Restrictions on the position of exh
The grammatical approach to scalar implicatures(SI) posits a covert operator exh whose semantic
contribution is similar to that of only (Fox 2007,Chierchia et al. 2012, a.o.).
 Certain “triggers” of SI in English —disjunction, unstressed some, and barenumerals — require an associated exh to be
as low as possible above the trigger.
• However, this requirement is lexicalized, andother triggers such as stressed SOME allow
for more delayed exhaustification.
Consequence• Overt sentential focus operators in somelanguages must adjoin as low as possible
while taking their focus in their scope.1
 Exh thus shares syntactic characteristics
with some overt focus particles.
1

Keng Ji Chow
Michael Yoshitaka Erlewine

Roadmap• We identify the position of exh for SI triggers
using additive also, building on Spector &Sudo 2017 and Marty & Romoli 2021.

Exh and also
• We study variation in SI triggers. Syntactic
features ensure the proper placement of exh.

Variation• We explain interactions between SI and again.

Exh and again• We derive the correct placement options for exhin cases of “presupposed ignorance.”

Ignorance Ignorance inferences may be generated inembedded positions, contra Meyer (2013)’s“Matrix K” theory.

See work on German (Jacobs 1983, Büring & Hartmann 2001; but see also Reis 2005, Smeets & Wagner 2018), Vietnamese(Erlewine 2017), Mandarin (Erlewine 2015, to appear), and English (Francis 2019: 57).

Exh and also

Restrictions on the position of exh

Additives such as also and too require a salient focus
alternative to be true (Kripke 1990/2009, Heim 1992).
(1)

exh

Mira teaches Arabic and Basque.
# [Nina]F also teaches Arabic or Basque.

Chow & Erlewine

An analysis in two parts:
1

High exh placement is possible in (2) but mustbe blocked in (1). Disjunction obeys (3):(3)Exh must adjoin to the lowest propositional
node while taking its trigger in its scope.

2

Additives take scope in their pronounced
position (e.g. Rullmann 2003) and can associatewith a focus that has moved out (Erlewine 2014).
(Here illustrated as reconstructed.)

exhLF: ∧i [TP [Nina]F also ∧ii [vP [Nina]F teaches A. or B.]]i. exh [ also [ANina ∨ BNina ]] (following Spector & Sudo)= also [ANina ∨ BNina ] ∧ ¬also [ANina ∧ BNina ]
also; (Ax ∨ Bx ) ∧ (Ax ∧ Bx ) for some xii. also [ exh [ANina ∨ BNina ]]also; exh(Ax ∨ Bx ) = (Ax ∨ Bx ) ∧ ¬(Ax ∧ Bx )Parse (i) predicts (1) to be felicitous, but it is not; S&S
acknowledge (p. 512) they cannot rule out this parse.
 Does exh always adjoin to vP?

However, (2) is felicitous! Exh in (2) must be able toadjoin high, taking its trigger (the subject) in its
scope, and therefore scopes over also.
(2)

Arabic and Basque are taught by Mira.
Arabic or Basque is also taught by [Nina]F .

Support for 2 :Exh adjoins to the same position in (4a,b): the lowest
propositional node above disjunction. Exh is then in
the scope of also in (4a) but above it in (4b):(4)The accomplice seems to the judge and thejury to be remorseful.
exha. # [The murderer]F also ∧ seems to [thejudge or the jury] to be remorseful.
b.

✓exh[The murderer]F ∧ seems to [the judgeor the jury] to also be remorseful.

Variation by SI trigger

Restrictions on the position of exh

Unstressed some (sm) and bare numerals exhibit
the same behavior as disjunction:(5)a.

Evy met all of the students.
# [Fran]F also met sm of the students.

But exh cannot be unboundedly far from SOME:(9)

Evy expects [that she’ll see all of the st’s].
# [F.]F also expects [that she’ll see SOME of them].
Evy expects [to meet all of the st’s].

(10)%b.
✓(6)a.

All of the students met Evy.
Sm of the students also met [Fran]F .

Proposal: SI triggers may bear syntactic featuresthat ensure exh placement (cf Chierchia 2013):

Five books were borrowed by Gary.

