v)) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 25 / 27

35 Parallel scope is predicted to be good (31) Every boy admires, and every girl detests, some saxophonist Using the object wide scope version for both conjuncts, we obtain: (32) λc» w : [(x : Ent) Sx] t : (u : [(x : Ent) Bx]) (@ π 1w» 1 ((c, w), u)) s : [(x : Ent) Sx] (v : [(x : Ent) Gx]) D(@ π 1s 1 (((c, t), s), v)) 1 = λcπ 1 π 2 π 1 c, we obtain the right interpretation Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 25 / 27

36 Mixed scope is predicted to be bad Using the subject wide scope version for the first conjunct and the object wide scope version for the second conjunct, we obtain: (33) λc t :» u : [(x : Ent) Sx] (w : [(x : Ent) Bx]) (@ π 1u 1 ((c, w), u))» s : [(x : Ent) Sx] (v : [(x : Ent) Gx]) D(π 1v, (@ π 1s 1 (((c, t), s), v)) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 26 / 27

37 Mixed scope is predicted to be bad Using the subject wide scope version for the first conjunct and the object wide scope version for the second conjunct, we obtain: (33) λc t :» u : [(x : Ent) Sx] (w : [(x : Ent) Bx]) (@ π 1u 1 ((c, w), u))» s : [(x : Ent) Sx] (v : [(x : Ent) Gx]) D(π 1v, (@ π 1s 1 (((c, t), s), v)) first 1 = λcπ 1 π 2 c second 1 = λcπ 1 π 2 π 1 c This time, there is no coherent way of resolving 1 operator Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 26 / 27

38 Open questions Our analysis predicts that the object existential quantifier cannot scope widely within the second conjunct in the following sentence: (34) John admires, and every girl detests, some saxophonist (35) λc» u : [(x : Ent) Sx] t : π 1u» 1 (c, t)) s : [(x : Ent) Sx] (v : [(x : Ent) Gx]) D(π 1v, (@ π 1s 1 (((c, t), s), v)) Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 27 / 27

39 Open questions Our analysis predicts that the object existential quantifier cannot scope widely within the second conjunct in the following sentence: (34) John admires, and every girl detests, some saxophonist (35) λc» u : [(x : Ent) Sx] t : π 1u» 1 (c, t)) s : [(x : Ent) Sx] (v : [(x : Ent) Gx]) D(π 1v, (@ π 1s 1 (((c, t), s), v)) More generally, when different numbers of quantifiers are present in the two conjuncts, a parallel in-conjunct wide scope reading is blocked Is this a good prediction? (36) Every merican detests, and every Japanese has some serious reservations for, some Nobel Prize winner namely, their respective most recent Literature Prize winners Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 27 / 27

40 Bekki, D (2014) Representing anaphora with dependent types In sher, N and Soloviev, S, editors, Logical spects of Computational Linguistics 2014, pages 1429, Heidelberg Springer de Groote, P (2001) Towards abstract categorial grammars In ssociation for Computational Linguistics, 39th nnual Meeting and 10th Conference of the European Chapter, pages Geach, P T (1972) program for syntax In Davidson, D and Harman, G H, editors, Semantics of Natural Language, pages D Reidel, Dordrecht Hirshbühler, P (1982) VP deletion and across-the-board quantifier scope In Pustejovsky, J and Sells, P, editors, Proceedings of the Twelfth nnual Meeting of the North Eastern Linguistic Society, pages University of Massachusetts at mherst Muskens, R (2003) Language, lambdas, and logic In Kruijff, G-J and Oehrle, R, editors, Resource Sensitivity in Binding and naphora, pages 2354 Kluwer, Dordrecht Oehrle, R T (1994) Term-labeled categorial type systems Linguistics and Philosophy, 17(6): Steedman, M (2012) Taking Scope MIT Press, Cambridge, Mass Yusuke Kubota, Robert Levine Scope parallelism in coordination in DTS 27 / 27