Focus Marking, Focus Interpretation & Focus Sensitivity

Focus Marking, 

Focus Interpretation & 

Focus Sensitivity 

Malte Zimmermann & Daniel Hole 

ESSLI 2009, Bordeaux

Session II: 21-07-09 

Focus and Discourse-Anaphoricity 

Malte Zimmermann & Daniel Hole 

mazimmer@rz.uni-potsdam.de 

holedan@googlemail.com

1. Context Sensitivity - 2. SM and/or AS? - 3. Focus Meaning 

• Schedule: 

i. The formal representation of focus 

ii. The discourse-anaphoric nature of focus 

iii. The meaning of marked focus constructions 

iv. Association with Focus: 

FOC-particles and Q-Adverbs 

v. Extensions and case studies 

Zimmermann / Hole: 

Focus Semantics 

3


• Plan for today: 

i. Discourse Anaphoricity: Restricted Alternatives 

ii. Structured Meaning and/or AS ? 

iii. The meaning contribution of focus 



4


• Discourse-Anaphoricity: Observations 

� All instantiations of focus are sensitive to the 

preceding discourse context. 

� The contextually relevant set of alternatives is 

typically (much) smaller than the unrestricted 

focus value. 



5


• Discourse-Anaphoricity 

(1) I know you invited Liz, Harry, and Will, but 

who actually came to the party? 

A: HARry and WILL F came to the party. 



6



(1) I know you invited Liz, Harry, and Will, but 

who actually came to the party? 

A: HARry and WILL F came to the party. 

[[φ]] f = {x came to the party| x ∈ D e } 

C = {x came to the party | 

x∈{liz, will, harry}} 



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(2) John brought Tom, Bill, and Harry to the party, 

but he only introduced BILL F to Sue. 



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but he only introduced BILL F to Sue. 

[[φ]] f = {John introduced x to Sue| x ∈ D e } 

C = {John introduced x to Sue| 

x∈{tom, bill, harry}} 



9



(3) A: I think John went to Paris this weekend. 

B: No, stupid! He went to LONdon F! 



10



(3) A: I think John went to Paris this weekend. 

B: No, stupid! He went to LONdon F! 

[[φ]] f = {John went to x | x ∈ D e } 

C = {John went to x | x∈{london, paris}} 



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(4) Q: Does Ede want tea or coffee? 

A: Ede wants TEA F. 



12



(4) Q: Does Ede want tea or coffee? 

A: Ede wants TEA F. 

[[φ]] f = {Ede wants x | x ∈ D e } 

C = {Ede wants x | x∈{tea, coffee}} 



13



(4’) Q: Does Ede want tea or coffee? 

A: #(neither) Ede wants #(just) WAter F. 

(4‘‘)Q: Would you like some tea or coffee? 

A: #(just) water, please ! 



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• Summary 

The set of relevant alternatives is typically 

restricted by contextual factors, i.e., the 

preceding discourse. ⇔ 

discourse anaphoricity 



15


• Formal Implementation: ~C 

(Rooth 1992) 

The relation between the unrestricted set of 

alternatives induced by focus marking and the 

contextually restricted set of relevant 

alternatives is mediated by a covert variable C 

and the squiggle operator ‚~’. 



16



F-marking: indicates the locus of variation in 

the sets of alternatives 

~C: indicates the scope of focus and 

its contextually relevant alternatives 



17



D 

S’ 8 3 

6 S 

Does Ede want tea or coffee? 3 

S ~C 8 

5 

Ede wants TEA F 



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� Like all free variables, C is assigned a value by 

a contextually determined assignment function g 

[[C i]] g = g(i) 



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� Adjunction of ~ at the sentence-level indicates 

the semantic type of the contextually relevant 

alternatives that make up the value of C: 

scope of focus 



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� If φ is a syntactic constituent and C a 

syntactically covert variable, then the sequence 

φ~C introduces the presupposition that C is a 

subset of [[φφφφ]] f that contains [[φφφφ]] 0 and at least 

one additional element. 