• Disjunction, sm, and bare numerals bear a“strong” [uexh*] feature; exh must adjoin assoon as possible to check [uexh*].

✓Four books were also borrowed by [Hlee]F .

Like disjunction, sm, and bare numerals require exh
to adjoin as low as possible (3).
 But not all triggers require exh as low as possible!

Exh for stressed SOME and superlative modified
numerals (SMNs) can scope above also in (7–8):

Evy met all of the students.
(cf 5a)✓[Fran]F also met SOME of the students.

(8)✓[Fran]F also expects [to meet SOME of them].

Gary borrowed five books.
# [Hlee]F also borrowed four books.

b.

(7)

Chow & Erlewine

Gary borrowed five books.
(cf 6a)[Hlee]F also borrowed at least four books.

• Stressed SOME and SMNs bear a “weak”[uexh] feature, which must be checked within
its minimal finite clause or just above its
embedding verb.
Scalar adjectives do not bear either syntactic
feature, allowing exh to adjoin at the matrix level:(11)✓Ari expects that it will be freezing in Boston.
[Brie]F also expects that it will be cold there.

Exh and again

Restrictions on the position of exh

Again presupposes an event description (or property;Beck & Johnson 2004) to hold at a prior time.
 Our account accurately predicts the position of
exh within or above the scope of again.
Unstressed sm and bare numerals require exh as
low as possible.
⇒ again > exh

Chow & Erlewine

For disjunction, we predict exh to be as low as
possible ⇒ again > exh . We therefore predict (16)and (17) to be infelicitous. But there is somespeaker variation.
(16)%

Yesterday, Masa ate an apple and an orange.
Today, he ate an apple or an orange again.

Context: Every year, Mary teaches a different group of students.

(12)

Last year, Mary failed all of her students.
exh# Now, she [[ ∧ failed sm of her students ] again].

Context: We’re building a new room. We bought a door and a(17)

window which were both built open, installed them, andagain

closed them both. Now it’s getting hot.

; she failed some but not all before.

%(13) Yesterday, Gary borrowed five books.
exhI’ll open the door or the window again.
cf. ✓ I’ll open the window again. (restitutive)# Today, he [[ ∧ borrowed four books] again].
again; he borrowed four but not five before.

Stressed SOME and superlative modified
numerals allow for delayed exh.
⇒ exh > again(14) Last year, Mary failed all of her students.
✓ We tentatively propose that this reflects adifference in the availability of including
again in Conjunction Reduction (possibly aform of gapping; see e.g. Hirsch 2017).

exh…she [ ∧ [failed SOME of her students again]].

(16’)

He [ate an apple again] or[ate an orange again].

(17’)

I’ll [open the door again] or[open the window again].

again; she failed some of her students before.
(15) Yesterday, Gary borrowed five books.
exh 2✓…he [ ∧ [borrowed at least four books again]].
again; he borrowed at least four books before.

Presupposed ignorance

Restrictions on the position of exh

Disjunction introduces ignorance inferences,argued to be due to another exh with a necessity
modal 2 (Chierchia 2013, Meyer 2013), as in (18).

(18)

 Now consider the addition of also in (18).

Chow & Erlewine

Mira speaks Arabic or Basque.
exh 2 [ exh [A ∨ B]](A ∨ B) ∧ ¬(A ∧ B) ∧ (¬2A ∧ ¬2B)´¹¹ ¹ ¹ ¹ ¹ ¹ ¹¸ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶´¹¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¸ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¹ ¶scalar implicature ignorance implicature

The felicitous disjunctive antecedent (19a) requires parse (20a). Marty & Romoli (2021) observe that a“split” antecedent (19b) is also grammatical, requiring parse (20b). However, the conjunctive antecedent(19c) is not possible, showing that parse (20c) is ungrammatical, unexplained by M&R.
(19)

a.
✓b.
✓c.

Mira teaches Arabic or Basque.
[Nina]F also teaches Arabic or Basque.

(20)

Mira teaches Arabic and Ora teaches Basque.
[Nina]F also teaches Arabic or Basque.

