1. Proposition Sets or Structured Meanings: Thats the Question. Manfred Krifka Humboldt-Universität & Zentrum für Allgemeine Sprachwissenschaft (ZAS) Berlin http://amor.rz.hu-berlin.de/~h2816i3x

2. Two Approaches to Questions The Proposition Set Approach (e.g., Hamblin 1958, 1973; Karttunen 1977; Groenendijk & Stokhof 1984,...): The meaning of a question is a set of propositions; a congruent answer to the question identifies one of them. [[ Which novel did Mary read? ]] = { read(ulysses)(mary), read(moby-dick)(mary)... } The Functional (= Structured Meaning, Categorial) Approach (e.g., Ajdukiewicz 1928, Cohen 1929, Hull 1975, Tichy 1978, Hausser & Zaefferer 1979, Stechow & Zimmermann 1984, Reich 2001): The meaning of a question is an unsaturated proposition; a congruent answer to the question saturates it. [[ Which novel did Mary read? ]] a. read(x novel )(mary) b. x novel [read(x)(mary)] c. x[read(x)(mary)], novel Q-Function, Q-Restriction [[ Ulysses. ]] = ulysses, x[read(x)(mary)](ulysses) = read(mary)(ulysses).

3. The Proposition Set Approach to Questions [[ Which novel did Mary read? ]] = { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Set of all possible worlds

4. The Proposition Set Approach to Questions [[ Which novel did Mary read? ]] = { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Mary read Ulysses Set of all possible worlds Proposition Mary read Ulysses

5. The Proposition Set Approach to Questions [[ Which novel did Mary read? ]] = { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Mary read Ulysses Mary read Moby-Dick Set of all possible worlds Proposition Mary read Ulysses Proposition Mary read Moby-Dick

6. The Proposition Set Approach to Questions [[ Which novel did Mary read? ]] = { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Set of all possible worlds Proposition Mary read Ulysses Proposition Mary read Moby-Dick Proposition Mary read Dr. Faust

7. The Proposition Set Approach to Questions [[ Which novel did Mary read? ]] = { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust } Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Set of all possible worlds Proposition Mary read Ulysses Proposition Mary read Moby-Dick Proposition Mary read Dr. Faust Exhaustive core of propositions: Mary read only Ulysses Mary read only Moby-Dick Maryread only Dr. Faust Exhaustive core: EXH([[Q]]): {p| p[p [[Q]] p = p {p [[Q]] | p p}] }

8. The Proposition Set Approach to Questions [[ Which novel did Mary read? ]] = { Mary read Ulysses, Mary read Moby-Dick, Mary read Dr. Faust} Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust John read Ulysses John read Dr. Faust John read Moby-Dick Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Specification of question meaning by exhaustive core of propositions (built into question semantics in Groenendijk & Stokhof, here just a didactic device)

9. The Proposition Set Approach to Questions [[ Who read Ulysses? ]] = { Mary read Ulysses, John read Ulysses, Kai read Ulysses} Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust John read Ulysses John read Dr. Faust John read Moby-Dick Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick

10. The Proposition Set Approach to Questions [[ Who read which novel? ]] = { Mary read Ulysses, John read Ulysses, Kai read Ulysses, Mary read Dr. Faust, John read Dr. Faust, Kai read Dr. Faust, Mary read Moby-Dick, John read Moby-Dick, Kai read Moby-Dick} Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust John read Ulysses John read Dr. Faust John read Moby-Dick Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick

11. Relationship between the PS and SM approach We can derive proposition set meanings from structured meanings: [[ Q ]] PS = { [[ Q ]] SM (y) | y DOM([[ Q ]] SM ) } e.g. [[ Which novel did Mary read? ]] PS = [[ Which novel did Mary read? ]] SM (y) | y DOM([[ Which novel did Mary read? ]] SM ) } = { x novel[Mary read x](y) | y novel } = { Mary read Ulysses, Mary read Moby-Dick,... } We cannot derive structured meanings from proposition set meanings (at least if propositions are not expressions in a representation language) Hence: The PS approach is the null hypothesis; adherents for the SM approach have to provide for arguments for it. Question: Are there linguistic phenomena that cannot be handled by the PS approach, but can be handled by the SM approach?

