Long-distance dependencies in continuation grammar
Cara Su-Yi Leong (cara@u.nus.edu) & Michael Yoshitaka Erlewine (mitcho@nus.edu.sg)
PACLIC 33, Future University Hakodate, September 2019
The Barker & Shan (B&S) framework: Shan and Barker 2006, Barker and Shan 2014, a.o.
develop a Combinatory Categorial Grammar that uses continuations to model semantic scope.
(1) Multi-level tower notation:(2) Composition with multi-level towers:
D E
C B
C D
C E
C( (A ) B)AA
A\ BB
expression : expression
left-exp right-exp  left-exp right-exp
λκ . f (κ (a))
f[ ]g[ ]h[ ]g(h[ ])axff (x)(3) lift:(4) lower:(5) bind:
A B
A DP . B
B BA SDPDPAAASbind↓lift⇒exp
exp
 exp
exp ⇒ exp
exp ⇒f[ ]f ([ ]x)
af (a)[]
f[ ]xxaa
One advertised feature of B&S’s proposal is its explanation for crossover effects (Postal 1971)
as in (6) — schematized in (7) — using linear evaluation.
(6) a.

Which girli did John introduce
to heri second cousin?
??
b. Which girli did John introduce heri second cousin to?

(7) a. Xwhi ...
i ... proib. *whi ... proi ...
i

Scope-taking across clause boundaries(8)# Someone said [everyone is married to Sue].

# ∃ > ∀, *∀ > ∃ (from Fox 2000: 62)(9) Scope Island Evaluation:(codifying an idea in Charlow 2014: 65)
If the expression is a scope island, apply lower as many times as possible (↓*).
(10)

a. X Which girli did you say [Mary sawi ]?

b. X Every girli said [Mary saw heri ].

 Scope Island Evaluation (9) blocks the binding of gaps (10a) and pronouns (10b) inembedded tensed clauses, contrary to fact.
(11) For embedded gaps: Intermediate gaps
DP ) S S
DPλy . [ ]yS S©
­
DP\ S­­­ Mary saw­­[]­« λx . saw x mª
®
®
®
® ®
®
®
¬

(12) For embedded pronouns: prolift
DP ) S S
B CDP . B CS
DP . AAprolift
Mary sawexpression ⇒ expression
λy . [ ]f[]
λx . f [ ]saw y mλx . g(x)g(x)

The revised B&S framework predicts the crossover violation in (13b) to be grammatical.
(13) a.
b.

Which girli do you think [ loves heri mother]?
?? Which girl do you think [her mother loves]?
ii

(13b)?? Which girl do you think [her mother lovesii]?

Calculate the embedded clause:
DP . (DP ) S) DP ) SDP ) S DP ) S(DP\ S) / DPloves[]

DPher mother
λd . [ ]mother dDPλx . [ ]SDP . (DP ) S)
lift⇒
⇒
her mother loves
λd . λx . loves x (mother d)Sher mother loves
λd . λx . [ ]loves x (mother d)xlovesDP . SSDP . (DP ) S)
her mother loves[]↓∗DP . (DP ) S) SDP ) S Sprolift⇒λd . λx . loves x (mother d)

SDP\ S
her mother loves
λd . [ ]λx . loves x (mother d)(We optionally shift A ) B categories on the lower level to A \ B with no change in denotation.)

Then calculate the higher clause, with the embedded clause and an intermediate, bind-ing gap:DP ) S DP ) SDPyou[]DP ) S DP . SDP ) S DP ) S(DP\ S) / S
think[]

youDP

λy . [ ] yythinkDP ) S S

 you thinkS
her mother loves
λy . [ ]↓∗⇒DP . S S
DP\ Sher mother loves
λd . [ ]λx . loves x (mother d)DP ) S
you thinkher mother loves
λ y . loves y (mother y)loves y (mother y)Finally, combine with the wh-phrase:
S/(DP ) S)
DP ) S
which girl
you think her m. loves
λκ . wh(λ g . girl g ∧ κ(g))λ y . loves y (mother y)S wh girl [do] you think her m. loves
wh(λ g . girl g ∧ loves g (mother g))

References
Barker, Chris, and Chung-Chieh Shan. 2014. Continuations and Natural Language. Oxford
University Press.
Charlow, Simon. 2014. On the semantics of exceptional scope. Doctoral Dissertation, NewYork University.
Fox, Danny. 2000. Economy and semantic interpretation. MIT Press.
Postal, Paul M. 1971. Cross-over Phenomena. Holt, Rinehart and Winston.
Shan, Chung-Chieh, and Chris Barker. 2006. Explaining Crossover and Superiority as Leftto-right Evaluation. Linguistics and Philosophy 29:91–134.