Mira teaches Arabic and Basque.
# [Nina]F also teaches Arabic or Basque. (=1)

 Our feature-checking proposal
correctly requires at least one
exh to adjoin as low as possible.
This allows for (20a,b) but not (20c).

a. also [ exh 2 [ exh [ANina ∨ BNina ]] ]✓also; (Ax ∨ Bx ) ∧ ¬(Ax ∧ Bx ) ∧ (¬2Ax ∧ ¬2Bx )b. exh 2 [ also [ exh [ANina ∨ BNina ]]]also; (Ax ∨ Bx ) ∧ ¬(Ax ∧ Bx ) ∧✓c. exh 2 [ exh [ also [ANina ∨ BNina ]]]also; (Ax ∧ Bx )×(Ay ∧ ¬By ) ∧ (¬Az ∧ Bz ) ← unpacking
exh aboveMeyer (2013) proposes that K/2 adjoins to the matrix clause root.
 The need for 2 below also in (20a) forms an argument against
Meyer’s “Matrix K” theory, and instead supports Chierchia’sview where 2 may occur in embedded positions.

References I
Email: kengji.chow@u.nus.edu, mitcho@nus.edu.sg
Beck, Sigrid & Kyle Johnson. 2004. Double objects again. Linguistic inquiry 35(1). 97–123.
Büring, Daniel & Katharina Hartmann. 2001. The syntax and semantics of focus-sensitive particles in German. NaturalLanguage & Linguistic Theory 19(2). 229–281.
Chierchia, Gennaro. 2013. Logic in grammar: Polarity, free choice, and intervention. Oxford: Oxford University Press.
Chierchia, Gennaro, Danny Fox & Benjamin Spector. 2012. Scalar implicature as a grammatical phenomenon. In
Semantics: An international handbook of natural language meaning, 2297–2332. de Gruyter.
Erlewine, Michael Yoshitaka. 2014. Movement out of focus. Cambridge, MA: Massachusetts Institute of Technology
dissertation.
Erlewine, Michael Yoshitaka. 2015. In defense of Closeness: focus-sensitive adverb placement in Vietnamese and MandarinChinese. Manuscript, McGill University.
Erlewine, Michael Yoshitaka. 2017. Vietnamese focus particles and derivation by phase. Journal of East Asian Linguistics
26(4). 325–349.
Erlewine, Michael Yoshitaka. to appear. Mandarin exhaustive focus shı̀ and the syntax of discourse congruence. InRemus Gergel, Ingo Reich & Augustin Speyer (eds.), Particles in German, English, and beyond, John Benjamins.
Fox, Danny. 2007. Free choice and the theory of scalar implicatures. In Presupposition and implicature in compositionalsemantics, 71–120. Springer.
Francis, Naomi Clair. 2019. Presuppositions in focus: Massachusetts Institute of Technology dissertation.
Heim, Irene. 1992. Presupposition projection and the semantics of attitude verbs. Journal of semantics 9(3). 183–221.
Hirsch, Aron. 2017. An inflexible semantics for cross-categorial operators. Cambridge, MA: Massachusetts Institute ofTechnology dissertation.
Jacobs, Joachim. 1983. Fokus und Skalen: Zur Syntax und Semantik der Gradpartikeln im Deutschen. Tübingen: Niemeyer.

References II

Kripke, Saul. 1990/2009. Presupposition and anaphora: Remarks on the formulation of the projection problem.
Linguistic Inquiry 40(3). 367–386.
Marty, Paul & Jacopo Romoli. 2021. Presuppositions, implicatures, and contextual equivalence. Natural Language
Semantics 29(2). 229–280.
Meyer, Marie-Christine. 2013. Ignorance and grammar. Cambridge, MA: Massachusetts Institute of Technology
dissertation.
Reis, Marga. 2005. On the syntax of so-called focus particles in German: A reply to Büring and Hartmann 2001. NaturalLanguage & Linguistic Theory 23. 459–483.
Rullmann, Hotze. 2003. Additive particles and polarity. Journal of semantics 20(4). 329–401.
Smeets, Liz & Michael Wagner. 2018. Reconstructing the syntax of focus operators. Semantics & Pragmatics 11(6). 1–27.
Spector, Benjamin & Yasutada Sudo. 2017. Presupposed ignorance and exhaustification: how scalar implicatures andpresuppositions interact. Linguistics and Philosophy 40(5). 473–517.