21



(5) [[ φ~C i ]] g = [[φ]] 0 ,defined iff 

i. [[C i]] g ⊆ [[φ]] f ∧∧∧∧ 

ii. [[φ]] 0 ∈∈∈∈ [[C i]] g ∧ 

iii. ∃ϕ ≠ [[φ]] 0 :ϕ∈∈∈∈ [[C i]] g 



22



� The three sublauses of the presupposition can 

independently lead to infelicity 



23



D 

S’ 8 3 

6 S 

Does Ede want tea or coffee? 3 

S ~C 8 

5 

Ede wants TEA F 



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� Adjunction of ‚~‘ at the sentential level (‚S‘) 

indicates that the contextually relevant 

alternatives to [[Ede wants TEA F]] in C must be 

of propositional type. 



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� In case of the Q-A-congruence example the 

relevant alternatives in C 8 are provided by the 

meaning of the preceding disjunctive question 

[[Does Ede want coffee or tea?]] = 

{that ede wants coffee, that Ede wants tea} 



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(6) [[ [Ede wants TEA F ] ~C 8]] = 

1 iff Ede wants tea; defined iff 

i. [[C 8]] g ⊆ [[Ede wants TEA F ]] f ∧∧∧∧ 

ii. [[Ede wants TEA F ]] 0 ∈∈∈∈ [[C 8]] g ∧ 

iii. ∃ϕ ≠ [[Ede wants TEA F ]] 0 :ϕ∈∈∈∈ [[C 8]] g 



27





i. {that Ede wants tea, that Ede wants coffee} ⊆ 

{that Ede wants x | x ∈ thing } � 



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ii. [[Ede wants TEA F ]] 0 ∈∈∈∈ [[C 8]] g 



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ii. that Ede wants tea ∈∈∈∈ 

{that Ede wants tea, that Ede wants coffee} � 



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iii. ∃ϕ ≠ [[Ede wants TEA F ]] 0 :ϕ∈∈∈∈ [[C 8]] g 



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iii. ∃ϕ ≠ that Ede wants tea: 

ϕ∈∈∈∈ {that Ede wants tea, that Ede wants 

coffee} � 



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� violation of clause (i.): 

(7) Q: [Does Ede want tea or coffee] 17? 

A: #EDe F wants tea ~C 17. 

[[C 17]] g ⊄ [[EDe F wants tea]] f 



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� violation of clause (i.): 

(7) Q: [Does Ede want tea or coffee] 17? 

A: #EDe F wants tea ~C 17. 

{that Ede wants tea, that Ede wants coffee} ⊄ 

{that x wants tea | x ∈ person} 



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� violation of clause (ii.): 

(7) Q: [Does Ede want tea or coffee] 9 ? 

A: #Ede wants #(just) WAter F ~C 9. 

[[Ede wants WAter F ]] 0 ∉∉∉∉ [[C 9]] g 



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� violation of clause (ii.): 

(7) Q: [Does Ede want tea or coffee] 9 ? 

A: #Ede wants #(just) WAter F ~C 9. 

that Ede wants water ∉∉∉∉ 

{that Ede wants tea, that Ede wants coffee} 



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� The intuitive import of clause (iii.) is that with 

any instance of focus there need to be at least 

two contextually relevant alternatives under 

discussion for an utterance with focus to be 

informative, i.e. by excluding a potential 

alternative. 



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• Formal Implementation: Exercise 

Ex.1: What provides the value for C in the 

following instance of corrective focus ? 

(8) A: John is going out with Mary. 

B: No, [John is going out with SUE F ]~C 



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• Formal Implementation: Exercise 

� Questions-under-Discussion (QUDs): 

(Roberts 1996, Büring 2003) 

Any informative sentence with focus accent 

relates to an explicit or implicit QUD that needs 

to be resolved; accent placement helps in 

finding out what the QUD is. 



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• The scope of the ~-operator 

� The ~-operator can attach at various syntactic 

levels, including NP (Rooth 1992, 1996). 

(9) A British farmer met [ NP [ NP a CaNAdian F farmer]~C 2 ] 

[[NP]] f = {an x farmer| x∈ nationality‘} 

[[C 2]] g = {a British farmer, a Canadian farmer} 



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• The scope of the ~-operator 

� Different attachment sites of ‘~’ play a crucial 

role in cases of (multiple) association with focus 

with focus particles; see below 



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• ~C and association with focus 

� Focus-sensitive expressions like the focus 

particle only make no longer direct reference to 

the focus value in their lexical meaning. 

