NEGATION, FOCUS AND INVERSE SCOPE
Hideharu Tanaka (Osaka University)
Introduction. Under Klima (1964), negation (Neg) must c-command α to take scope over it. In
English (1), however, the universal quantifier (UQ) can obtain wider scope than Neg.
(1) John didn’t invite every student.

Neg > every, every > Neg

Although one might claim that Quantifier Raising (QR) works to raise the UQ above Neg, such a QR
view is hopeless for Japanese: while the object UQ can take scope over Neg in (2), seemingly
supporting a QR analysis, Klima’s condition strictly applies as it is in (3), where the UQ is positioned
in [Spec, TP] as illustrated in (4).
(2) John-ga zen’in-o nagura-nakat-ta.
John-Nom all-Acc hit-Neg-Past(3) Zen’in-ga John-o nagura-nakat-ta.
all-Nom John-Acc hit-Neg-Past(4) [TP UQ-ga [T´[NegP [vP [VP John-o ]]] V-v-Neg-T]]

Neg > all, all > Neg*Neg > all, all > Neg

Now that we cannot appeal to QR, what causes inverse scope in (2)? My aim is to propose a PFresolution of the inverse scope puzzle, following Reinhart (2006).
Framework. Regarding Focus as what is not presupposed, Reinhart (2006) proposes the reference
set computation of Focus Set (5).
(5) Focus Set
The Focus set of a derivation D includes all and only the constituents that contain the main stressof D.
Discourse factors specify one of the ‘potential’ foci in the set as the actual Focus. Note that mainstress is determined by Nuclear Stress Rule (NSR) and Stress-Shift (SS) (Cinque 1993): NSR puts
main stress on the syntactically lowest element, whereas SS replaces it anywhere to produce a new
Focus Set: as illustrated in (6b), if Subj is to be the Focus, SS must apply.
(6) a. NSR(bold = stress bearer)[TP Subj T [VP V Obj ]]]Focus Set: {Obj, VP, TP}

b. MSS[TP Subj T [VP V Obj ]]]Focus Set: {Subj}
Proposal. It is generally accepted that it is Focus that Neg can affect. This finding is crucial to myproposal: as well as Klima’s condition, (7) applies as an LF condition on what element Neg actuallytakes scope over.
(7) Focus-Visibility Condition
Only the actual Focus, selected from a given Focus Set, is ‘visible’ to Neg at LF.

Crucially, I argue that partial negation obtains only if UQ is itself the Focus and c-commanded
by Neg: it does not obtain, even if UQ is contained, e.g., in the VP defined as the Focus. This is
attested by considering Japanese cleft sentences. Assuming that the cleft constituent (CC) isidentified as the Focus (cf. È. Kiss (1998)), consider (8a), where the CC is UQ, and (8b), where it isintended to be whole VP.
(8) a. [John-ga nagutta]-no-wa [zen’in]-de-wa-nai.
Only Neg > all
John-Nom hit-C-Top all -copula-Foc-Neg‘It is not all that John hit.’b. [John-ga sita]-no-wa [zen’in-o naguru-toiu-koto]-de-wa-nai.
Only all > Neg
John-Nom did -C-Top all-Acc
hit-C-fact-copula-Foc-Neg‘It is not to hit all that John did.’In (8b), the whole predicate is negated, namely, it is irrelevant whether the UQ contained there isaffected by Neg.
Analysis. Let us then see why (1) and (2) can show inverse scope. A single account can explain
both of them. Suppose that the Focus Set established by NSR is {Obj (UQ), VP, TP} and Obj is
c-commanded by Neg. If the object UQ is defined as the Focus, we get partial negation reading: if
another member, e.g., VP is specified as the Focus, we obtain total negation reading (recall thediscussion of (8)).
Ishihara (2000) notes that scrambling changes the potential members of a Focus Set to bedefined by NSR: while the main stress is assigned to the object in (9a), it falls on the VP-adverb in(9b), where object scrambling to vP-Spec occurs.
(9) a. [TP John-ga [T´[vP itotekini [VP zen’in-o]] sikara-nakat-ta]]
Neg > all, all > Neg
John-Nom intentionally all-Acc scold-Neg-Past
b. [TP John-ga [T´[vP zen’ini-o [vP itotekini [VP ti ]]] sikara-nakat-ta]] *Neg > all, all > Neg

Notice that (9b) disallows partial negation. This can be expected since the UQ without main stressdoes not belong to the Focus Set. If the scrambled UQ acquires the main stress through SS, we canget partial negation as in (10), where it can be the Focus, and is c-commanded by Neg.
(10) [TP John-ga [T´[vP zen’ini-o [vP itotekini [VP ti ]]] sikara-nakat-ta]]

Neg > all, all > Neg

Conclusion. Based on Reinhart’s (2006) Focus Set, I have argued that Neg takes scope over theactual Focus it c-commands. If my analysis is correct, it will favor for the view of PF-coding ofFocus.
Selected References
Ishihara, Shinichiro (2000). Stress, focus, and scrambling in Japanese. MIT working papers inlinguistics 39, 142-175.
Reinhart, Tanya (2006). Focus: The PF Interface. In Interface Strategies: Optimal and CostlyComputation, MIT press, 125-163.