12. Aims of this talk Krifka (2001), For a structured meaning account of questions and answers: There are such phenomena, hence we need an SM approach to questions. (In particular, alternative questions, multiple questions, focus marking in answers) Büring (2002), Question-Answer-Congruence: Unstructured: gives arguments that try to refute the arguments of Krifka (2001), arguing that the PS approach to questions is sufficient. Aims of this talk: - Restate the arguments of Krifka (2001) - Discuss the counterarguments of Büring (2002) - Conclude that the PS approach to questions is insufficient, and that the SM approach does better. Here: Restricted to an argument concerning focus marking

13. Congruent Answers to Questions Congruent and incongruent answers: Q: Which novel did Mary read? A:Mary read Ulysses. #A:Mary read Exiles. #A:Mary danced. Congruence criterion, first version: An answer A is congruent to a question Q iff [[A]] [[Q]] [[Which novel did Mary read?]] = {read(x)(mary) | novel(x)}, = Q [[Mary read Ulysses.]] = read(ulysses)(mary), Q [[Mary read Exiles.]] = read(exiles)(mary), Q With exhaustive cores of question meanings: An answer A is congruent to a question Q iff there is a unique p EXH([[Q]]) such that p [[A]]

14. Congruent Answers to Questions Congruent answer: Q: Which novel did Mary read? A:Mary read Ulysses. Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust John read Ulysses John read Dr. Faust John read Moby-Dick Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles

15. Congruent Answers to Questions Incongruent answers: Q: Which novel did Mary read? #A:Mary read Exiles. Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust John read Ulysses John read Dr. Faust John read Moby-Dick Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles

16. Congruent Answers and Focus Question-answer congruence; first systematic observation: Hermann Paul 1889. Congruent question / answer pairs indicated by focus of the answer: Q:What did Mary read? A:Mary read ULYSses F.Focus o.k. Wrong focus placements: A :*MAry F read Ulysses.Focus in wrong place.

17. Focus in Answers in the PS Account Optimally matched: Proposition set theory of questions / Alternative Semantics to focus cf. Rooth 1985, Rooth 1992, von Stechow 1990. Alternative semantics to focus: Two levels of interpretation: Meaning proper, Alternatives. Focus marking introduces alternatives; the meaning proper is an element of the set of alternatives. Examples: [[ Mary read ULYSses F. ]] = read(ulysses)(mary) [[ Mary read ULYSses F. ]] A = {read(x)(mary) | x ALT(ulysses)} [[ MAry F read Ulysses. ]] = read(ulysses)(mary) [[ MAry F read Ulysses. ]] A = {read(ulysses)(x) | x ALT(mary)} Conditions for congruent Q/A-pairs: Question meaning corresponds to the alternatives of the answer. Examples: [[ Which novel did Mary read? ]] = {read(x)(mary) | x novel} o.k.: Mary read ULYSses F, as question meaning {read(x)(mary) | x novel} corresponds to alternatives: {read(x)(mary) | x ALT(ulysses)} not: MAry F read Ulysses, as question meaning does not correspond to alternatives: {read(ulysses)(x) | x ALT(mary)} But what does correspond mean?

18. Q/A pairs in PS: What does correspond mean? Rooth (1992): Alternatives = all possible denotations of the appropriate type Congruence criterion, second version: An answer A is congruent to a question Q iff (i)[[A]] [[Q]] (ii)[[Q]] [[A]] A Example: Q: Which novel did Mary read? A: Mary read ULYSses F. as {read(x)(mary) | x novel} {read(x)(mary) | x D e } Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust Kai read Exiles John read Ulysses John read Dr. Faust John read Moby-Dick John read Exiles Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles Question meaning: Q: Which novel did Mary read?

19. Q/A pairs in PS: What does correspond mean? Rooth (1992): Alternatives = all possible denotations of the appropriate type Congruence criterion, second version: An answer A is congruent to a question Q iff (i)[[A]] [[Q]] (ii)[[Q]] [[A]] A Example: Q: Which novel did Mary read? A: Mary read ULYSses F. as {read(x)(mary) | x novel} {read(x)(mary) | x D e } Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust Kai read Exiles John read Ulysses John read Dr. Faust John read Moby-Dick John read Exiles Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles Question meaning: Q: Which novel did Mary read? Answer alternatives: A: Mary read ULYSses F. [[Q]] [[A]] A, shown in terms of exhaustive cores: EXH([[Q]]) EXH([[A]] A )

20. Q/A pairs in PS: What does correspond mean? Rooth (1992): Alternatives = all possible denotations of the appropriate type Congruence criterion, second version: An answer A is congruent to a question Q iff (i)[[A]] [[Q]] (ii)[[Q]] [[A]] A Example: Q: Which novel did Mary read? *A: MAry F read Ulysses. as {read(x)(mary) | x novel} {read(ulysses)(y) | y D e } Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust Kai read Exiles John read Ulysses John read Dr. Faust John read Moby-Dick John read Exiles Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles Question meaning: Q: Which novel did Mary read? Answer alternatives: A: MAry F read Ulysses. EXH([[Q]]) EXH([[A]] A )