� Only quantifies over the covert variable C. 



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(10) John only introduced BILL F to Sue. 

LF: [ S only C [ S [ S John introduced BILL F to Sue] ~C ]] 



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� Compatibility of C with the focus value is 

ensured by the presence of ‚~‘ and its subset 

presupposition. 



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� Focus interpretation at the level of the syntactic 

complement of only, here S, restricts the type of 

possible values for C, here propositions. 



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� The lexical meaning of only no longer makes 

reference to the focus value of its complement, 

but only to C 



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(11) [[only]] = λC.λp. ∀q [q ∈ C ∧ ∨ q ↔ q = p] 



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(11) [[only]] = λC.λp. ∀q [q ∈ C ∧ ∨ q ↔ q = p] 

� Tri-partite quantificational structure: 

only (C) (S) 



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but [[ he only introduced BILL F to Sue ]] = 1 iff 

∀q [q ∈ {that J. introduced Bill to S., that J. 

introduced Tom to S., that J. introduced Harry 

to S.} ∧ ∨ q ↔ q = that J. introduced Bill to Sue]; 



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but [[ he only introduced BILL F to Sue ]]; 

defined iff C = {that J. introduced Bill to Sue, 

that J. introduced Tom to Sue, that J. introduced 

Harry to Sue} ⊆ {that J. introduced x to Sue | x 

∈ person’} = [[S]] f 



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• ~C: Conclusion 

i. The interpretation of focus depends on a 

syntactically covert variable C whose semantics 

value must be contextually resolved, typically 

by recourse to a syntactic antecedent. 

� The identification of C‘s value with the meaning 

of the antecedent is a classical instance of 

anaphora resolution. 



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ii. The ‚~‘-operator establishes the relation 

between C and the focus value by introducing 

the presupposition that the pragmatically 

determined value for C be a subset of the 

grammatically determined focus value. 

� Focus value plays only an indirect role for the 

interpretation of focus. 



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iii. The introduction of the ‚~‘-operator and the 

context variable C allow for a unified treatment 

of all focus types, including association with 

focus. 

� Construction-specific rules, such as rules for 

Q-A congruence, no longer required. 



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• Restricted Alternatives: Exercise 

Ex.2 Why is the following example from von 

Stechow (1990) problematic for the original 

AS-analysis of only as quantifying over all 

the elements in the focus value ? 



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(12) Context: John hosts a dinner party and has to 

introduce every person to his or her designated 

partner at table. The party has just begun and 

there are four guests, i.e. Bill and Sue (partners) 

and Charles and Lucy (partners). John has 

already introduced Bill to Sue and Bill to Lucy. 



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(12) A: Did John introduce every gentleman to his 

partner at table ? 

B: No, John only introduced BILL to SUE. 

� What is a plausible value for C in (12B) ? 

� How are the correct truth conditions for (12B) 

derived on the ~C- restriction account? 



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• Evaluation: AS, SM, or both? 

� Multiple Association with focus: 

AS + movement 

� Association with Focus Phrases in Islands: 

Structured Meaning + Alternative Projection? 



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• A problem for AS: Multiple Association 

(Rooth 1996) 

(13) a. John only introduced Bill F to Mary. 

b. He also only [introduced Bill F to Sue F.] 



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(Rooth 1996) 

(13) a. John only introduced Bill F to Mary. 

b. He also only [introduced Bill F to Sue F.] 

ASS: John introduced nobody but Bill to Sue. 

PRES: There is somebody else to whom John 

introduced nobody but Bill. 



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In the absence of indexing, or designated 

variables, S-adjoined only associates with both 

S-internal focus constituents at the same time, 

thus rendering the focused NP Sue F inaccessible 

for the later association with also. 



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� Without further assumptions, only is predicted 

to act as an unselective binder over foci (Wold 

1996): AS is not expressive enough! 



