FACULTY OF ARTS
Masaryk University
Semantics of distributivity in Czech Sign Language
Sign Language Syntax and Linguistic Theory, GLOW, 14.4. 2018
Mojmír Dočekal, Hana Strachoňová, Ondřej Klofáč, Mirka Tylová and Ivana Kupčíkova
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Outline of this talk
1. Introduction: distributivity markers
2. Two strategies: binominal 'each' vs. dependent indefinites
3. Interpretation of sign repetition on R-loci in CSL
4. PCDRT solution
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Introduction: distributivity markers
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Introduction: distributivity markers
• distributivity markers
(1)     a.   The girls saw two dogs each.
b.    Die Mädchen haben jeweils zwei Hunde gesehen. 'The girls saw two dogs each.'
• binominal each (standard terminology): the girls sorting key, two dogs distributed share
• spoken languages: lot of attention (Balusu 2006, Dotlačil 2012, Champollion 2012, Safir and Stowell 1988 among many others)
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• SL data: Kimmelman 2015,2017; Quer 2012; Kuhn 2017 semantics of dependent indefinites
(2)     DAUGHTER MY THEY-THREE DOG TWOj TWOj TWOk BATHj BATHj BATHk
(My three daughters bathed two dogs each.'
• sign repetition on Reference loci (R-loci): positions in space that realize discourse referents/logical variables (Schlenker et al. 2013)
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main claim: CSL sign repetition (R-loci) is distributive operator (similar to binominal each)
our goal: semantic account for (multiple) distributivity marking in Czech sign language
Two strategies: binominal 'each' vs. dependent indefinites
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• two closely related phenomena:
1. binominal each
2. dependent indefinites: (3) from Kuhn (2017)
(3)     EACH-EACH-a PROFESSOR NOMINATE ONE-redup-a STUDENT.
'Each professor nominated one student .'[ASL, Kuhn 2017]
• common: atomicity on sorting key, distributed share of required cardinality
• distinction: compatibility with distributive universal quantifier (ungrammatical vs. preferred)
(4)   #Each boy had one apple each.
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Figure 2: Dependent indefinites in CSL: THEY-arc, TWO-arc
• CSL: repetition on R-loci and dependent indefinites: different marking - Dl - Figure 2, (5)
(5)    GIRL THEY-arc-a DOG TWO-arc-a BATH-arc-a HI 'The girls bathed two dogs each.'
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Distributive universal quantifier vs. R-loci repetition
• preferential strategy in CSL: distributive each with dependent indefinites - (6)
• reduplication of numeral with EACH in CSL disprefered - (7)
• evidence against treating the reduplication on R-loci as dependent indefinites (Dl)
(6)    GIRL EACH-arc-a DOG TWO-arc-a BATH-arc-a GDI 'The girls bathed two dogs each.'
(7)
#/?? DAUGHTER MY 3ijk EACH-arcijk DOG TWO\TWOiTWOk BATH
'Each of my daughters bathed two dogs each.'
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Interpretation of sign repetition on R-loci in
CSL
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Terminology: individual vs. occasional distribution
• adverbial German jeweils vs. English each
(8) Die Mädchen haben jeweils zwei Hunde gesehen.
a. # cumulative
b. individual distributivity (each girl... two dogs)
c. occasional distributivity (each time ... two dogs)
(9) The girls saw two dogs each.
a. # cumulative
b. individual distributivity
c. #occasional distributivity
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CSL: Gathering data
• data survey with two Deaf signers
• truth judgements task
• variation of R-loci reduplication structures
• comments on the video-situation pairing (grammaticality and appropriateness)
• Situations: 3 daughters, 2 or 6 dogs, bathing events
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Figure 3: individual distributive
Figure 4: occasional distributive
Figure 5: cumulative
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Examples from CSL I: cumulative
cumulative reading video: flfflS
(10)     DAUGHTER MY PL DOG PL BATH BATH 'My daughters bathed the dogs.'
a. individual
b. #occasional
c. cumulative
• weak truth conditions, non-scopal reading
• the most salient interpretation of a sentence with plurality denoting subject and object is cumulative
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Examples from CSL II: distributive: OH
(11)     DAUGHTER 3ijkTHEY MY DOG TWOjTW0jTW0k BATH 'My three daughters bathed two dogs each.'