21. Over- and Underfocused Answers Congruent question / answer pairs indicated by focus of the answer: Q:What did Mary read? A:Mary read ULYSses F.Focus o.k. Wrong focus placements: A :*MAry F read Ulysses.Focus on wrong place. Over-and underfocused answers: A :*MAry F read ULYSses F. Overfocused; too many foci. A : Mary read Ulysses.Underfocused; no focus. Q:Which student read which novel? A:MAry F read ULYSses F.Focus o.k. (except for list answer) A :Mary read ULYSses F.Underfocused; too few foci. Q:What did Mary do? A:Mary [read ULYSses] F.Focus o.k.; focus projection A :*Mary READ F Ulysses.Underfocused; focus too narrow. Q:What did Mary do with Ulysses? A:Mary READ F Ulysses.Focus o.k. A :*Mary [read ULYsses] F.Overfocused; focus too wide.

22. Banning Underfocused Answers Example: No focus at all. Q: Which novel did Mary read? *A: Mary read Ulysses. as {read(x)(mary) | x novel} {read(ulysses)(mary)} Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust Kai read Exiles John read Ulysses John read Dr. Faust John read Moby-Dick John read Exiles Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles

23. Banning Underfocused Answers Example: Too few foci. Q: Who read which novel? *A: MAry F read Ulysses. as {read(x)(y) | y person, x novel} {read(ulysses)(x) | x D e } Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust Kai read Exiles John read Ulysses John read Dr. Faust John read Moby-Dick John read Exiles Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles

24. No Banning of Overfocused Answers Example: Too many foci. Q: Which novel did Mary read? *A: MAry F read ULYSses F. but {read(x)(mary) | x novel} {read(x)(y) | x, y D e } Kai read Ulysses Kai read Moby-Dick Kai read Dr. Faust Kai read Exiles John read Ulysses John read Dr. Faust John read Moby-Dick John read Exiles Mary read Ulysses Mary read Dr. Faust Mary read Moby-Dick Mary read Exiles

25. A Preference for Minimal Focus? Congruence criterion, third version: An answer A is congruent to a question Q iff (i)[[A]] [[Q]] (ii)[[Q]] [[A]] A ( or EXH([[Q]]) EXH([[A]] A ) ) (iii)There is no A that is like A with the exception that it has less focus marking than A, that satisfies (i) and (ii). Preference for minimal focus: Avoid Focus, Schwarzschild 1999. Example: Q: Which novel did Mary read? A: Mary read ULYSses F. *A: MAry F read ULYSses F. *A:Mary read Ulysses. Both A, A satsfy (i) and (ii), but A has less focus marking, so A is ruled out. A has less focus marking than A, but it doesnt have enough to satisfy (ii). In general: Have enough focus marking to express congruence with answer (ii), but use focus marking sparingly (iii). Can be formulated as antagonistic constraints in OT.

26. But what is less focus marking? Example: VP focus Q: What did John do? {P(john) | P D et, P: activity} a.A:John [read ULYSses] F. (focus projection / accent percolation) b.*A:John read ULYSses F.(narrow focus, realized like A) c.*A:John READ F Ulysses.(narrow focus on verb) d.*A:[John read ULYSses] F.(sentence focus, realized like A) All answers satisfy clause (i), as [[A]] [[Q]] Answers (b) and (c) are ruled out due to clause (ii), as [[Q]] [[A]] A Answer (d) should be ruled out due to clause (iii), as there is a possible answer with less focus marking, (a), that satisfies clauses (i) and (ii) and has less (= smaller) focus marking. Hence: Less focus marking can mean focus marking on a smaller constituent; [ X [U V F W] Y] has less focus marking than [X [U V W] F Y]

27. Less Focus Marking It is quite natural to interpret less focus marking as smaller focus marking, because it leads to a reduction of alternative sets in terms of exhaustive cores: EXH([[Mary read ULYSses F ]] A ) EXH([[Mary [read ULYSses] F ]]), EXH([[Mary [read ULYSses] F ]] A ) EXH([[[Mary read ULYSses] F ]]) This suggests to replace clause (iii) of congruence criterion by: (iii)There is no A that satisfies (i) and (ii) and EXH([[A]] A ) EXH([[A]] A )