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(14) a. also only [ S [Foc1... Foc2]~C] 

b. [[only]] = λCλp.∀q [q∈C & ∨ q ↔ q = p ] 



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(14) c. [[ only(C)[John introduced Bill F to Sue F ]~C ]] = 1 iff 

d. ∀q [q∈C & ∨ q ↔ 

q = that John introduced to Bill to Sue] 

e. = 1 iff the only contextually relevant true 

proposition is the proposition that John 

introduced Bill to Sue. 



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Q: What of John‘s introducing Bill to Mary? 



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• A solution: Movement 

� Rooth (1996): The meaning of (13b) comes out 

correct if the second focus Sue F is moved to a 

position outside the c-domain of only, leaving 

behind a trace (= individual variable). 



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(15) a. [also(D)[Sue F1 [only(C)[ VP J introduced B F to y 1 ]~C]]~D] 

b. [[ only(C)[John introduced Bill F to y 1 ]~C = 

c. ∀q [q∈ {that John introduced B to M, that John 

introduced B to S} & ∨ q ↔ 

q = that John introduced B to y] 



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(15) a. [also(D)[Sue F1 [only(C)[ VP J introduced B F to y 1 ]~C]]~D] 

b. [[ only(C)[John introduced Bill F to y 1 ]~C = 

c. ∀q [q∈ {that John introduced B to M, that John 

introduced B to S} & ∨ q ↔ 

q = that John introduced B to y] 

⇒ All contextually relevant propositions are of the form 

John introduced Bill to y. � 



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� Analogous treatement for instances of nested 

focus (Krifka 1991, Rooth 1996: 288) 

(16) a. Last month John only drank beer. 

b. He has also only drunk WINE F. 



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• Remaining Problems 

i. Necessary movement of focus takes some of the 

initial appeal of AS as an in situ theory of focus 

ii. The meaning of only is either locally computed, 

or else the focused NP Sue must be interpreted 

as a quantifier taking scope over only. 

iii. Association into islands still mysterious! (Wold 

1996:315) 



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• Remaining Problems 

(17) a. Dr. Svenson only told SUE F about 

[the proposal that Bill submitted.] 

b. Dr. Svenson also only told SUE F about 

[the proposal that JOHN F submitted.] 

c. *also JOHN F only [... t John ...] 



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• Possible Responses: 

� Focus Interpretation as selective variable 

binding (SVB) with the following scale of 

expressiveness (Wold 1996) : 

SM >> SVB >> AS 

� Association with focus phrases (Drubig 1994, 

Krifka 2006) 



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• Association with focus phrases 

(Krifka 2006) 

� Association with focus IS island-sensitive 

� Focus particles don‘t associate with foci inside 

syntactic islands, but with the syntactic islands 

containing the foci (= focus phrases, FPs) 

� Association with focus involves both movement 

(



� Explicit contrast involves FPs 

(18) Mary didn‘t invite the man in a BLACK F suit to 

the party, 

a. but [ the man in a PURple F suit] 

b. *but in a PURple F suit / *but a PURple F suit / 

but PURple F 



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� Explicit contrast involves FPs 

(18) Mary didn‘t invite [ FP 

the party, 

a. but [ FP the man in a PURple F suit] 

the man in a BLACK F suit] to 

b. *but in a PURple F suit / *but a PURple F suit / 

but PURple F 



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� Multiple Association involves movement of FP: 

(17) b. Dr. Svenson also only told SUE F about 

[the proposal that JOHN F submitted]. 

c. Dr. Svenson also [the proposal that JOHN F 

submitted] 1 only told SUE F about t 1 . 



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but: Focus alternatives still play a role! 

(19) a. John only liked [the man that introduced BIll F to Sue] 

b. John only liked [the man that introduced Bill to SUe F ] 

(19a) and (19b) differ in truth conditions and in their 

discourse-anaphoric potential as answers to different 

implicit questions under discussion (QUDs). 



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Ex.3 Identify appropriate questions that could be 

answered by (19ab), respectively, as well as 

two situations, S1 and S2, such that S1 makes 

(19a) true and (19b) false and S2 makes (19a) 

false and (19b) true. 