• readings:
1. individual
2. # occasional
3. # cumulative
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Examples from CSL: occasional distributivity: OH
(12)     DAUGHTER MY THEY-THREE DOG TWOj TWOj TWOk BATHj BATHj BATHk
'My three daughters bathed two dogs each / each time.'
a. individual
b. occasional
c. #cumulative
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PCDRT solution
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Cumulative reading
cumulative reading video: flfflS
(13)     DAUGHTER MY PL DOG PL BATH BATH
a. individual
b. #occasional
c. cumulative
• weak truth conditions, non-scopal reading
• the most salient interpretation of a sentence with plurality denoting subject and object is cumulative
• sets of assignments: team logic, PCDRT,...
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very elegant PCDRT solution essentially following Dotlacil (2012) 'fastidious' PCDRT: rows assignments to discourse referents, columns: values of discourse referents in all assignments
adding events as primitive type following Minor (2017): e
adding group-shifting (|) after Landman «—► 1-1 mapping of events and 0-roles
cumulative:
J	ei	Ui	u2
J1	ei	T(daughter1 &2)	dog1
J*2	e2	daughter 3	dog 2
DP(rtt)
VP(rt>
D
NP(rt)
V
DP(rtt)
EC"1   my daughters   bath     D NP(rt)
EC"2 dogs
(15)    [ui|];[|ui| >1][|daughters{ui}];[u2|][|u2| > 1][|dogs{u2}]; [|bath{u1,u2}]
pluralization is due to repetition of verb and pluralization of NPs
PCDRT: ingredients
• following Brasoveanu 2008, Dotlačil 2012:
(16)    a.    [daughters] = Avr.[ |daughter(s){v}] (r,
b. [bath] = ÁQrtitÁvr.Q([\v' .[{bath {v, v'}])
c. {three} = APrtAvr. [ | |v| = 3]; P(v)
d. {dogs} = Avr.[|dog(s)(s){v}] (r,t)
e. [EC""] = APrtAQrt.[un|]; P(un); Q(un) {r,t) ^ ({r,t),t)
weak truth conditions: cumulative or collective plurality of daughters (ui) and plurality of dogs (1/2) predicate bath applied to the {ui, 1/2}
Individual distributive reading
(17)     DAUGHTER 3ijkTHEY MY DOG TWOjTW0jTW0k BATH (My three daughters bathed two dogs each.'
• readings:
1. individual
2. # occasional
3. # cumulative
• distributive operator: carried by TWO TWO TWO (reduplicated on DAUGHTERS R-loci), anaphoric to the sorting key
• Schlenker at al. (2013): R-loci positions that can realize discourse referents(logical variables)
(18)     DAUGHTER 3ijkTHEY MY DOG TWOjTWOjTWOk BATH 'My three daughters bathed two dogs each.'
(19)
DPu, (rt,t)
EC
NP(r.t)
V
DP(rtt)
my 3 daughters   bath   NP(rt) 5
"1
2 dogs
reduplication happens in the object position, fastidious via binding into dref ui
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• semantic interpretation: binominal each as a quantifier over atoms in the sorting key denotation
• formalization (Dotlačil 2012): atomicity | Uun' l= 1 plus right cardinality for the distributed share, each is essentially the distributive operator plus two arguments, one anaphoric and distributed over, second: the distributed share
• adding (20-b) enforces (21):
(20)
a.
b.
Distributivity operator: <5Un(D) := ÁlstÁJst.unl = unJ A Vd e un/(| \Junl \= 1 A D(/ | un=d)(J | un=d)) [eacM = XPrtXQrt.[um |]; 5Un(P(um)); Q(um)
(21)
J		U1	u2
J1	ei	daughter 1	T(dog1&2)
J*2	e2	daughter 2	t(dog3&4)
J*3	e3	daughter 3	í(dog5&6)
Interpretation:
(22)    [ ui | ]; [ |ui | = 3] [ |daughters { ui} ]; [ u21 ]; aUl ([ |u21 = 2] [ |dogs { u2 } ]); [ | bath { m, u2 } ]
• cumulative reading out: share is of the wrong cardinality
• reduplication/bn each introduces (like EC) one dref (um): share
• reduplication anaphoric to un: key
• reduplication is determiner: (r, t) —> ((r, t), t)
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Occasional distributivity
(23)    DAUGHTER MY THEY-THREE DOG TWOj TWOj TWOk BATHj BATHj BATHk
(My three daughters bathed two dogs.'