28. A Conflict for Less Focus Marking Q: What did Mary do with which novel? {R(x)(mary) | novel(x), R D eet, R: activity } a.A:Mary READ F ULYSses F (and BURNED F [Finnegans WAKE] F ). {R(x)(mary) | x D e, R D eet } b.*A:Mary [read ULYSses] F {P(mary) | P D et } Both (a) and (b) satisfy clauses (i) and (ii) of congruence criterion, as [[A]] [[Q]] and [[Q]] [[A]] A Which answer is excluded by (iii)? (a) has smaller foci, but (b) has fewer foci. As (a) is the congruent answer, the size of foci appears to violate Avoid Focus less than the number of foci. This is consonant with the revised criterion (iii), as e.g. EXH([[Mary READ F ULYSses F ]] A ) EXH([[Mary [read ULYSses] F ]] A )

29. Another Conflict for Less Focus Marking Q: What did Mary do? {P(mary) | P D et, P: activity } a.A:Mary [read ULYSses] F {P(mary) | P D et } b.*A:Mary READ F ULYSses F (and BURNED F [Finnegans WAKE] F ). {R(x)(mary) | x D e, R D eet } Both (a) and (b) satisfy clauses (i) and (ii) of congruence criterion, as [[A]] [[Q]] and [[Q]] [[A]] A Notice: [[Q]] [[A]] A holds for (b), as x, R are completely unrestricted; for every P, P D et we can take an arbitrary x and define R as: R = x y[P(y)] Which answer is excluded by (iii)? (a) has fewer foci, but (b) has smaller foci. As (a) is the congruent answer, the number of foci now appears to violate Avoid Focus less than the size of foci. Hence: We cannot fix, in general, whether it is better to have fewer foci, or to have smaller foci: A serious problem for the proposition set account of questions!

30. A Problem for Focus Projection Selkirk (1984): Focus on the larger constituent is licensed by focus projection. Focus on an argument licenses focus on the head. Focus on the head licenses focus on the whole constituent. This is how VP focus is generated, step by step: a.John [read ULYSses F ].(focus licensed by accent) b.John [read F ULYSses F ].(focus of head licensed by focus on argument) c.John [read F ULYSses F ] F.(focus on VP licensed by focus on head) Compare this with focus on verb and object NP: d.John [READ F ULYSses F ]. Notice that (d) has fewer focus features than (c), hence everything else (d) should be preferred over (c), and in general multiple focus should be preferred over broad focus. False prediction: Q: What did John do? *A: John READ F ULYSses F.(2 F-features) A: John [read F ULYSses F ] F. (3 F-features, should be dispreferred)

31. Focus in Answers in the SM Account Focus in the SM approach (von Stechow 1981, 1990; Jacobs 1984): Focus marking induces a partition between background and focus; the background applied to the focus yields the standard proposition. Examples: [[ Mary read ULYSses F. ]] = x[read(x)(mary)], ulysses [[ MAry F read Ulysses. ]] = x[read(ulysses)], mary Conditions for congruent Q/A pairs: Background condition: Background of the answer = Question function Focus condition: Focus of the answer Question restriction Examples: [[ Which novel did Mary read? ]] = x[read(x)(mary), novel o.k.: [[ Mary read ULYSses F. ]], = x[read(x)(mary)], ulysses identical backgrounds, ulysses novel not ok: [[ MAry F read Ulysses. ]], = x[read(ulysses)], mary Background condition violated. not o.k: [[ Mary read Exiles F. ]], = x[read(x)(mary)], exiles Focus condition violated, exiles novel

32. Under / Overfocusation in the SM Account Cases of underfocusation and overfocusation are excluded: Underfocusation, too few foci: [[ Which student read which novel? ]], = xy[read(y)(x)], student novel o.k.: [[ MAry F read ULYSses F ]], = xy[read(y)(x)], mary, ulysses, identical backgrounds, mary, ulysses student novel not o.k.: [[ Mary read ULYSses F. ]], = x[read(x)(mary)], ulysses, Background condition and focus condition violated Underfocusation, focus too small: [[ What did Mary do?]], = P[P(mary)], activity o.k.: [[ Mary [read ULYSses] F. ]], = P[P(mary)], x[read(ulysses)(x)] identical backgrounds, x[read(ulysses)(x)] activity not o.k: [[ Mary READ F Ulysses. ]], = R[R(ulysses)(mary)], read Background condition (and focus condition) violated. Overfocusation: [[ What did Mary do with Ulysses? ]], = R[R(ulysses)(mary)], transitive_activity o.k.: [[ Mary READ F Ulysses. ]], = R[R(ulysses)(mary)], read identical backgrounds, read transitive activity not o.k.: [[ Mary [read ULYSses F ]. ]], = P[P(mary)], x[read(ulysses)(x)] Background and focus condition violated.