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• The hybrid approach at work 

[[FP (19a) ]] = [[ the man that introduced BILL F to Sue]] f 

= {ιx [man(x) ∧ introd(Sue)(y)(x)] | y ∈ ALT(BILL)} 

= {ιx [man(x) ∧ x introduced Bill to Sue], ιx [man(x) ∧ 

x introduced Peter to Sue], ιx [man(x) ∧ x introduced 

Mary to Sue], … 



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[[FP (19b) ]] = [[ the man that introduced Bill to SUE F]] f 

= {ιx [man(x) ∧ introd(y)(Bill)(x)] | y ∈ ALT(SUE)} 

= {ιx [man(x) ∧ x introduced Bill to Sue], ιx [man(x) ∧ 

x introduced Bill to Mary], ιx [man(x) ∧ x introduced 

Maria to Gwendolyne], … 



79



[[(19a)]] = 1iff 

∀x∈[[the man that introduced BILL F to Sue]] f : 

[liked(x)(John) � x = [[the man that introduced Bill to Sue]] 

= ∀x∈{ιx [man(x) ∧ introd(Sue)(y)(x)] | y ∈ ALT(BILL)}: 

[liked(x)(John) � x = ιx [man(x) ∧ introd(Sue)(Bill)(x)] 

= 1 iff of all the men that introduced somebody to Sue, John only 

likes the man that introduced BILL to Sue. 



80



[[(19b)]] = 1iff 

∀x∈[[the man that introduced Bill to SUE F ]] f : 

[liked(x)(John) � x = [[the man that introduced Bill to Sue]] 

= ∀x∈{ιx [man(x) ∧ introd(y)(Bill)(x)] | y ∈ ALT(SUE)}: 

[liked(x)(John) � x = ιx [man(x) ∧ introd(Sue)(Bill)(x)] 

= 1 iff of all the men that introduced Bill to somebody, John only 

likes the man that introduced Bill to SUE. 



81


• Conclusions: 

i. Even though AS accounts for the bulk of the 

focus data in a satuisfactory manner, its lack of 

expressive power creates problems with certain 

cases of multiple association with focus 



82



ii. For these cases, the basic in situ AS-mechanism 

must be enriched, e.g. by assuming LFmovement 

of focus constituents or, in case of 

islands, FPs (⇒ structured meaning account). 



83



iii. Assuming association with FPs takes the force 

out of the original argument in favour of the in 

situ AS account, and against the SM+movement 

acccount 



84



iv. Alternative projection also plays a role for the 

semantic interpretation of association with FPs. 

(⇒ AS-account) 



85



v. At least association with focus into syntactic 

islands seems to require a hybrid account 

involving structured meaning + movement of 

FPs anf alternative projection. 



86


• The Meaning of Focus: 

Q1: Do focus accents contribute any semantic 

meaning over and beyond the partition into 

focus and background, or the introduction of a 

restricted set of alternatives by means of the ~operator‘s 

presupposition? 

Q2: What is the semantic nature of backgrounding 

indicated by focus accent? 



87


• The Background-Presupposition Rule 

(BPR): Geurts & van der Sandt (2004) 

Whenever focusing gives rise to a background 

λx. φ(x), there is a presupposition to the effect 

that λλλλx. φφφφ(x) holds of some individual. 



88


• Predictions of the BPR 

i. Focus accenting gives rise to existence 

presuppositions 



89



i. Focus accenting gives rise to existence 


(20) John likes MAry F. 

PRES: ∃x [John likes x] 



90



ii. Focus presuppositions should behave like any 

other presuppositions in terms of projection 

behaviour and licensing conditions, e.g. those 

triggered by the additive particle also 

(uniformity hypothesis) 



91



� Both predictions appear to be incorrect. 



92



i. Against existence presuppositions (Rooth 1996) 

Context: A football pool is held every week. participants 

place bets by predicting the scoe of games. The contesdt 

is set up so that at most one person can win in a given 

week. If nobody makes a correct prediction, nobody 

wins, and the jackpot stays. 



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(21) A: Did anyone win the football pool this week? 

B: I doubt it, because it‘s unlikely [that Mary F won it] 

and I know that nobody else did. 

� Presuppositions project out of the complement of likely 

(Karttunen & Peters 1979), but still (21B) is felicitous 



94





B: I doubt it, because it‘s unlikely [that Mary F won it] 

and I know that nobody else did. 