a. individual
b. occasional
c. #cumulative
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Occasional distributive reading
• 2 reduplications:
1. TWO on DAUGHTERS R-loci
2. BATH on DAUGHTERS R-loci
• following Schlenker et al (2013): Agens modifying pronouns with incorporated numerals introduce split key antecedents
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NP(r,t) VP(rtt)
bath   NP(r#t) 5 2 dogs
J		U1	u2
J1	ei	T(daughter1 & 2&3)	T(dog1&2)
J*2	e2	T(daughter1 & 2&3)	t(dog3&4)
J*3	e3	T(daughter 1 & 2&3)	T(dog5&6)
(26)    [ ui | ]; [ |ui | = 3] [ |daughters{m } ]; [ u21 ]; aUl ([ |u21 =
2][|dogs{u2}]); [ei];a6l([|ei| > 1][|bath{ei, uh u2}])
Ambiguity: both reduplications require atomicity both in e and u:
1. atomicity via groups —> occasional reading
2. atomicity via individuals —> individual reading
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Reduplication of object: atomicity only in u
• two o operators: both anaphoric - one (aWl) to subject, another (aei) to the events
• individual reading: entailed (less complex - no group-shifting) by the occasional interpretation - preferred by signers
(27)
J		U1	u2
J1	ei	daughter 1	T(dog1&2)
J*2	e2	daughter 2	T(dog3&4)
J*3	e3	daughter 3	T(dog5&6)
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Summary
• CSL distributive reduplication (reduplication od R-loci) is a realization of the distributive fastidious operator o
• two reduplications     ambiguity (TWO TWO TWO BATH BATH BATH)
• alternative proposal: Kimmelman (Russian SL) solves by proposing a syntactic concord analysis (following Zeijlstra's Negative Concord theory; abstract D, marking agrees with D, multiple marking possible but not necessary)
• unclear predictions (e.g. for nominal/numeral reduplication vs. verbal reduplication) - probably cannot explain occasional reading without stipulations
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• our proposal:
- every distributive reduplication marking in CSL is a a operator
- o operator is selective/fastidious to the sorting key (ui/ei ... individual/occasional distribution reading); R-loci are anaphoric (Schlenker)
• our analysis:
- accounts for the multiple distributivity marking in SL
- uses previous theoretical work on distributivity in spoken languages and referentiality in sign languages
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Thanks!
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References
• Balusu, R. (2006). Distributive reduplication in Telegu. In Proceedings of NELS (Vol. 36, No. 1, p. 39).
• Burzio, L. (1986). Italian syntax: A government-binding approach (Vol. 1). Springer Science & Business Media.
• Dotlačil, J. (2011). Fastidious distributivity. In Semantics and Linguistic Theory (Vol. 21, pp. 313-332).
• Dotlačil, J. (2012). Binominal each as an anaphoric determiner: Compositional analysis. In Sinn und Bedeutung (Vol. 16, pp. 211-224).
• Champollion, L. (2012). Each vs. jeweils: A cover-based view on distance distributivity. In Logic, Language and Meaning (pp. 251-260). Springer, Berlin, Heidelberg.
• Kimmelman, V. (2015). Quantifiers in RSL: distributivity and compositionality. Donum Semanticum, 121.
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References
• Kimmelman, V. (2017). Quantifiers in Russian Sign Language. In Handbook of Quantifiers in Natural Language: Volume II (pp. 803-855). Springer, Cham.
• Kuhn, J. (2017). Dependent indefinites: the view from sign language. Journal of Semantics, 34(3), 407-446.
• Quer, J. (2012). Quantificational strategies across language modalities. In Logic, Language and Meaning (pp. 82-91). Springer, Berlin, Heidelberg.
• Safir, K., & Stowell, T. (1988). Binominal each. In Proceedings of NELS (Vol. 18, pp. 426-450).
• Schlenker, Lamberton and Santoro (2013). Iconic Variables. Linguistics and Philosophy.
• Zimmermann, M. (2002). Boys buying two sausages each: On the syntax and semantics of distance-distributivity (Vol. 62). LOT.
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