(22) it‘s unlikely that [[Mary F won it]~C] and I know that 

nobody else did. 



95



Compare to focus clefts (Rooth 1996) 


B: #I doubt it, because it‘s unlikely [that it is Mary F 

who won it] and I know that nobody else did. 

� Focus clefts DO introduce existence 

presuppositions ⇒ next session ! 



96



A simpler example (Büring 2004) 

(22) (My team didn‘t score a goal) 

a. If the OTHERS scored a goal, my team is out of the 

tournament by now. 

b.Thank god, the OTHERS didn‘t score a goal. 

� Context does not entail P = ∃x [x scored a goal] 



97



ii. The restrictions on accessible antecedents for 

accented foci and ordinary presupposition 

triggers differ (Büring 2004) 



98



(24) (Muslims think Allah is almighty). 

a. But Buddhists don’t think BUDdha F is almighty. 

b. Do Buddhists think BUDdha F is almighty? 

� Focus on Buddha licensed by the antecedent clause 

Allah is almighty, which is embedded under an attitude 

verb ! 



99



(25) (Sue thinks Bob married Christie). 

Does Steve think Bob (#also) Married NAna F ? 

� Presupposition of also not licensed by the antecedent 

clause Bob married Christie, which is embedded under 

an attitude verb ! 



100


• Summary 

� Material in antecedent clauses embedded under 

attitude verbs can license the background of a 

focus under givenness, but not the 

presuppositions triggered by also. 

� Accent Focus does not trigger existence 




101


• Focus Suppositions (Büring 2004) 

„intuitively, presuppositions are about 

assumptions and commitments, while Focus 

Suppositions seem to be about something much 

weaker, i.e. that something is under discussion, 

or just simply previously mentioned.“ 

� Givenness Theories of Focus (Schwarzschild 1999) 

� Activation (Beaver & Clark 2008) 



102


• Exercises 

Ex.4 Determine the value of C in (26A) in the following 

question context and show how the presupposition of 

the ~-operator is satisfied: 

(26) Q: Did Peter go to Rome or did he go to Paris? 

A: [Peter went to ROme F ]~C 

Ex.5 Determine appropriate values for C and D in (15a), the 

LF-representation of (13b). 

(15) a. [also(D)[Sue F1 [only(C)[ VP John introduced Bill F to y 1 ]~C]]~D] 



103


• Exercises 

Ex.6 Determine focus-background structure and the 

alternative propositions, respectively, that are introduced 

by the verum focus in (27) 

(27) A: I wonder whether or not John passed the exam. 

B: [He DID F pass the exam]. 

What would be an appropriate value for C attached at 

the sentential level in (27B)? 



104


Literature 

Beaver, D. & B. Clark (2008). Sense and sensitivity. How focus 

determines meaning. Oxford: Blackwell. 

Büring, D. (2003). On D-Trees, Beans, and B-Accents. Linguistics & 

Philosophy 26: 511-545. 

Büring, D. (2004). Focus Suppositions. Theoretical Linguistics 30. 

Geurts & van der Sandt (2004). Interpreting Focus. Theoretical 

Linguistics 30: 1-44. 

Krifka, M. (2006). Association with focus phrases. In V.Molnar and S. 

Winkler, (eds.), Architecture of Focus, Berlin: Mouton de Gruyter. 

105-136. 

Roberts, C. (1996). Information Structure in Discourse. Towards an 

Integrated Formal Theory of Pragmatics. OSU Papers in Linguistics 

49. Papers in Semantics. 



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Literature 

Rooth, M. (1992). A theory of focus interpretation. Natural Language 

Semantics 1: 75–116. 

Rooth, M. (1996). Focus. In: S. Lappin (ed.), The Handbook of 

Contemporary Semantic Theory. Oxford: Blackwell. 271–297. 

Schwarzschild, R. (1999). Givenness, AvoidF and other constraints on the 

placement of accent. Natural Language Semantics 7: 141-177. 

Wold, D. (1996). Long Distance Selective Binding. The Case of Focus. 

Proceedings of Semantics and Lingusitics Theory 6: 311-327. 



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Focus Marking, Focus Interpretation & Focus Sensitivity

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